TSTP Solution File: ITP003+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ITP003+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 22:45:41 EDT 2022
% Result : Theorem 1.73s 216.88s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 33
% Syntax : Number of formulae : 181 ( 47 unt; 0 def)
% Number of atoms : 573 ( 146 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 681 ( 289 ~; 325 |; 23 &)
% ( 9 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 19 con; 0-2 aty)
% Number of variables : 200 ( 0 sgn 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(boolext,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax_false_p) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax_true_p) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Ebool_2ET) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Ebool_2EF) ).
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Ebool_2E_7E) ).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Emin_2E_3D_3D_3E) ).
fof(ax_neg_p,axiom,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax_neg_p) ).
fof(ax_imp_p,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X5),X6))
<=> ( p(X5)
=> p(X6) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax_imp_p) ).
fof(conj_thm_2Ebool_2ENOT__EXISTS__THM,axiom,
! [X9] :
( ne(X9)
=> ! [X22] :
( mem(X22,arr(X9,bool))
=> ( ~ ? [X23] :
( mem(X23,X9)
& p(ap(X22,X23)) )
<=> ! [X24] :
( mem(X24,X9)
=> ~ p(ap(X22,X24)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Ebool_2ENOT__EXISTS__THM) ).
fof(bool_ne,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',bool_ne) ).
fof(mem_c_2Earithmetic_2EEVEN,axiom,
mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Earithmetic_2EEVEN) ).
fof(conj_thm_2Earithmetic_2EMOD__2,conjecture,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,X12),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,X12)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EMOD__2) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Ebool_2E_21) ).
fof(mem_c_2Earithmetic_2EODD,axiom,
mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Earithmetic_2EODD) ).
fof(ax_all_p,axiom,
! [X1] :
( ne(X1)
=> ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax_all_p) ).
fof(conj_thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ! [X14] :
( mem(X14,ty_2Enum_2Enum)
=> ! [X15] :
( mem(X15,ty_2Enum_2Enum)
=> ( ? [X16] :
( mem(X16,ty_2Enum_2Enum)
& X14 = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,X16),X12)),X15)
& p(ap(ap(c_2Eprim__rec_2E_3C,X15),X12)) )
=> ap(ap(c_2Earithmetic_2EMOD,X14),X12) = X15 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EMOD__UNIQUE) ).
fof(conj_thm_2Earithmetic_2EMULT__COMM,axiom,
! [X10] :
( mem(X10,ty_2Enum_2Enum)
=> ! [X11] :
( mem(X11,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2A,X10),X11) = ap(ap(c_2Earithmetic_2E_2A,X11),X10) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EMULT__COMM) ).
fof(mem_c_2Enum_2ESUC,axiom,
mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Enum_2ESUC) ).
fof(conj_thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [X10] :
( mem(X10,ty_2Enum_2Enum)
=> ! [X11] :
( mem(X11,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,X10)),ap(c_2Enum_2ESUC,X11)))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,X10),X11)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2ELESS__MONO__EQ) ).
fof(conj_thm_2Eprim__rec_2ELESS__0,axiom,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,X12))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Eprim__rec_2ELESS__0) ).
fof(conj_thm_2Earithmetic_2EEVEN__ODD,axiom,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,X12))
<=> ~ p(ap(c_2Earithmetic_2EODD,X12)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EEVEN__ODD) ).
fof(conj_thm_2Earithmetic_2EADD__0,axiom,
! [X10] :
( mem(X10,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2E_2B,X10),c_2Enum_2E0) = X10 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EADD__0) ).
fof(mem_c_2Earithmetic_2E_2A,axiom,
mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Earithmetic_2E_2A) ).
fof(conj_thm_2Earithmetic_2EADD1,axiom,
! [X10] :
( mem(X10,ty_2Enum_2Enum)
=> ap(c_2Enum_2ESUC,X10) = ap(ap(c_2Earithmetic_2E_2B,X10),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EADD1) ).
fof(conj_thm_2Earithmetic_2EONE,axiom,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,c_2Enum_2E0),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EONE) ).
fof(mem_c_2Enum_2E0,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mem_c_2Enum_2E0) ).
fof(conj_thm_2Earithmetic_2ETWO,axiom,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2ETWO) ).
fof(conj_thm_2Earithmetic_2EODD__EXISTS,axiom,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EODD,X12))
<=> ? [X13] :
( mem(X13,ty_2Enum_2Enum)
& X12 = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X13)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EODD__EXISTS) ).
fof(conj_thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ( p(ap(c_2Earithmetic_2EEVEN,X12))
<=> ? [X13] :
( mem(X13,ty_2Enum_2Enum)
& X12 = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X13) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Earithmetic_2EEVEN__EXISTS) ).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X9] :
( ne(X9)
=> ! [X18] :
( mem(X18,X9)
=> ! [X19] :
( mem(X19,X9)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2ET),X18),X19) = X18
& ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2EF),X18),X19) = X19 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_thm_2Ebool_2ECOND__CLAUSES) ).
