%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ITP003+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 22:45:40 EDT 2022
% Result : Theorem 0.31s 12.51s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 40 unt; 0 def)
% Number of atoms : 150 ( 94 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 119 ( 48 ~; 47 |; 16 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 121 ( 30 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [X18,X20,X21] :
( ? [X22] :
( s(tyop_2Enum_2Enum,X20) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X22),s(tyop_2Enum_2Enum,X18))),s(tyop_2Enum_2Enum,X21)))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X21),s(tyop_2Enum_2Enum,X18)))) )
=> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X20),s(tyop_2Enum_2Enum,X18))) = s(tyop_2Enum_2Enum,X21) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EMOD__UNIQUE) ).
fof(thm_2Earithmetic_2EADD1,axiom,
! [X16] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X16))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X16),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EADD1) ).
fof(thm_2Earithmetic_2EADD__0,axiom,
! [X16] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X16),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,X16),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EADD__0) ).
fof(thm_2Earithmetic_2EONE,axiom,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EONE) ).
fof(thm_2Earithmetic_2EODD__EXISTS,axiom,
! [X18] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X18))))
<=> ? [X19] : s(tyop_2Enum_2Enum,X18) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X19))))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EODD__EXISTS) ).
fof(thm_2Earithmetic_2ETWO,axiom,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2ETWO) ).
fof(thm_2Eprim__rec_2ELESS__0,axiom,
! [X18] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X18)))))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Eprim__rec_2ELESS__0) ).
fof(thm_2Earithmetic_2EMOD__2,conjecture,
! [X18] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X18),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X18))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EMOD__2) ).
fof(thm_2Earithmetic_2EMULT__COMM,axiom,
! [X16,X17] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X16),s(tyop_2Enum_2Enum,X17))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X17),s(tyop_2Enum_2Enum,X16))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EMULT__COMM) ).
fof(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Ebool_2EEQ__CLAUSES) ).
fof(thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [X16,X17] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X16))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X17))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X16),s(tyop_2Enum_2Enum,X17))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2ELESS__MONO__EQ) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [X8] :
( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reserved_2Eho_2Ebool__cases__ax) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reserved_2Eho_2Etruth) ).
fof(thm_2Earithmetic_2EEVEN__ODD,axiom,
! [X18] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X18))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X18)))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EEVEN__ODD) ).
fof(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1,X23,X24] :
( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X23),s(X1,X24))) = s(X1,X23)
& s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X23),s(X1,X24))) = s(X1,X24) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Ebool_2ECOND__CLAUSES) ).
fof(thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [X18] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X18))))
<=> ? [X19] : s(tyop_2Enum_2Enum,X18) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X19))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thm_2Earithmetic_2EEVEN__EXISTS) ).
fof(c_0_16,plain,
! [X23,X24,X25,X26] :
( s(tyop_2Enum_2Enum,X24) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X26),s(tyop_2Enum_2Enum,X23))),s(tyop_2Enum_2Enum,X25)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X25),s(tyop_2Enum_2Enum,X23))))
| s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X24),s(tyop_2Enum_2Enum,X23))) = s(tyop_2Enum_2Enum,X25) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EMOD__UNIQUE])])])])]) ).
fof(c_0_17,plain,
! [X17] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X17))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X17),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD1]) ).
fof(c_0_18,plain,
! [X17] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X17),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,X17),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD__0]) ).
cnf(c_0_19,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))) = s(tyop_2Enum_2Enum,X3)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2))))
| s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X4),s(tyop_2Enum_2Enum,X2))),s(tyop_2Enum_2Enum,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EONE]) ).
fof(c_0_22,plain,
! [X20,X20,X22] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X20))))
| s(tyop_2Enum_2Enum,X20) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,esk3_1(X20)))))) )
& ( s(tyop_2Enum_2Enum,X20) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X22)))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X20)))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EODD__EXISTS])])])])])]) ).
cnf(c_0_23,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2ETWO]) ).
cnf(c_0_24,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X19] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X19)))))),
inference(variable_rename,[status(thm)],[thm_2Eprim__rec_2ELESS__0]) ).
fof(c_0_26,negated_conjecture,
~ ! [X18] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X18),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X18))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(assume_negation,[status(cth)],[thm_2Earithmetic_2EMOD__2]) ).
