0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC 0.13/0.34 % Computer : n029.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 16:17:25 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 # Version: 2.6rc1-ho 0.13/0.35 # No SInE strategy applied 0.13/0.35 # Trying AutoSched0 for 59 seconds 59.13/59.36 # AutoSched0-Mode selected heuristic G_E___301_C18_F1_URBAN_S5PRR_S0Y 59.13/59.36 # and selection function SelectMaxLComplexAvoidPosPred. 59.13/59.36 # 59.13/59.36 # Preprocessing time : 0.071 s 59.34/59.55 # No success with AutoSched0 59.34/59.55 # Trying AutoSched1 for 26 seconds 85.28/85.58 # AutoSched1-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S2S 85.28/85.58 # and selection function SelectNewComplexAHP. 85.28/85.58 # 85.28/85.58 # Preprocessing time : 0.048 s 85.28/85.58 # Presaturation interreduction done 85.49/85.73 # No success with AutoSched1 85.49/85.73 # Trying AutoSched2 for 8 seconds 93.49/93.75 # AutoSched2-Mode selected heuristic G_E___303_C18_F1_URBAN_S0Y 93.49/93.75 # and selection function SelectMaxLComplexAvoidPosPred. 93.49/93.75 # 93.49/93.75 # Preprocessing time : 0.072 s 93.49/93.81 # No success with AutoSched2 93.49/93.81 # Trying AutoSched3 for 7 seconds 96.34/96.59 # AutoSched3-Mode selected heuristic U_____206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN 96.34/96.59 # and selection function SelectComplexExceptUniqMaxHorn. 96.34/96.59 # 96.34/96.59 # Preprocessing time : 0.023 s 96.34/96.59 # Presaturation interreduction done 96.34/96.59 96.34/96.59 # Proof found! 96.34/96.59 # SZS status Theorem 96.34/96.59 # SZS output start CNFRefutation 96.34/96.59 thf(stp_iso_mem_o, axiom, ![X4:$i]:(mem @ X4 @ bool=>(X4)=(inj__o @ (p @ X4))), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax', stp_iso_mem_o)). 96.34/96.59 thf(stp_eq_fo_c_2Enum_2ESUC, axiom, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X10))=(ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Enum_2ESUC)). 96.34/96.59 thf(ax_false_p, axiom, ~(p @ c_2Ebool_2EF), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ax_false_p)). 96.34/96.59 thf(ap_tp, axiom, ![X1:del, X2:del, X7:$i]:(![X4:$i]:(mem @ (ap @ X7 @ X4) @ X2<=mem @ X4 @ X1)<=mem @ X7 @ (arr @ X1 @ X2)), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax', ap_tp)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EMOD__2, conjecture, ![X23:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X23)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X23))) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EMOD__2)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2EBIT1, axiom, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X10))=(ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2EBIT1)). 96.34/96.59 thf(stp_inj_surj_ty_2Enum_2Enum, axiom, ![X25:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X25))=(X25), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_inj_surj_ty_2Enum_2Enum)). 96.34/96.59 thf(stp_eq_fo_c_2Enum_2E0, axiom, (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)=(c_2Enum_2E0), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Enum_2E0)). 96.34/96.59 thf(mem_c_2Ebool_2EF, axiom, mem @ c_2Ebool_2EF @ bool, file('/export/starexec/sandbox/benchmark/theBenchmark.p', mem_c_2Ebool_2EF)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL, axiom, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X10))=(ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2ENUMERAL)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2EZERO, axiom, (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)=(c_2Earithmetic_2EZERO), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2EZERO)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EONE, axiom, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EONE)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EEVEN__ODD, axiom, ![X23:tp__ty_2Enum_2Enum]:(~(p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X23)))<=>p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EEVEN__ODD)). 96.34/96.59 thf(mem_c_2Earithmetic_2EEVEN, axiom, mem @ c_2Earithmetic_2EEVEN @ (arr @ ty_2Enum_2Enum @ bool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mem_c_2Earithmetic_2EEVEN)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2EBIT2, axiom, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X10))=(ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2EBIT2)). 96.34/96.59 thf(stp_iso_mem_ty_2Enum_2Enum, axiom, ![X4:$i]:(mem @ X4 @ ty_2Enum_2Enum=>(X4)=(inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_iso_mem_ty_2Enum_2Enum)). 96.34/96.59 thf(stp_inj_mem_ty_2Enum_2Enum, axiom, ![X35:tp__ty_2Enum_2Enum]:mem @ (inj__ty_2Enum_2Enum @ X35) @ ty_2Enum_2Enum, file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_inj_mem_ty_2Enum_2Enum)). 96.34/96.59 thf(mem_c_2Earithmetic_2EODD, axiom, mem @ c_2Earithmetic_2EODD @ (arr @ ty_2Enum_2Enum @ bool), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mem_c_2Earithmetic_2EODD)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EMOD__UNIQUE, axiom, ![X23:tp__ty_2Enum_2Enum, X50:tp__ty_2Enum_2Enum, X51:tp__ty_2Enum_2Enum]:((surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X50)) @ (inj__ty_2Enum_2Enum @ X23)))=(X51)<=?