fof(ne_ty_2Enum_2Enum,axiom,
ne(ty_2Enum_2Enum),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ne_ty_2Enum_2Enum) ).
fof(c_0_33,plain,
! [X7,X8] :
( ( ~ p(X7)
| ~ p(X8)
| X7 = X8
| ~ mem(X8,bool)
| ~ mem(X7,bool) )
& ( p(X7)
| p(X8)
| X7 = X8
| ~ mem(X8,bool)
| ~ mem(X7,bool) ) ),
inference(distribute,[status(thm)],[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)],[boolext])])])])])]) ).
fof(c_0_34,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
p(c_2Ebool_2ET),
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
cnf(c_0_37,plain,
mem(c_2Ebool_2ET,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
cnf(c_0_38,plain,
( X1 = X2
| p(X2)
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_40,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_41,plain,
! [X5,X6,X7,X8] :
( ~ mem(X7,arr(X5,X6))
| ~ mem(X8,X5)
| mem(ap(X7,X8),X6) ),
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)],[ap_tp])])])])]) ).
cnf(c_0_42,plain,
( X1 = c_2Ebool_2ET
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_43,plain,
( X1 = c_2Ebool_2EF
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
( mem(ap(X1,X2),X3)
| ~ mem(X2,X4)
| ~ mem(X1,arr(X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
cnf(c_0_46,plain,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(split_conjunct,[status(thm)],[mem_c_2Emin_2E_3D_3D_3E]) ).
fof(c_0_47,plain,
! [X6] :
( ( ~ p(ap(c_2Ebool_2E_7E,X6))
| ~ p(X6)
| ~ mem(X6,bool) )
& ( p(X6)
| p(ap(c_2Ebool_2E_7E,X6))
| ~ mem(X6,bool) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax_neg_p])])])]) ).
cnf(c_0_48,plain,
( X1 = c_2Ebool_2ET
| X1 = c_2Ebool_2EF
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
( mem(ap(c_2Ebool_2E_7E,X1),bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( mem(ap(c_2Emin_2E_3D_3D_3E,X1),arr(bool,bool))
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_51,plain,
( p(ap(c_2Ebool_2E_7E,X1))
| p(X1)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2ET
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_53,plain,
! [X7,X8] :
( ( ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ p(X7)
| p(X8)
| ~ mem(X8,bool)
| ~ mem(X7,bool) )
& ( p(X7)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| ~ mem(X7,bool) )
& ( ~ p(X8)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| ~ mem(X7,bool) ) ),
inference(distribute,[status(thm)],[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)],[ax_imp_p])])])])])]) ).
cnf(c_0_54,plain,
( mem(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2),bool)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
fof(c_0_55,plain,
! [X25,X26,X28,X30] :
( ( mem(esk6_2(X25,X26),X25)
| ~ mem(X28,X25)
| ~ p(ap(X26,X28))
| ~ mem(X26,arr(X25,bool))
| ~ ne(X25) )
& ( p(ap(X26,esk6_2(X25,X26)))
| ~ mem(X28,X25)
| ~ p(ap(X26,X28))
| ~ mem(X26,arr(X25,bool))
| ~ ne(X25) )
& ( mem(esk7_2(X25,X26),X25)
| ~ mem(X30,X25)
| ~ p(ap(X26,X30))
| ~ mem(X26,arr(X25,bool))
| ~ ne(X25) )
& ( p(ap(X26,esk7_2(X25,X26)))
| ~ mem(X30,X25)
| ~ p(ap(X26,X30))
| ~ mem(X26,arr(X25,bool))
| ~ ne(X25) ) ),
inference(distribute,[status(thm)],[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)],[inference(fof_simplification,[status(thm)],[conj_thm_2Ebool_2ENOT__EXISTS__THM])])])])])])])]) ).
cnf(c_0_56,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2ET
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_40]) ).
cnf(c_0_57,plain,
( p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2) = c_2Ebool_2ET
| ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2) = c_2Ebool_2EF
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_59,plain,
( mem(esk7_2(X1,X2),X1)
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,X3))
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,plain,
ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_56]),c_0_39])]) ).
cnf(c_0_61,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2) = c_2Ebool_2ET
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40]) ).
cnf(c_0_62,plain,
( mem(esk7_2(X1,c_2Ebool_2E_7E),X1)
| ~ mem(c_2Ebool_2E_7E,arr(X1,bool))
| ~ mem(c_2Ebool_2EF,X1)
| ~ ne(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_36])]) ).
cnf(c_0_63,plain,
ne(bool),
inference(split_conjunct,[status(thm)],[bool_ne]) ).
cnf(c_0_64,plain,
mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Earithmetic_2EEVEN]) ).
fof(c_0_65,negated_conjecture,
~ ! [X12] :
( mem(X12,ty_2Enum_2Enum)
=> ap(ap(c_2Earithmetic_2EMOD,X12),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,X12)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ),
inference(assume_negation,[status(cth)],[conj_thm_2Earithmetic_2EMOD__2]) ).