cnf(c_0_27,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))),s(tyop_2Enum_2Enum,X3))),s(tyop_2Enum_2Enum,X2))) = s(tyop_2Enum_2Enum,X3)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2)))) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_29,plain,
! [X18,X19] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X18),s(tyop_2Enum_2Enum,X19))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X19),s(tyop_2Enum_2Enum,X18))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMULT__COMM]) ).
fof(c_0_30,plain,
! [X9,X9,X9,X9,X9,X9,X9,X9] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,X9)
| p(s(tyop_2Emin_2Ebool,X9)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X9))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X9) )
& ( s(tyop_2Emin_2Ebool,X9) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X9)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X9))
| s(tyop_2Emin_2Ebool,X9) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,X9)
| ~ p(s(tyop_2Emin_2Ebool,X9)) )
& ( p(s(tyop_2Emin_2Ebool,X9))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X9) )
& ( s(tyop_2Emin_2Ebool,X9) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X9)) )
& ( p(s(tyop_2Emin_2Ebool,X9))
| s(tyop_2Emin_2Ebool,X9) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES])])])])]) ).
cnf(c_0_31,plain,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1))))
| s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X2))))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),
inference(rw,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_33,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,X2)))) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_34,plain,
p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1)))))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,negated_conjecture,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,esk1_0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_36,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))),s(tyop_2Enum_2Enum,X2))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_28]) ).
cnf(c_0_37,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( s(tyop_2Enum_2Enum,X1) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,esk3_1(X1))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_39,plain,
! [X18,X19] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X18))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X19))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X18),s(tyop_2Enum_2Enum,X19))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__MONO__EQ]) ).
cnf(c_0_40,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1))))
| s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,X2))))) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X2))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_34])]) ).
fof(c_0_43,plain,
! [X9] :
( s(tyop_2Emin_2Ebool,X9) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X9) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
cnf(c_0_44,negated_conjecture,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,esk1_0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))),s(tyop_2Enum_2Enum,X1))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,X1)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,esk3_1(X1)))))) = s(tyop_2Enum_2Enum,X1)
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(rw,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_47,plain,
s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_49,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth]) ).
fof(c_0_50,plain,
! [X19,X19] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X19))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X19)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X19))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X19)))) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[thm_2Earithmetic_2EEVEN__ODD])])])])]) ).
cnf(c_0_51,plain,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,X1)))))))),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_52,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X2))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),
inference(er,[status(thm)],[c_0_42]) ).
fof(c_0_53,plain,
! [X25,X26,X27,X25,X26,X27] :
( s(X25,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X25,X26),s(X25,X27))) = s(X25,X26)
& s(X25,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X25,X26),s(X25,X27))) = s(X25,X27) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES])])]) ).
cnf(c_0_54,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,esk1_0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_21]),c_0_32]) ).
cnf(c_0_56,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_57,plain,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X1))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
( ~ p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_59,plain,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_37]) ).
cnf(c_0_60,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X2),s(X1,X3))) = s(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,esk1_0)))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
( s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(spm,[status(thm)],[c_0_40,c_0_57]) ).
cnf(c_0_64,plain,
s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X2),s(X1,X3),s(X1,X4))) = s(X1,X4)
| s(tyop_2Emin_2Ebool,X5) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X5) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))))
| s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_49])]) ).
cnf(c_0_67,plain,
( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X2),s(X1,X3),s(X1,X4))) = s(X1,X4)
| s(tyop_2Emin_2Ebool,X2) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_64]) ).
cnf(c_0_68,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_69,plain,
! [X20,X20,X22] :
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X20))))
| s(tyop_2Enum_2Enum,X20) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,esk2_1(X20)))) )
& ( s(tyop_2Enum_2Enum,X20) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X22)))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X20)))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EEVEN__EXISTS])])])])])]) ).
cnf(c_0_70,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0)))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_71,plain,
( s(tyop_2Enum_2Enum,X1) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,esk2_1(X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,esk1_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(spm,[status(thm)],[c_0_40,c_0_70]) ).
cnf(c_0_73,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X2),s(X1,X3))) = s(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_74,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Enum_2Enum,X2))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
cnf(c_0_75,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,esk2_1(X1)))) = s(tyop_2Enum_2Enum,X1)
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(rw,[status(thm)],[c_0_71,c_0_32]) ).
cnf(c_0_76,negated_conjecture,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,esk1_0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_72]),c_0_73]) ).
cnf(c_0_77,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X1)))) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_72]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP003+1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n018.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 : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 23:41:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.31/12.51 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.31/12.51 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.31/12.51 # Preprocessing time : 0.030 s
% 0.31/12.51
% 0.31/12.51 # Proof found!