[X52:tp__ty_2Enum_2Enum]:((X50)=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X52)) @ (inj__ty_2Enum_2Enum @ X23))) @ (inj__ty_2Enum_2Enum @ X51)))&p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X51)) @ (inj__ty_2Enum_2Enum @ X23)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EMOD__UNIQUE)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EADD1, axiom, ![X15:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X15)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X15)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EADD1)). 96.34/96.59 thf(conj_thm_2Earithmetic_2ELESS__MONO__EQ, axiom, ![X15:tp__ty_2Enum_2Enum, X20:tp__ty_2Enum_2Enum]:(p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X15)) @ (inj__ty_2Enum_2Enum @ X20))<=>p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X15))) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2ELESS__MONO__EQ)). 96.34/96.59 thf(conj_thm_2Eprim__rec_2ELESS__0, axiom, ![X23:tp__ty_2Enum_2Enum]:p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Eprim__rec_2ELESS__0)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2EMOD, axiom, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EMOD @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2EMOD)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2E_2A, axiom, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2A @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2E_2A)). 96.34/96.59 thf(stp_eq_fo_c_2Earithmetic_2E_2B, axiom, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2B @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', stp_eq_fo_c_2Earithmetic_2E_2B)). 96.34/96.59 thf(conj_thm_2Earithmetic_2ETWO, axiom, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2ETWO)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EODD__EXISTS, axiom, ![X23:tp__ty_2Enum_2Enum]:(?[X24:tp__ty_2Enum_2Enum]:(X23)=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ X24))))<=>p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EODD__EXISTS)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EMULT__COMM, axiom, ![X15:tp__ty_2Enum_2Enum, X20:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X15)) @ (inj__ty_2Enum_2Enum @ X20)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X20)) @ (inj__ty_2Enum_2Enum @ X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EMULT__COMM)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EADD__0, axiom, ![X15:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X15)) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))=(X15), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EADD__0)). 96.34/96.59 thf(mem_c_2Ebool_2ET, axiom, mem @ c_2Ebool_2ET @ bool, file('/export/starexec/sandbox/benchmark/theBenchmark.p', mem_c_2Ebool_2ET)). 96.34/96.59 thf(ax_true_p, axiom, p @ c_2Ebool_2ET, file('/export/starexec/sandbox/benchmark/theBenchmark.p', ax_true_p)). 96.34/96.59 thf(conj_thm_2Ebool_2ECOND__CLAUSES, axiom, ![X19:del, X21:$i]:(mem @ X21 @ X19=>![X22:$i]:(mem @ X22 @ X19=>((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X19) @ c_2Ebool_2ET) @ X21) @ X22)=(X21)&(ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X19) @ c_2Ebool_2EF) @ X21) @ X22)=(X22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Ebool_2ECOND__CLAUSES)). 96.34/96.59 thf(mem_c_2Enum_2E0, axiom, mem @ c_2Enum_2E0 @ ty_2Enum_2Enum, file('/export/starexec/sandbox/benchmark/theBenchmark.p', mem_c_2Enum_2E0)). 96.34/96.59 thf(conj_thm_2Earithmetic_2EEVEN__EXISTS, axiom, ![X23:tp__ty_2Enum_2Enum]:(p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X23))<=>?[X24:tp__ty_2Enum_2Enum]:(X23)=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ X24)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_thm_2Earithmetic_2EEVEN__EXISTS)). 96.34/96.59 thf(c_0_34, axiom, ![X4:$i]:(mem @ X4 @ bool=>((~p @ X4|(X4)=(inj__o @ $true))&(p @ X4|(X4)=(inj__o @ $false)))), inference(fool_unroll,[status(thm)],[stp_iso_mem_o])). 96.34/96.59 thf(c_0_35, plain, ![X307:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X307))=(ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X307)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Enum_2ESUC])). 96.34/96.59 thf(c_0_36, plain, ![X255:$i]:((~p @ X255|(X255)=(inj__o @ $true)|~mem @ X255 @ bool)&(p @ X255|(X255)=(inj__o @ $false)|~mem @ X255 @ bool)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])). 96.34/96.59 thf(c_0_37, plain, ~p @ c_2Ebool_2EF, inference(fof_simplification,[status(thm)],[ax_false_p])). 96.34/96.59 thf(c_0_38, plain, ![X1:del, X2:del, X7:$i]:(mem @ X7 @ (arr @ X1 @ X2)=>![X4:$i]:(mem @ X4 @ X1=>mem @ (ap @ X7 @ X4) @ X2)), inference(fof_simplification,[status(thm)],[ap_tp])). 96.34/96.59 thf(c_0_39, negated_conjecture, ~(![X23:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X23)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X23))) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))), inference(assume_negation,[status(cth)],[conj_thm_2Earithmetic_2EMOD__2])). 96.34/96.59 thf(c_0_40, plain, ![X381:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X381))=(ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X381)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2EBIT1])). 96.34/96.59 thf(c_0_41, plain, ![X288:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X288))=(X288), inference(variable_rename,[status(thm)],[stp_inj_surj_ty_2Enum_2Enum])). 