fof(c_0_66,plain,
! [X10] :
( ~ ne(X10)
| mem(c_2Ebool_2E_21(X10),arr(arr(X10,bool),bool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2E_21])]) ).
cnf(c_0_67,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,X1),esk7_2(bool,c_2Ebool_2E_7E)) = c_2Ebool_2ET
| p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_45]),c_0_39]),c_0_63])]) ).
cnf(c_0_68,plain,
( mem(ap(c_2Earithmetic_2EEVEN,X1),bool)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_44,c_0_64]) ).
fof(c_0_69,negated_conjecture,
( mem(esk27_0,ty_2Enum_2Enum)
& ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])]) ).
cnf(c_0_70,plain,
( ~ mem(X1,bool)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_71,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_72,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,X1)),esk7_2(bool,c_2Ebool_2E_7E)) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EEVEN,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
mem(esk27_0,ty_2Enum_2Enum),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| ~ p(X1)
| ~ mem(ap(c_2Ebool_2E_7E,X1),bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_70,c_0_43]) ).
cnf(c_0_75,plain,
( mem(ap(c_2Ebool_2E_21(X1),X2),bool)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_71]) ).
cnf(c_0_76,plain,
( p(ap(X2,esk7_2(X1,X2)))
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,X3))
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_77,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,esk27_0)),esk7_2(bool,c_2Ebool_2E_7E)) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EEVEN,esk27_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
( esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET
| esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_62]),c_0_45]),c_0_39]),c_0_63])]) ).
cnf(c_0_79,plain,
( ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_36]),c_0_37])]) ).
cnf(c_0_80,plain,
mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Earithmetic_2EODD]) ).
cnf(c_0_81,plain,
( X1 = c_2Ebool_2EF
| X2 = X1
| ~ p(X2)
| ~ mem(X1,bool)
| ~ mem(X2,bool) ),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
fof(c_0_82,plain,
! [X6,X7,X8] :
( ( ~ p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X8,X6)
| p(ap(X7,X8))
| ~ mem(X7,arr(X6,bool))
| ~ ne(X6) )
& ( mem(esk3_2(X6,X7),X6)
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| ~ ne(X6) )
& ( ~ p(ap(X7,esk3_2(X6,X7)))
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| ~ ne(X6) ) ),
inference(distribute,[status(thm)],[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)],[ax_all_p])])])])])])]) ).
cnf(c_0_83,plain,
( ap(c_2Ebool_2E_21(X1),X2) = c_2Ebool_2ET
| ap(c_2Ebool_2E_21(X1),X2) = c_2Ebool_2EF
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_75]) ).
fof(c_0_84,plain,
! [X17,X18,X19,X20] :
( ~ mem(X17,ty_2Enum_2Enum)
| ~ mem(X18,ty_2Enum_2Enum)
| ~ mem(X19,ty_2Enum_2Enum)
| ~ mem(X20,ty_2Enum_2Enum)
| X18 != ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,X20),X17)),X19)
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,X19),X17))
| ap(ap(c_2Earithmetic_2EMOD,X18),X17) = X19 ),
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)],[conj_thm_2Earithmetic_2EMOD__UNIQUE])])])])]) ).
fof(c_0_85,plain,
! [X12,X13] :
( ~ mem(X12,ty_2Enum_2Enum)
| ~ mem(X13,ty_2Enum_2Enum)
| ap(ap(c_2Earithmetic_2E_2A,X12),X13) = ap(ap(c_2Earithmetic_2E_2A,X13),X12) ),
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)],[conj_thm_2Earithmetic_2EMULT__COMM])])])])]) ).
cnf(c_0_86,plain,
mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)),
inference(split_conjunct,[status(thm)],[mem_c_2Enum_2ESUC]) ).
fof(c_0_87,plain,
! [X12,X13] :
( ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,X12)),ap(c_2Enum_2ESUC,X13)))
| p(ap(ap(c_2Eprim__rec_2E_3C,X12),X13))
| ~ mem(X13,ty_2Enum_2Enum)
| ~ mem(X12,ty_2Enum_2Enum) )
& ( ~ p(ap(ap(c_2Eprim__rec_2E_3C,X12),X13))
| p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,X12)),ap(c_2Enum_2ESUC,X13)))
| ~ mem(X13,ty_2Enum_2Enum)
| ~ mem(X12,ty_2Enum_2Enum) ) ),
inference(distribute,[status(thm)],[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)],[conj_thm_2Earithmetic_2ELESS__MONO__EQ])])])])])]) ).
fof(c_0_88,plain,
! [X13] :
( ~ mem(X13,ty_2Enum_2Enum)
| p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eprim__rec_2ELESS__0])]) ).