% 0.31/12.51 # SZS status Theorem
% 0.31/12.51 # SZS output start CNFRefutation
% See solution above
% 0.31/12.51 # Proof object total steps : 79
% 0.31/12.51 # Proof object clause steps : 49
% 0.31/12.51 # Proof object formula steps : 30
% 0.31/12.51 # Proof object conjectures : 11
% 0.31/12.51 # Proof object clause conjectures : 8
% 0.31/12.51 # Proof object formula conjectures : 3
% 0.31/12.51 # Proof object initial clauses used : 20
% 0.31/12.51 # Proof object initial formulas used : 16
% 0.31/12.51 # Proof object generating inferences : 22
% 0.31/12.51 # Proof object simplifying inferences : 24
% 0.31/12.51 # Training examples: 0 positive, 0 negative
% 0.31/12.51 # Parsed axioms : 95
% 0.31/12.51 # Removed by relevancy pruning/SinE : 32
% 0.31/12.51 # Initial clauses : 351
% 0.31/12.51 # Removed in clause preprocessing : 243
% 0.31/12.51 # Initial clauses in saturation : 108
% 0.31/12.51 # Processed clauses : 8480
% 0.31/12.51 # ...of these trivial : 57
% 0.31/12.51 # ...subsumed : 7873
% 0.31/12.51 # ...remaining for further processing : 550
% 0.31/12.51 # Other redundant clauses eliminated : 0
% 0.31/12.51 # Clauses deleted for lack of memory : 154018
% 0.31/12.51 # Backward-subsumed : 24
% 0.31/12.51 # Backward-rewritten : 42
% 0.31/12.51 # Generated clauses : 344853
% 0.31/12.51 # ...of the previous two non-trivial : 315537
% 0.31/12.51 # Contextual simplify-reflections : 3332
% 0.31/12.51 # Paramodulations : 344522
% 0.31/12.51 # Factorizations : 278
% 0.31/12.51 # Equation resolutions : 53
% 0.31/12.51 # Current number of processed clauses : 484
% 0.31/12.51 # Positive orientable unit clauses : 29
% 0.31/12.51 # Positive unorientable unit clauses: 11
% 0.31/12.51 # Negative unit clauses : 5
% 0.31/12.51 # Non-unit-clauses : 439
% 0.31/12.51 # Current number of unprocessed clauses: 113904
% 0.31/12.51 # ...number of literals in the above : 447138
% 0.31/12.51 # Current number of archived formulas : 0
% 0.31/12.51 # Current number of archived clauses : 66
% 0.31/12.51 # Clause-clause subsumption calls (NU) : 154865
% 0.31/12.51 # Rec. Clause-clause subsumption calls : 107554
% 0.31/12.51 # Non-unit clause-clause subsumptions : 8948
% 0.31/12.51 # Unit Clause-clause subsumption calls : 315
% 0.31/12.51 # Rewrite failures with RHS unbound : 0
% 0.31/12.51 # BW rewrite match attempts : 9796
% 0.31/12.51 # BW rewrite match successes : 49
% 0.31/12.51 # Condensation attempts : 0
% 0.31/12.51 # Condensation successes : 0
% 0.31/12.51 # Termbank termtop insertions : 16056611
% 0.31/12.51
% 0.31/12.51 # -------------------------------------------------
% 0.31/12.51 # User time : 11.717 s
% 0.31/12.51 # System time : 0.103 s
% 0.31/12.51 # Total time : 11.820 s
% 0.31/12.51 # Maximum resident set size: 146036 pages
% 0.34/23.43 eprover: CPU time limit exceeded, terminating
% 0.34/23.43 eprover: CPU time limit exceeded, terminating
% 0.34/23.43 eprover: CPU time limit exceeded, terminating
% 0.34/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.45 eprover: No such file or directory
% 0.34/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.45 eprover: No such file or directory
% 0.34/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.45 eprover: No such file or directory
% 0.34/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.45 eprover: No such file or directory
% 0.34/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.45 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.46 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.47 eprover: No such file or directory
% 0.34/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.48 eprover: No such file or directory
% 0.34/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.48 eprover: No such file or directory
% 0.34/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.48 eprover: No such file or directory
% 0.34/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.48 eprover: No such file or directory
% 0.34/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.48 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.49 eprover: No such file or directory
% 0.34/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.50 eprover: No such file or directory
% 0.34/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.50 eprover: No such file or directory
% 0.34/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------