96.34/96.59 thf(c_0_42, plain, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X10))=(ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X10)), inference(split_conjunct,[status(thm)],[c_0_35])). 96.34/96.59 thf(c_0_43, plain, (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)=(c_2Enum_2E0), inference(split_conjunct,[status(thm)],[stp_eq_fo_c_2Enum_2E0])). 96.34/96.59 thf(c_0_44, plain, ![X4:$i]:(p @ X4|(X4)=(inj__o @ $false)|~mem @ X4 @ bool), inference(split_conjunct,[status(thm)],[c_0_36])). 96.34/96.59 thf(c_0_45, plain, mem @ c_2Ebool_2EF @ bool, inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF])). 96.34/96.59 thf(c_0_46, plain, ~p @ c_2Ebool_2EF, inference(split_conjunct,[status(thm)],[c_0_37])). 96.34/96.59 thf(c_0_47, plain, ![X251:del, X252:del, X253:$i, X254:$i]:(~mem @ X253 @ (arr @ X251 @ X252)|(~mem @ X254 @ X251|mem @ (ap @ X253 @ X254) @ X252)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])). 96.34/96.59 thf(c_0_48, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ esk10_0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])). 96.34/96.59 thf(c_0_49, plain, ![X402:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X402))=(ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X402)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2ENUMERAL])). 96.34/96.59 thf(c_0_50, plain, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X10))=(ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X10)), inference(split_conjunct,[status(thm)],[c_0_40])). 96.34/96.59 thf(c_0_51, plain, (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)=(c_2Earithmetic_2EZERO), inference(split_conjunct,[status(thm)],[stp_eq_fo_c_2Earithmetic_2EZERO])). 96.34/96.59 thf(c_0_52, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))), inference(split_conjunct,[status(thm)],[conj_thm_2Earithmetic_2EONE])). 96.34/96.59 thf(c_0_53, plain, ![X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X10))=(X10), inference(split_conjunct,[status(thm)],[c_0_41])). 96.34/96.59 thf(c_0_54, plain, (inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0))=(ap @ c_2Enum_2ESUC @ c_2Enum_2E0), inference(spm,[status(thm)],[c_0_42, c_0_43])). 96.34/96.59 thf(c_0_55, plain, ![X23:tp__ty_2Enum_2Enum]:(~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X23))<=>p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X23))), inference(fof_simplification,[status(thm)],[conj_thm_2Earithmetic_2EEVEN__ODD])). 96.34/96.59 thf(c_0_56, plain, (inj__o @ $false)=(c_2Ebool_2EF), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])). 96.34/96.59 thf(c_0_57, plain, ![X2:del, X7:$i, X4:$i, X1:del]:(mem @ (ap @ X4 @ X7) @ X2|~mem @ X4 @ (arr @ X1 @ X2)|~mem @ X7 @ X1), inference(split_conjunct,[status(thm)],[c_0_47])). 96.34/96.59 thf(c_0_58, plain, mem @ c_2Earithmetic_2EEVEN @ (arr @ ty_2Enum_2Enum @ bool), inference(split_conjunct,[status(thm)],[mem_c_2Earithmetic_2EEVEN])). 96.34/96.59 thf(c_0_59, plain, ![X414:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X414))=(ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X414)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2EBIT2])). 96.34/96.59 thf(c_0_60, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ esk10_0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), inference(split_conjunct,[status(thm)],[c_0_48])). 96.34/96.59 thf(c_0_61, plain, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X10))=(ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X10)), inference(split_conjunct,[status(thm)],[c_0_49])). 96.34/96.59 thf(c_0_62, plain, (inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ fo__c_2Earithmetic_2EZERO))=(ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO), inference(spm,[status(thm)],[c_0_50, c_0_51])). 96.34/96.59 thf(c_0_63, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO)))=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_51]), c_0_43])). 96.34/96.59 thf(c_0_64, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0))=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_53, c_0_54])). 96.34/96.59 thf(c_0_65, plain, ![X341:tp__ty_2Enum_2Enum]:((p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X341))|p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X341)))&(~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X341))|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X341)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])). 96.34/96.59 thf(c_0_66, plain, ![X380:$i]:(~mem @ X380 @ ty_2Enum_2Enum|(X380)=(inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X380))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_ty_2Enum_2Enum])])). 96.34/96.59 thf(c_0_67, plain, ![X4:$i]:((X4)=(c_2Ebool_2EF)|p @ X4|~mem @ X4 @ bool), inference(rw,[status(thm)],[c_0_44, c_0_56])). 96.34/96.59 thf(c_0_68, plain, ![X4:$i]:(mem @ (ap @ c_2Earithmetic_2EEVEN @ X4) @ bool|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_57, c_0_58])). 96.34/96.59 thf(c_0_69, plain, ![X349:tp__ty_2Enum_2Enum]:mem @ (inj__ty_2Enum_2Enum @ X349) @ ty_2Enum_2Enum, inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Enum_2Enum])). 96.34/96.59 thf(c_0_70, plain, mem @ c_2Earithmetic_2EODD @ (arr @ ty_2Enum_2Enum @ bool), inference(split_conjunct,[status(thm)],[mem_c_2Earithmetic_2EODD])). 96.34/96.59 thf(c_0_71, plain, ![X23:tp__ty_2Enum_2Enum, X50:tp__ty_2Enum_2Enum, X51:tp__ty_2Enum_2Enum]:(?