fof(c_0_89,plain,
! [X13] :
( ( ~ p(ap(c_2Earithmetic_2EEVEN,X13))
| ~ p(ap(c_2Earithmetic_2EODD,X13))
| ~ mem(X13,ty_2Enum_2Enum) )
& ( p(ap(c_2Earithmetic_2EODD,X13))
| p(ap(c_2Earithmetic_2EEVEN,X13))
| ~ mem(X13,ty_2Enum_2Enum) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[conj_thm_2Earithmetic_2EEVEN__ODD])])])]) ).
cnf(c_0_90,plain,
( p(ap(c_2Ebool_2E_7E,esk7_2(X1,c_2Ebool_2E_7E)))
| ~ mem(c_2Ebool_2E_7E,arr(X1,bool))
| ~ mem(c_2Ebool_2EF,X1)
| ~ ne(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_60]),c_0_36])]) ).
cnf(c_0_91,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Ebool_2EF) = c_2Ebool_2ET
| esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EEVEN,esk27_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_92,plain,
ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_49]),c_0_37])]) ).
cnf(c_0_93,plain,
( mem(ap(c_2Earithmetic_2EODD,X1),bool)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_44,c_0_80]) ).
fof(c_0_94,plain,
! [X11] :
( ~ mem(X11,ty_2Enum_2Enum)
| ap(ap(c_2Earithmetic_2E_2B,X11),c_2Enum_2E0) = X11 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Earithmetic_2EADD__0])]) ).
cnf(c_0_95,plain,
mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))),
inference(split_conjunct,[status(thm)],[mem_c_2Earithmetic_2E_2A]) ).
cnf(c_0_96,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| X2 = ap(c_2Ebool_2E_7E,X1)
| ~ p(X2)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_81,c_0_49]) ).
cnf(c_0_97,plain,
( p(ap(X2,X3))
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_98,plain,
( ap(c_2Ebool_2E_21(X1),X2) = c_2Ebool_2ET
| c_2Ebool_2EF != c_2Ebool_2ET
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(ef,[status(thm)],[c_0_83]) ).
cnf(c_0_99,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),X2) = X3
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,X3),X2))
| X1 != ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,X4),X2)),X3)
| ~ mem(X4,ty_2Enum_2Enum)
| ~ mem(X3,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_100,plain,
( ap(ap(c_2Earithmetic_2E_2A,X1),X2) = ap(ap(c_2Earithmetic_2E_2A,X2),X1)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_101,plain,
! [X11] :
( ~ mem(X11,ty_2Enum_2Enum)
| ap(c_2Enum_2ESUC,X11) = ap(ap(c_2Earithmetic_2E_2B,X11),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Earithmetic_2EADD1])]) ).
cnf(c_0_102,plain,
( mem(ap(c_2Enum_2ESUC,X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_44,c_0_86]) ).
cnf(c_0_103,plain,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,c_2Enum_2E0),
inference(split_conjunct,[status(thm)],[conj_thm_2Earithmetic_2EONE]) ).
cnf(c_0_104,plain,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
inference(split_conjunct,[status(thm)],[mem_c_2Enum_2E0]) ).
cnf(c_0_105,plain,
( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,X1)),ap(c_2Enum_2ESUC,X2)))
| ~ mem(X1,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_106,plain,
( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,X1)))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_107,plain,
( ~ mem(X1,ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EODD,X1))
| ~ p(ap(c_2Earithmetic_2EEVEN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_108,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Ebool_2EF) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EEVEN,esk27_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_45]),c_0_39]),c_0_63])]),c_0_40]) ).
cnf(c_0_109,plain,
( X1 = ap(c_2Earithmetic_2EODD,X2)
| p(ap(c_2Earithmetic_2EODD,X2))
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X2,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_38,c_0_93]) ).
cnf(c_0_110,plain,
( ap(ap(c_2Earithmetic_2E_2B,X1),c_2Enum_2E0) = X1
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_111,plain,
( mem(ap(c_2Earithmetic_2E_2A,X1),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_44,c_0_95]) ).
cnf(c_0_112,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| X2 = ap(c_2Ebool_2E_7E,X1)
| X2 = c_2Ebool_2EF
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_96,c_0_43]) ).
cnf(c_0_113,plain,
( p(ap(X1,X2))
| c_2Ebool_2EF != c_2Ebool_2ET
| ~ mem(X1,arr(X3,bool))
| ~ mem(X2,X3)
| ~ ne(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_36])]) ).
cnf(c_0_114,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),X2) = X3
| X1 != ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,X2),X4)),X3)
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,X3),X2))
| ~ mem(X4,ty_2Enum_2Enum)
| ~ mem(X3,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_115,plain,
( ap(c_2Enum_2ESUC,X1) = ap(ap(c_2Earithmetic_2E_2B,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_116,plain,
mem(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)),ty_2Enum_2Enum),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104])]) ).
cnf(c_0_117,plain,
( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,X1)))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_103]),c_0_104])]) ).
cnf(c_0_118,plain,
ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),
inference(split_conjunct,[status(thm)],[conj_thm_2Earithmetic_2ETWO]) ).
