fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,![A_27b, A_27c, A_27e]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27e),X2_2E0))),s(A_27b,X3_2E0))))).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27e_20mono_2EA_27d_20mono_2EA_27a,axiom,![A_27a, A_27d, A_27e]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0))),s(A_27a,X3_2E0))))).
fof(patternMatchesTheory_2EPMATCH__ROW__REMOVE__FUN__VAR,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![F0_2E0, F1_2E0]: (![V4g_2E0, V2f_2E0, V12x_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27c,V12x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V12x_2E0)))))) => (![V5r_2E0, V2f_2E0, V13x_2E0]: (s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27c,V13x_2E0))) = s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V13x_2E0)))))) => ![V0v_2E0, V1v_27_2E0, V2f_2E0, V3p_2E0, V4g_2E0, V5r_2E0, V6p_27_2E0]: ((![V7x_27_2E0]: ((s(A_27b,V1v_27_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V6p_27_2E0),s(A_27c,V7x_27_2E0)))) <=> (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V7x_27_2E0))))) = s(A_27a,V0v_2E0))) & (![V8x_2E0]: ((s(A_27a,V0v_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V8x_2E0)))) => ?[V9x_27_2E0]: (s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V9x_27_2E0))) = s(A_27d,V8x_2E0))) & ![V10x_2E0, V11y_2E0]: ((s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V10x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V11y_2E0)))) => (s(A_27d,V10x_2E0) = s(A_27d,V11y_2E0))))) => (s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),V6p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27b,V1v_27_2E0)))))))).