[X52:tp__ty_2Enum_2Enum]:((X50)=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X52)) @ (inj__ty_2Enum_2Enum @ X23))) @ (inj__ty_2Enum_2Enum @ X51)))&p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X51)) @ (inj__ty_2Enum_2Enum @ X23)))=>(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X50)) @ (inj__ty_2Enum_2Enum @ X23)))=(X51)), inference(fof_simplification,[status(thm)],[conj_thm_2Earithmetic_2EMOD__UNIQUE])). 96.34/96.59 thf(c_0_72, plain, ![X393:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X393)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X393)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), inference(variable_rename,[status(thm)],[conj_thm_2Earithmetic_2EADD1])). 96.34/96.59 thf(c_0_73, plain, ![X339:tp__ty_2Enum_2Enum, X340:tp__ty_2Enum_2Enum]:((~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X339)) @ (inj__ty_2Enum_2Enum @ X340))|p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X339))) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X340))))&(~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X339))) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X340)))|p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X339)) @ (inj__ty_2Enum_2Enum @ X340)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Earithmetic_2ELESS__MONO__EQ])])). 96.34/96.59 thf(c_0_74, plain, ![X10:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X10))=(ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X10)), inference(split_conjunct,[status(thm)],[c_0_59])). 96.34/96.59 thf(c_0_75, plain, ![X396:tp__ty_2Enum_2Enum]:p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X396))), inference(variable_rename,[status(thm)],[conj_thm_2Eprim__rec_2ELESS__0])). 96.34/96.59 thf(c_0_76, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ c_2Enum_2E0) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO))))!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ esk10_0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_51]), c_0_43]), c_0_51])). 96.34/96.59 thf(c_0_77, plain, (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO))=(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT1 @ fo__c_2Earithmetic_2EZERO))), inference(spm,[status(thm)],[c_0_61, c_0_62])). 96.34/96.59 thf(c_0_78, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO)))=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0), inference(rw,[status(thm)],[c_0_63, c_0_64])). 96.34/96.59 thf(c_0_79, plain, ![X10:tp__ty_2Enum_2Enum]:(~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_65])). 96.34/96.59 thf(c_0_80, plain, ![X4:$i]:((X4)=(inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X4))|~mem @ X4 @ ty_2Enum_2Enum), inference(split_conjunct,[status(thm)],[c_0_66])). 96.34/96.59 thf(c_0_81, plain, ![X4:$i]:((ap @ c_2Earithmetic_2EEVEN @ X4)=(c_2Ebool_2EF)|p @ (ap @ c_2Earithmetic_2EEVEN @ X4)|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_67, c_0_68])). 96.34/96.59 thf(c_0_82, plain, ![X10:tp__ty_2Enum_2Enum]:mem @ (inj__ty_2Enum_2Enum @ X10) @ ty_2Enum_2Enum, inference(split_conjunct,[status(thm)],[c_0_69])). 96.34/96.59 thf(c_0_83, plain, ![X4:$i]:(mem @ (ap @ c_2Earithmetic_2EODD @ X4) @ bool|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_57, c_0_70])). 96.34/96.59 thf(c_0_84, plain, ![X439:tp__ty_2Enum_2Enum, X440:tp__ty_2Enum_2Enum, X441:tp__ty_2Enum_2Enum, X442:tp__ty_2Enum_2Enum]:((X440)!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X442)) @ (inj__ty_2Enum_2Enum @ X439))) @ (inj__ty_2Enum_2Enum @ X441)))|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X441)) @ (inj__ty_2Enum_2Enum @ X439))|(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X440)) @ (inj__ty_2Enum_2Enum @ X439)))=(X441)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])). 96.34/96.59 thf(c_0_85, plain, ![X296:tp__ty_2Enum_2Enum, X297:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EMOD @ X296 @ X297))=(ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X296)) @ (inj__ty_2Enum_2Enum @ X297)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2EMOD])). 96.34/96.59 thf(c_0_86, plain, ![X261:tp__ty_2Enum_2Enum, X262:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2A @ X261 @ X262))=(ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X261)) @ (inj__ty_2Enum_2Enum @ X262)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2E_2A])). 96.34/96.59 thf(c_0_87, plain, ![X378:tp__ty_2Enum_2Enum, X379:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2B @ X378 @ X379))=(ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X378)) @ (inj__ty_2Enum_2Enum @ X379)), inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Earithmetic_2E_2B])). 96.34/96.59 thf(c_0_88, plain, ![X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X10)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), inference(split_conjunct,[status(thm)],[c_0_72])). 96.34/96.59 thf(c_0_89, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X10))) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X11)))|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11))), inference(split_conjunct,[status(thm)],[c_0_73])). 96.34/96.59 thf(c_0_90, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))), inference(split_conjunct,[status(thm)],[conj_thm_2Earithmetic_2ETWO])). 96.34/96.59 thf(c_0_91, plain, (inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO))=(ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO), inference(spm,[status(thm)],[c_0_74, c_0_51])). 