cnf(c_0_119,plain,
p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_103]),c_0_104])]) ).
cnf(c_0_120,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Ebool_2EF) = c_2Ebool_2ET
| ~ p(ap(c_2Earithmetic_2EODD,esk27_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_73])]) ).
cnf(c_0_121,plain,
( ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2EF
| p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_39]),c_0_40]) ).
cnf(c_0_122,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),X2) = c_2Enum_2E0
| X1 != ap(ap(c_2Earithmetic_2E_2A,X3),X2)
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),X2))
| ~ mem(ap(ap(c_2Earithmetic_2E_2A,X3),X2),ty_2Enum_2Enum)
| ~ mem(X3,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_110]),c_0_104])]) ).
cnf(c_0_123,plain,
( mem(ap(ap(c_2Earithmetic_2E_2A,X1),X2),ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_44,c_0_111]) ).
cnf(c_0_124,plain,
( esk7_2(bool,c_2Ebool_2E_7E) = ap(c_2Ebool_2E_7E,X1)
| esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_62]),c_0_45]),c_0_39]),c_0_63])]) ).
cnf(c_0_125,plain,
( p(ap(c_2Ebool_2E_7E,X1))
| c_2Ebool_2EF != c_2Ebool_2ET
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_45]),c_0_63])]) ).
cnf(c_0_126,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),X2) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| X1 != ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,X2),X3))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))
| ~ mem(ap(ap(c_2Earithmetic_2E_2A,X2),X3),ty_2Enum_2Enum)
| ~ mem(X3,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_127,plain,
p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_116])]) ).
cnf(c_0_128,plain,
mem(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)),ty_2Enum_2Enum),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_118]),c_0_116])]) ).
fof(c_0_129,plain,
! [X14,X16] :
( ( mem(esk5_1(X14),ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EODD,X14))
| ~ mem(X14,ty_2Enum_2Enum) )
& ( X14 = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),esk5_1(X14)))
| ~ p(ap(c_2Earithmetic_2EODD,X14))
| ~ mem(X14,ty_2Enum_2Enum) )
& ( ~ mem(X16,ty_2Enum_2Enum)
| X14 != ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X16))
| p(ap(c_2Earithmetic_2EODD,X14))
| ~ mem(X14,ty_2Enum_2Enum) ) ),
inference(distribute,[status(thm)],[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)],[conj_thm_2Earithmetic_2EODD__EXISTS])])])])])])]) ).
cnf(c_0_130,plain,
( p(X2)
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_131,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Ebool_2EF) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_73])]) ).
cnf(c_0_132,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),X2) = c_2Enum_2E0
| X1 != ap(ap(c_2Earithmetic_2E_2A,X3),X2)
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),X2))
| ~ mem(X3,ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_133,plain,
p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_118]),c_0_116])]) ).
cnf(c_0_134,plain,
( esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_7E,ap(c_2Ebool_2E_7E,X1)))
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_124]),c_0_45]),c_0_39]),c_0_63])]) ).
cnf(c_0_135,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_92]),c_0_37])]),c_0_40]) ).
cnf(c_0_136,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| X1 != ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2))
| ~ mem(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2),ty_2Enum_2Enum)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]) ).
cnf(c_0_137,plain,
( X1 = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),esk5_1(X1)))
| ~ mem(X1,ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EODD,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_138,negated_conjecture,
( ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| ~ p(ap(c_2Earithmetic_2EEVEN,esk27_0))
| ~ mem(ap(c_2Earithmetic_2EEVEN,esk27_0),bool) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_36]),c_0_39])]),c_0_40]) ).
cnf(c_0_139,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| X1 != ap(ap(c_2Earithmetic_2E_2A,X2),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_128])]) ).
fof(c_0_140,plain,
! [X14,X16] :
( ( mem(esk4_1(X14),ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EEVEN,X14))
| ~ mem(X14,ty_2Enum_2Enum) )
& ( X14 = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),esk4_1(X14))
| ~ p(ap(c_2Earithmetic_2EEVEN,X14))
| ~ mem(X14,ty_2Enum_2Enum) )
& ( ~ mem(X16,ty_2Enum_2Enum)
| X14 != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X16)
| p(ap(c_2Earithmetic_2EEVEN,X14))
| ~ mem(X14,ty_2Enum_2Enum) ) ),
inference(distribute,[status(thm)],[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)],[conj_thm_2Earithmetic_2EEVEN__EXISTS])])])])])])]) ).
cnf(c_0_141,plain,
( p(ap(c_2Earithmetic_2EEVEN,X1))
| p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_142,plain,
( ap(c_2Earithmetic_2EEVEN,X1) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EEVEN,X1) = c_2Ebool_2EF
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_48,c_0_68]) ).
cnf(c_0_143,plain,
esk7_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_39]),c_0_60]),c_0_60]),c_0_92]),c_0_135]),c_0_40]) ).
cnf(c_0_144,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ~ p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),esk5_1(X1)),ty_2Enum_2Enum)
| ~ mem(esk5_1(X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137])]) ).