96.34/96.59 thf(c_0_92, plain, ![X10:tp__ty_2Enum_2Enum]:p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) @ (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_75])). 96.34/96.59 thf(c_0_93, plain, ![X363:tp__ty_2Enum_2Enum, X364:tp__ty_2Enum_2Enum, X365:tp__ty_2Enum_2Enum]:(((X363)!=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ X364))))|p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X363)))&(~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X365))|(X365)=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ (esk18_1 @ X365))))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Earithmetic_2EODD__EXISTS])])])])])). 96.34/96.59 thf(c_0_94, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ c_2Enum_2E0) @ (inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT1 @ fo__c_2Earithmetic_2EZERO)))))!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ esk10_0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO)))), inference(rw,[status(thm)],[c_0_76, c_0_77])). 96.34/96.59 thf(c_0_95, plain, (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT1 @ fo__c_2Earithmetic_2EZERO))=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_77]), c_0_53])). 96.34/96.59 thf(c_0_96, plain, ![X4:$i]:(~p @ (ap @ c_2Earithmetic_2EEVEN @ X4)|~p @ (ap @ c_2Earithmetic_2EODD @ X4)|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_79, c_0_80])). 96.34/96.59 thf(c_0_97, plain, ![X10:tp__ty_2Enum_2Enum]:((ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2EF)|p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(spm,[status(thm)],[c_0_81, c_0_82])). 96.34/96.59 thf(c_0_98, plain, ![X4:$i]:((ap @ c_2Earithmetic_2EODD @ X4)=(c_2Ebool_2EF)|p @ (ap @ c_2Earithmetic_2EODD @ X4)|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_67, c_0_83])). 96.34/96.59 thf(c_0_99, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum, X20:tp__ty_2Enum_2Enum, X15:tp__ty_2Enum_2Enum]:((surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X15)))=(X20)|(X10)!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X11)) @ (inj__ty_2Enum_2Enum @ X15))) @ (inj__ty_2Enum_2Enum @ X20)))|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X20)) @ (inj__ty_2Enum_2Enum @ X15))), inference(split_conjunct,[status(thm)],[c_0_84])). 96.34/96.59 thf(c_0_100, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EMOD @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), inference(split_conjunct,[status(thm)],[c_0_85])). 96.34/96.59 thf(c_0_101, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2A @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), inference(split_conjunct,[status(thm)],[c_0_86])). 96.34/96.59 thf(c_0_102, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2B @ X10 @ X11))=(ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)), inference(split_conjunct,[status(thm)],[c_0_87])). 96.34/96.59 thf(c_0_103, plain, ![X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO))))=(fo__c_2Enum_2ESUC @ X10), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88, c_0_42]), c_0_53]), c_0_51])). 96.34/96.59 thf(c_0_104, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X10))) @ (inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X11)))|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_42]), c_0_42])). 96.34/96.59 thf(c_0_105, plain, (surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO))))=(surj__ty_2Enum_2Enum @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_51]), c_0_51])). 96.34/96.59 thf(c_0_106, plain, (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO))=(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO))), inference(spm,[status(thm)],[c_0_61, c_0_91])). 96.34/96.59 thf(c_0_107, plain, ![X10:tp__ty_2Enum_2Enum]:p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0) @ (inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X10))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_43]), c_0_42])). 96.34/96.59 thf(c_0_108, plain, ![X10:tp__ty_2Enum_2Enum]:((X10)=(surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ (esk18_1 @ X10)))))|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_93])). 96.34/96.59 thf(c_0_109, plain, ![X277:tp__ty_2Enum_2Enum, X278:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X277)) @ (inj__ty_2Enum_2Enum @ X278)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X278)) @ (inj__ty_2Enum_2Enum @ X277))), inference(variable_rename,[status(thm)],[conj_thm_2Earithmetic_2EMULT__COMM])). 96.34/96.59 thf(c_0_110, plain, ![X270:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X270)) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))=(X270), inference(variable_rename,[status(thm)],[conj_thm_2Earithmetic_2EADD__0])). 96.34/96.59 thf(c_0_111, plain, ![X4:$i]:((X4)=(inj__o @ $true)|~p @ X4|~mem @ X4 @ bool), inference(split_conjunct,[status(thm)],[c_0_36])). 96.34/96.59 thf(c_0_112, plain, mem @ c_2Ebool_2ET @ bool, inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET])). 96.34/96.59 thf(c_0_113, plain, p @ c_2Ebool_2ET, inference(split_conjunct,[status(thm)],[ax_true_p])). 96.34/96.59 thf(c_0_114, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ c_2Enum_2E0) @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)))!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ esk10_0)) @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94, c_0_95]), c_0_54])). 96.34/96.59 thf(c_0_115, plain, ![X10:tp__ty_2Enum_2Enum]:((ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2EF)|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_82])])). 96.34/96.59 thf(c_0_116, plain, ![X10:tp__ty_2Enum_2Enum]:((ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2EF)|p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(spm,[status(thm)],[c_0_98, c_0_82])). 96.34/96.59 thf(c_0_117, plain, ![X10:tp__ty_2Enum_2Enum, X15:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2EMOD @ (fo__c_2Earithmetic_2E_2B @ (fo__c_2Earithmetic_2E_2A @ X10 @ X11) @ X15) @ X11)=(X15)|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X15)) @ (inj__ty_2Enum_2Enum @ X11))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99, c_0_100]), c_0_53]), c_0_101]), c_0_102]), c_0_53])])). 96.34/96.59 thf(c_0_118, plain, ![X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2E_2B @ X10 @ (fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0))=(fo__c_2Enum_2ESUC @ X10), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_77]), c_0_102]), c_0_53]), c_0_95])). 96.34/96.59 thf(c_0_119, plain, ![X10:tp__ty_2Enum_2Enum]:(p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)) @ (inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X10)))|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0) @ (inj__ty_2Enum_2Enum @ X10))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_54]), c_0_43])). 96.34/96.59 thf(c_0_120, plain, (fo__c_2Enum_2ESUC @ (fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0))=(fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_77]), c_0_42]), c_0_53]), c_0_106]), c_0_53]), c_0_95])). 96.34/96.59 thf(c_0_121, plain, p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0) @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)), inference(spm,[status(thm)],[c_0_107, c_0_54])). 96.34/96.59 thf(c_0_122, plain, ![X10:tp__ty_2Enum_2Enum]:((surj__ty_2Enum_2Enum @ (ap @ c_2Enum_2ESUC @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO))) @ (inj__ty_2Enum_2Enum @ (esk18_1 @ X10)))))=(X10)|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(rw,[status(thm)],[c_0_108, c_0_51])). 96.34/96.59 thf(c_0_123, plain, ![X11:tp__ty_2Enum_2Enum, X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ X11)))=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X11)) @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_109])). 96.34/96.59 thf(c_0_124, plain, ![X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))=(X10), inference(split_conjunct,[status(thm)],[c_0_110])). 96.34/96.59 thf(c_0_125, plain, (inj__o @ $true)=(c_2Ebool_2ET), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112]), c_0_113])])). 96.34/96.59 thf(c_0_126, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))) @ c_2Enum_2E0) @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)))!=(fo__c_2Earithmetic_2EMOD @ esk10_0 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_106]), c_0_100]), c_0_53])). 96.34/96.59 thf(c_0_127, plain, ![X10:tp__ty_2Enum_2Enum]:((ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2EF)|(ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2EF)), inference(spm,[status(thm)],[c_0_115, c_0_116])). 96.34/96.59 thf(c_0_128, plain, ![X322:del, X323:$i, X324:$i]:(((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X322) @ c_2Ebool_2ET) @ X323) @ X324)=(X323)|~mem @ X324 @ X322|~mem @ X323 @ X322)&((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X322) @ c_2Ebool_2EF) @ X323) @ X324)=(X324)|~mem @ X324 @ X322|~mem @ X323 @ X322)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2ECOND__CLAUSES])])])])). 96.34/96.59 thf(c_0_129, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2EMOD @ (fo__c_2Enum_2ESUC @ (fo__c_2Earithmetic_2E_2A @ X10 @ X11)) @ X11)=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0)|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)) @ (inj__ty_2Enum_2Enum @ X11))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_54]), c_0_118])). 96.34/96.59 thf(c_0_130, plain, p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)) @ (inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120]), c_0_54]), c_0_121])])). 96.34/96.59 thf(c_0_131, plain, ![X10:tp__ty_2Enum_2Enum]:((fo__c_2Enum_2ESUC @ (fo__c_2Earithmetic_2E_2A @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)) @ (esk18_1 @ X10)))=(X10)|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122, c_0_106]), c_0_101]), c_0_42]), c_0_53])). 96.34/96.59 thf(c_0_132, plain, ![X11:tp__ty_2Enum_2Enum, X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2E_2A @ X10 @ X11)=(fo__c_2Earithmetic_2E_2A @ X11 @ X10), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_101]), c_0_53]), c_0_101]), c_0_53])). 96.34/96.59 thf(c_0_133, plain, ![X10:tp__ty_2Enum_2Enum]:(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ c_2Enum_2E0))=(X10), inference(rw,[status(thm)],[c_0_124, c_0_43])). 96.34/96.59 thf(c_0_134, plain, ![X10:tp__ty_2Enum_2Enum]:(ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X10)) @ c_2Enum_2E0)=(inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2E_2B @ X10 @ fo__c_2Enum_2E0)), inference(spm,[status(thm)],[c_0_102, c_0_43])). 96.34/96.59 thf(c_0_135, plain, ![X4:$i]:((X4)=(c_2Ebool_2ET)|~mem @ X4 @ bool|~p @ X4), inference(rw,[status(thm)],[c_0_111, c_0_125])). 