cnf(c_0_145,negated_conjecture,
( ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| ap(c_2Earithmetic_2EEVEN,esk27_0) = c_2Ebool_2EF
| ~ mem(ap(c_2Earithmetic_2EEVEN,esk27_0),bool) ),
inference(spm,[status(thm)],[c_0_138,c_0_43]) ).
cnf(c_0_146,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| X1 != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2)
| ~ mem(X2,ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_100]),c_0_128])]) ).
cnf(c_0_147,plain,
( X1 = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),esk4_1(X1))
| ~ mem(X1,ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EEVEN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_148,plain,
( ap(c_2Earithmetic_2EEVEN,X1) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_40]) ).
cnf(c_0_149,plain,
( ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2EF
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_48,c_0_93]) ).
cnf(c_0_150,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,X1)),c_2Ebool_2EF) = c_2Ebool_2ET
| p(ap(c_2Earithmetic_2EEVEN,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(rw,[status(thm)],[c_0_72,c_0_143]) ).
cnf(c_0_151,negated_conjecture,
ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_152,plain,
! [X20,X21,X22] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X20),c_2Ebool_2ET),X21),X22) = X21
| ~ mem(X22,X20)
| ~ mem(X21,X20)
| ~ ne(X20) )
& ( ap(ap(ap(c_2Ebool_2ECOND(X20),c_2Ebool_2EF),X21),X22) = X22
| ~ mem(X22,X20)
| ~ mem(X21,X20)
| ~ ne(X20) ) ),
inference(distribute,[status(thm)],[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)],[conj_thm_2Ebool_2ECOND__CLAUSES])])])])])]) ).
cnf(c_0_153,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ~ p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(esk5_1(X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_123]),c_0_128])]) ).
cnf(c_0_154,plain,
( mem(esk5_1(X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EODD,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_155,negated_conjecture,
( ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| ap(c_2Earithmetic_2EEVEN,esk27_0) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_68]),c_0_73])]) ).
cnf(c_0_156,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| ~ p(ap(c_2Earithmetic_2EEVEN,X1))
| ~ mem(esk4_1(X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147])]) ).
cnf(c_0_157,plain,
( mem(esk4_1(X1),ty_2Enum_2Enum)
| ~ mem(X1,ty_2Enum_2Enum)
| ~ p(ap(c_2Earithmetic_2EEVEN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_158,plain,
( ap(c_2Earithmetic_2EEVEN,X1) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2ET
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_40]) ).
cnf(c_0_159,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,X1)),c_2Ebool_2EF) = c_2Ebool_2ET
| ~ p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_107,c_0_150]) ).
cnf(c_0_160,negated_conjecture,
( ap(c_2Earithmetic_2EEVEN,esk27_0) = c_2Ebool_2ET
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),c_2Ebool_2EF),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) != ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_142]),c_0_73])]) ).
cnf(c_0_161,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2EF),X2),X3) = X3
| ~ ne(X1)
| ~ mem(X2,X1)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_162,plain,
ne(ty_2Enum_2Enum),
inference(split_conjunct,[status(thm)],[ne_ty_2Enum_2Enum]) ).
cnf(c_0_163,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ~ p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_164,negated_conjecture,
( ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| p(ap(c_2Earithmetic_2EODD,esk27_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_155]),c_0_73])]),c_0_40]) ).
cnf(c_0_165,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| ~ p(ap(c_2Earithmetic_2EEVEN,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,negated_conjecture,
( ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_158]),c_0_73])]) ).
cnf(c_0_167,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Earithmetic_2EEVEN,X1)),c_2Ebool_2EF) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2EF
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_159,c_0_121]) ).
cnf(c_0_168,negated_conjecture,
( ap(c_2Earithmetic_2EEVEN,esk27_0) = c_2Ebool_2ET
| ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_116]),c_0_104]),c_0_162])]) ).
cnf(c_0_169,negated_conjecture,
( ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_73])]) ).
cnf(c_0_170,plain,
( ap(ap(c_2Earithmetic_2EMOD,X1),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| p(ap(c_2Earithmetic_2EODD,X1))
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(spm,[status(thm)],[c_0_165,c_0_141]) ).
cnf(c_0_171,negated_conjecture,
( ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_166]),c_0_36]),c_0_39]),c_0_37])]),c_0_40]) ).
cnf(c_0_172,plain,
( ap(c_2Earithmetic_2EODD,X1) = c_2Ebool_2EF
| ~ p(ap(c_2Earithmetic_2EEVEN,X1))
| ~ mem(ap(c_2Earithmetic_2EEVEN,X1),bool)
| ~ mem(X1,ty_2Enum_2Enum) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_167]),c_0_36]),c_0_39])]),c_0_40]) ).
cnf(c_0_173,negated_conjecture,
( ap(c_2Earithmetic_2EEVEN,esk27_0) = c_2Ebool_2ET
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_174,negated_conjecture,
( ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0
| ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_73])]),c_0_40]) ).