96.34/96.59 thf(c_0_136, negated_conjecture, ((ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ esk10_0))=(c_2Ebool_2EF)|(surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ c_2Ebool_2EF) @ c_2Enum_2E0) @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)))!=(fo__c_2Earithmetic_2EMOD @ esk10_0 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))), inference(spm,[status(thm)],[c_0_126, c_0_127])). 96.34/96.59 thf(c_0_137, plain, ![X7:$i, X4:$i, X1:del]:((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2EF) @ X4) @ X7)=(X7)|~mem @ X7 @ X1|~mem @ X4 @ X1), inference(split_conjunct,[status(thm)],[c_0_128])). 96.34/96.59 thf(c_0_138, plain, mem @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0) @ ty_2Enum_2Enum, inference(spm,[status(thm)],[c_0_82, c_0_54])). 96.34/96.59 thf(c_0_139, plain, mem @ c_2Enum_2E0 @ ty_2Enum_2Enum, inference(split_conjunct,[status(thm)],[mem_c_2Enum_2E0])). 96.34/96.59 thf(c_0_140, plain, ![X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2EMOD @ (fo__c_2Enum_2ESUC @ (fo__c_2Earithmetic_2E_2A @ X10 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))) @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_129, c_0_130])). 96.34/96.59 thf(c_0_141, plain, ![X10:tp__ty_2Enum_2Enum]:((fo__c_2Enum_2ESUC @ (fo__c_2Earithmetic_2E_2A @ (esk18_1 @ X10) @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO))))=(X10)|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(spm,[status(thm)],[c_0_131, c_0_132])). 96.34/96.59 thf(c_0_142, plain, ![X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2E_2B @ X10 @ fo__c_2Enum_2E0)=(X10), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133, c_0_134]), c_0_53])). 96.34/96.59 thf(c_0_143, plain, ![X4:$i]:((ap @ c_2Earithmetic_2EEVEN @ X4)=(c_2Ebool_2ET)|~p @ (ap @ c_2Earithmetic_2EEVEN @ X4)|~mem @ X4 @ ty_2Enum_2Enum), inference(spm,[status(thm)],[c_0_135, c_0_68])). 96.34/96.59 thf(c_0_144, plain, ![X10:tp__ty_2Enum_2Enum]:(p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))|p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_65])). 96.34/96.59 thf(c_0_145, negated_conjecture, ((ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ esk10_0))=(c_2Ebool_2EF)|(fo__c_2Earithmetic_2EMOD @ esk10_0 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))!=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_64]), c_0_138]), c_0_139])])). 96.34/96.59 thf(c_0_146, plain, ![X10:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2EMOD @ X10 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))=(fo__c_2Enum_2ESUC @ fo__c_2Enum_2E0)|~p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(spm,[status(thm)],[c_0_140, c_0_141])). 96.34/96.59 thf(c_0_147, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2EMOD @ (fo__c_2Earithmetic_2E_2A @ X10 @ X11) @ X11)=(fo__c_2Enum_2E0)|~p @ (ap @ (ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0) @ (inj__ty_2Enum_2Enum @ X11))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_43]), c_0_142])). 96.34/96.59 thf(c_0_148, plain, ![X284:tp__ty_2Enum_2Enum, X286:tp__ty_2Enum_2Enum, X287:tp__ty_2Enum_2Enum]:((~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X284))|(X284)=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ (esk3_1 @ X284)))))&((X286)!=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ X287)))|p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X286)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Earithmetic_2EEVEN__EXISTS])])])])])). 96.34/96.59 thf(c_0_149, plain, ![X10:tp__ty_2Enum_2Enum]:((ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))=(c_2Ebool_2ET)|p @ (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ X10))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_144]), c_0_82])])). 96.34/96.59 thf(c_0_150, negated_conjecture, (ap @ c_2Earithmetic_2EODD @ (inj__ty_2Enum_2Enum @ esk10_0))=(c_2Ebool_2EF), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_116])). 96.34/96.59 thf(c_0_151, plain, ![X10:tp__ty_2Enum_2Enum, X11:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2EMOD @ (fo__c_2Earithmetic_2E_2A @ X10 @ (fo__c_2Enum_2ESUC @ X11)) @ (fo__c_2Enum_2ESUC @ X11))=(fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_147, c_0_107])). 96.34/96.59 thf(c_0_152, plain, ![X10:tp__ty_2Enum_2Enum]:((X10)=(surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) @ (inj__ty_2Enum_2Enum @ (esk3_1 @ X10))))|~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(split_conjunct,[status(thm)],[c_0_148])). 96.34/96.59 thf(c_0_153, negated_conjecture, (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ esk10_0))=(c_2Ebool_2ET), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150]), c_0_46])). 96.34/96.59 thf(c_0_154, plain, ![X11:tp__ty_2Enum_2Enum, X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2EMOD @ (fo__c_2Earithmetic_2E_2A @ (fo__c_2Enum_2ESUC @ X10) @ X11) @ (fo__c_2Enum_2ESUC @ X10))=(fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_151, c_0_132])). 96.34/96.59 thf(c_0_155, plain, ![X10:tp__ty_2Enum_2Enum]:((surj__ty_2Enum_2Enum @ (ap @ (ap @ c_2Earithmetic_2E_2A @ (ap @ c_2Earithmetic_2ENUMERAL @ (ap @ c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO))) @ (inj__ty_2Enum_2Enum @ (esk3_1 @ X10))))=(X10)|~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(rw,[status(thm)],[c_0_152, c_0_51])). 