cnf(c_0_175,negated_conjecture,
ap(c_2Earithmetic_2EODD,esk27_0) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_36]),c_0_37]),c_0_73])]) ).
cnf(c_0_176,negated_conjecture,
ap(ap(c_2Earithmetic_2EMOD,esk27_0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_175]),c_0_135]) ).
cnf(c_0_177,negated_conjecture,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,esk27_0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) != c_2Enum_2E0,
inference(rw,[status(thm)],[c_0_151,c_0_176]) ).
cnf(c_0_178,negated_conjecture,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),c_2Ebool_2ET),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) != c_2Enum_2E0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_158]),c_0_175]),c_0_73])]),c_0_135]) ).
cnf(c_0_179,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2ET),X2),X3) = X2
| ~ ne(X1)
| ~ mem(X2,X1)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_180,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_116]),c_0_104]),c_0_162])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP003+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n026.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 : Fri Jun 3 12:07:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.40/23.42 eprover: CPU time limit exceeded, terminating
% 0.40/23.42 eprover: CPU time limit exceeded, terminating
% 0.40/23.44 eprover: CPU time limit exceeded, terminating
% 0.40/23.45 eprover: CPU time limit exceeded, terminating
% 0.56/46.44 eprover: CPU time limit exceeded, terminating
% 0.56/46.46 eprover: CPU time limit exceeded, terminating
% 0.56/46.46 eprover: CPU time limit exceeded, terminating
% 0.56/46.46 eprover: CPU time limit exceeded, terminating
% 0.72/69.45 eprover: CPU time limit exceeded, terminating
% 0.72/69.47 eprover: CPU time limit exceeded, terminating
% 0.72/69.48 eprover: CPU time limit exceeded, terminating
% 0.72/69.51 eprover: CPU time limit exceeded, terminating
% 0.88/92.47 eprover: CPU time limit exceeded, terminating
% 0.88/92.49 eprover: CPU time limit exceeded, terminating
% 0.88/92.52 eprover: CPU time limit exceeded, terminating
% 0.88/92.53 eprover: CPU time limit exceeded, terminating
% 1.04/115.48 eprover: CPU time limit exceeded, terminating
% 1.04/115.53 eprover: CPU time limit exceeded, terminating
% 1.04/115.53 eprover: CPU time limit exceeded, terminating
% 1.04/115.55 eprover: CPU time limit exceeded, terminating
% 1.20/138.50 eprover: CPU time limit exceeded, terminating
% 1.20/138.55 eprover: CPU time limit exceeded, terminating
% 1.20/138.57 eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 1.20/138.57
% 1.36/161.52 eprover: CPU time limit exceeded, terminating
% 1.36/161.56 eprover: CPU time limit exceeded, terminating
% 1.36/161.58 eprover: CPU time limit exceeded, terminating
% 1.36/161.59 eprover: CPU time limit exceeded, terminating
% 1.52/184.54 eprover: CPU time limit exceeded, terminating
% 1.52/184.58 eprover: CPU time limit exceeded, terminating
% 1.52/184.60 eprover: CPU time limit exceeded, terminating
% 1.52/184.61 eprover: CPU time limit exceeded, terminating
% 1.67/207.56 eprover: CPU time limit exceeded, terminating
% 1.67/207.59 eprover: CPU time limit exceeded, terminating
% 1.67/207.61 eprover: CPU time limit exceeded, terminating
% 1.67/207.62 eprover: CPU time limit exceeded, terminating
% 1.73/216.88 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 1.73/216.88 # Preprocessing time : 0.032 s
% 1.73/216.88 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # Preprocessing time : 0.034 s
% 1.73/216.88 # Running protocol protocol_eprover_eb48853eb71ccd2a6fdade56c25b63f5692e1a0c for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # Preprocessing time : 0.032 s
% 1.73/216.88 # Running protocol protocol_eprover_761a0d093d9701c0eed884aebb46468e8d439c31 for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,hypos,1.2,,,100,1.0)
% 1.73/216.88 # Preprocessing time : 0.035 s
% 1.73/216.88 # Running protocol protocol_eprover_bb5e3cecdbc7660bd3a6f864cadb7769d8aea26a for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,,500,1.0)
% 1.73/216.88 # Preprocessing time : 0.032 s
% 1.73/216.88 # Running protocol protocol_eprover_e252f7803940d118fa0ef69fc2319cb55aee23b9 for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,,1.4,,03,100,1.0)
% 1.73/216.88 # Preprocessing time : 0.019 s
% 1.73/216.88 # Running protocol protocol_eprover_b1d72019af42f5b571a6c0b233a5b6d1de064075 for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,500,1.0)
% 1.73/216.88 # Preprocessing time : 0.034 s
% 1.73/216.88 # Running protocol protocol_eprover_e96ef4641ae500918cdd95fcfce21e29f2ac5eec for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,,6.0,,03,100,1.0)
% 1.73/216.88 # Preprocessing time : 0.043 s
% 1.73/216.88 # Running protocol protocol_eprover_1f734394cb6ce69b36c9826f6782d3567d6ecd6c for 23 seconds:
% 1.73/216.88
% 1.73/216.88 # Failure: Resource limit exceeded (time)
% 1.73/216.88 # OLD status Res
% 1.73/216.88 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,02,20000,1.0)
% 1.73/216.88 # Preprocessing time : 0.033 s
% 1.73/216.88 # Running protocol protocol_eprover_e9eb28a402764e1f99b41605245cd0a359f475fb for 23 seconds:
% 1.73/216.88 # Preprocessing time : 0.035 s
% 1.73/216.88
% 1.73/216.88 # Proof found!