96.34/96.59 thf(c_0_156, negated_conjecture, (surj__ty_2Enum_2Enum @ (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ ty_2Enum_2Enum) @ c_2Ebool_2ET) @ c_2Enum_2E0) @ (ap @ c_2Enum_2ESUC @ c_2Enum_2E0)))!=(fo__c_2Earithmetic_2EMOD @ esk10_0 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO))), inference(rw,[status(thm)],[c_0_126, c_0_153])). 96.34/96.59 thf(c_0_157, plain, ![X7:$i, X4:$i, X1:del]:((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X1) @ c_2Ebool_2ET) @ X4) @ X7)=(X4)|~mem @ X7 @ X1|~mem @ X4 @ X1), inference(split_conjunct,[status(thm)],[c_0_128])). 96.34/96.59 thf(c_0_158, plain, (surj__ty_2Enum_2Enum @ c_2Enum_2E0)=(fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_53, c_0_43])). 96.34/96.59 thf(c_0_159, plain, ![X10:tp__ty_2Enum_2Enum]:(fo__c_2Earithmetic_2EMOD @ (fo__c_2Earithmetic_2E_2A @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)) @ X10) @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))=(fo__c_2Enum_2E0), inference(spm,[status(thm)],[c_0_154, c_0_120])). 96.34/96.59 thf(c_0_160, plain, ![X10:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2E_2A @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)) @ (esk3_1 @ X10))=(X10)|~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155, c_0_106]), c_0_101]), c_0_53])). 96.34/96.59 thf(c_0_161, negated_conjecture, (fo__c_2Earithmetic_2EMOD @ esk10_0 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))!=(fo__c_2Enum_2E0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_157]), c_0_158]), c_0_138]), c_0_139])])). 96.34/96.59 thf(c_0_162, plain, ![X10:tp__ty_2Enum_2Enum]:((fo__c_2Earithmetic_2EMOD @ X10 @ (fo__c_2Earithmetic_2ENUMERAL @ (fo__c_2Earithmetic_2EBIT2 @ fo__c_2Earithmetic_2EZERO)))=(fo__c_2Enum_2E0)|~p @ (ap @ c_2Earithmetic_2EEVEN @ (inj__ty_2Enum_2Enum @ X10))), inference(spm,[status(thm)],[c_0_159, c_0_160])). 96.34/96.59 thf(c_0_163, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162]), c_0_153]), c_0_113])]), ['proof']). 96.34/96.59 # SZS output end CNFRefutation 96.34/96.59 # Proof object total steps : 164 96.34/96.59 # Proof object clause steps : 101 96.34/96.59 # Proof object formula steps : 63 96.34/96.59 # Proof object conjectures : 15 96.34/96.59 # Proof object clause conjectures : 12 96.34/96.59 # Proof object formula conjectures : 3 96.34/96.59 # Proof object initial clauses used : 37 96.34/96.59 # Proof object initial formulas used : 34 96.34/96.59 # Proof object generating inferences : 40 96.34/96.59 # Proof object simplifying inferences : 84 96.34/96.59 # Training examples: 0 positive, 0 negative 96.34/96.59 # Parsed axioms : 152 96.34/96.59 # Removed by relevancy pruning/SinE : 0 96.34/96.59 # Initial clauses : 461 96.34/96.59 # Removed in clause preprocessing : 286 96.34/96.59 # Initial clauses in saturation : 175 96.34/96.59 # Processed clauses : 14656 96.34/96.59 # ...of these trivial : 514 96.34/96.59 # ...subsumed : 9680 96.34/96.59 # ...remaining for further processing : 4462 96.34/96.59 # Other redundant clauses eliminated : 6 96.34/96.59 # Clauses deleted for lack of memory : 0 96.34/96.59 # Backward-subsumed : 109 96.34/96.59 # Backward-rewritten : 308 96.34/96.59 # Generated clauses : 187177 96.34/96.59 # ...of the previous two non-trivial : 177143 96.34/96.59 # Contextual simplify-reflections : 35 96.34/96.59 # Paramodulations : 186766 96.34/96.59 # Factorizations : 281 96.34/96.59 # NegExts : 0 96.34/96.59 # Equation resolutions : 7 96.34/96.59 # Propositional unsat checks : 0 96.34/96.59 # Propositional check models : 0 96.34/96.59 # Propositional check unsatisfiable : 0 96.34/96.59 # Propositional clauses : 0 96.34/96.59 # Propositional clauses after purity: 0 96.34/96.59 # Propositional unsat core size : 0 96.34/96.59 # Propositional preprocessing time : 0.000 96.34/96.59 # Propositional encoding time : 0.000 96.34/96.59 # Propositional solver time : 0.000 96.34/96.59 # Success case prop preproc time : 0.000 96.34/96.59 # Success case prop encoding time : 0.000 96.34/96.59 # Success case prop solver time : 0.000 96.34/96.59 # Current number of processed clauses : 3864 96.34/96.59 # Positive orientable unit clauses : 516 96.34/96.59 # Positive unorientable unit clauses: 1 96.34/96.59 # Negative unit clauses : 4 96.34/96.59 # Non-unit-clauses : 3343 96.34/96.59 # Current number of unprocessed clauses: 160981 96.34/96.59 # ...number of literals in the above : 935890 96.34/96.59 # Current number of archived formulas : 0 96.34/96.59 # Current number of archived clauses : 594 96.34/96.59 # Clause-clause subsumption calls (NU) : 1056500 96.34/96.59 # Rec. Clause-clause subsumption calls : 387337 96.34/96.59 # Non-unit clause-clause subsumptions : 7554 96.34/96.59 # Unit Clause-clause subsumption calls : 20850 96.34/96.59 # Rewrite failures with RHS unbound : 0 96.34/96.59 # BW rewrite match attempts : 1149 96.34/96.59 # BW rewrite match successes : 127 96.34/96.59 # Condensation attempts : 0 96.34/96.59 # Condensation successes : 0 96.34/96.59 # Termbank termtop insertions : 7410621 96.34/96.60 96.34/96.60 # ------------------------------------------------- 96.34/96.60 # User time : 92.995 s 96.34/96.60 # System time : 3.206 s 96.34/96.60 # Total time : 96.201 s 96.34/96.60 # Maximum resident set size: 1860 pages 96.34/96.60 EOF