% 1.73/216.88 # SZS status Theorem
% 1.73/216.88 # SZS output start CNFRefutation
% See solution above
% 1.73/216.88 # Proof object total steps : 181
% 1.73/216.88 # Proof object clause steps : 128
% 1.73/216.88 # Proof object formula steps : 53
% 1.73/216.88 # Proof object conjectures : 26
% 1.73/216.88 # Proof object clause conjectures : 23
% 1.73/216.88 # Proof object formula conjectures : 3
% 1.73/216.88 # Proof object initial clauses used : 42
% 1.73/216.88 # Proof object initial formulas used : 33
% 1.73/216.88 # Proof object generating inferences : 83
% 1.73/216.88 # Proof object simplifying inferences : 130
% 1.73/216.88 # Training examples: 0 positive, 0 negative
% 1.73/216.88 # Parsed axioms : 98
% 1.73/216.88 # Removed by relevancy pruning/SinE : 0
% 1.73/216.88 # Initial clauses : 399
% 1.73/216.88 # Removed in clause preprocessing : 231
% 1.73/216.88 # Initial clauses in saturation : 168
% 1.73/216.88 # Processed clauses : 45128
% 1.73/216.88 # ...of these trivial : 557
% 1.73/216.88 # ...subsumed : 39730
% 1.73/216.88 # ...remaining for further processing : 4841
% 1.73/216.88 # Other redundant clauses eliminated : 19
% 1.73/216.88 # Clauses deleted for lack of memory : 213831
% 1.73/216.88 # Backward-subsumed : 925
% 1.73/216.88 # Backward-rewritten : 1037
% 1.73/216.88 # Generated clauses : 399917
% 1.73/216.88 # ...of the previous two non-trivial : 367433
% 1.73/216.88 # Contextual simplify-reflections : 0
% 1.73/216.88 # Paramodulations : 399754
% 1.73/216.88 # Factorizations : 59
% 1.73/216.88 # Equation resolutions : 92
% 1.73/216.88 # Current number of processed clauses : 2874
% 1.73/216.88 # Positive orientable unit clauses : 65
% 1.73/216.88 # Positive unorientable unit clauses: 0
% 1.73/216.88 # Negative unit clauses : 8
% 1.73/216.88 # Non-unit-clauses : 2801
% 1.73/216.88 # Current number of unprocessed clauses: 37449
% 1.73/216.88 # ...number of literals in the above : 197087
% 1.73/216.88 # Current number of archived formulas : 0
% 1.73/216.89 # Current number of archived clauses : 1962
% 1.73/216.89 # Clause-clause subsumption calls (NU) : 12153501
% 1.73/216.89 # Rec. Clause-clause subsumption calls : 801581
% 1.73/216.89 # Non-unit clause-clause subsumptions : 39273
% 1.73/216.89 # Unit Clause-clause subsumption calls : 29686
% 1.73/216.89 # Rewrite failures with RHS unbound : 0
% 1.73/216.89 # BW rewrite match attempts : 450
% 1.73/216.89 # BW rewrite match successes : 16
% 1.73/216.89 # Condensation attempts : 0
% 1.73/216.89 # Condensation successes : 0
% 1.73/216.89 # Termbank termtop insertions : 18682997
% 1.73/216.89
% 1.73/216.89 # -------------------------------------------------
% 1.73/216.89 # User time : 9.067 s
% 1.73/216.89 # System time : 0.127 s
% 1.73/216.89 # Total time : 9.194 s
% 1.73/216.89 # Maximum resident set size: 140468 pages
% 1.73/230.61 eprover: CPU time limit exceeded, terminating
% 1.73/230.63 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.73/230.63 eprover: No such file or directory
% 1.73/230.63 eprover: CPU time limit exceeded, terminating
% 1.73/230.63 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.73/230.63 eprover: No such file or directory
% 1.73/230.65 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.73/230.65 eprover: No such file or directory
% 1.73/230.65 eprover: CPU time limit exceeded, terminating
% 1.73/230.65 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.73/230.65 eprover: No such file or directory
% 1.73/230.67 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.73/230.67 eprover: No such file or directory
% 1.73/230.67 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.73/230.67 eprover: No such file or directory
%------------------------------------------------------------------------------