%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP012+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:53:37 PM UTC 2026
% Result : Theorem 0.95s 0.78s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 30 unt; 0 def)
% Number of atoms : 276 ( 39 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 325 ( 135 ~; 147 |; 12 &)
% ( 8 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
! [X24] :
( mem(X24,ty_2Einteger_2Eint)
=> ! [X25] :
( mem(X25,ty_2Einteger_2Eint)
=> ! [X26] :
( mem(X26,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),X25))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),ap(ap(c_2Einteger_2Eint__sub,X26),X25)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,X24),X26)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RSUB) ).
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(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(mem_c_2Einteger_2Eint__divides,axiom,
mem(c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__divides) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(mem_c_2Einteger_2Eint__sub,axiom,
mem(c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__sub) ).
fof(conj_thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
! [X24] :
( mem(X24,ty_2Einteger_2Eint)
=> ! [X25] :
( mem(X25,ty_2Einteger_2Eint)
=> ! [X26] :
( mem(X26,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),X25))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),ap(ap(c_2Einteger_2Eint__add,X26),X25)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,X24),X26)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RADD) ).
fof(ax_thm_2Einteger_2Eint__sub,axiom,
! [X22] :
( mem(X22,ty_2Einteger_2Eint)
=> ! [X23] :
( mem(X23,ty_2Einteger_2Eint)
=> ap(ap(c_2Einteger_2Eint__sub,X22),X23) = ap(ap(c_2Einteger_2Eint__add,X22),ap(c_2Einteger_2Eint__neg,X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Einteger_2Eint__sub) ).
fof(mem_c_2Einteger_2Eint__neg,axiom,
mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Einteger_2Eint__neg) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
fof(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
! [X24] :
( mem(X24,ty_2Einteger_2Eint)
=> ! [X25] :
( mem(X25,ty_2Einteger_2Eint)
=> ( ( p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X24)),X25))
<=> p(ap(ap(c_2Einteger_2Eint__divides,X24),X25)) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,X24),ap(c_2Einteger_2Eint__neg,X25)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,X24),X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__NEG) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
fof(ax_neg_p,axiom,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
fof(c_0_15,negated_conjecture,
~ ! [X24] :
( mem(X24,ty_2Einteger_2Eint)
=> ! [X25] :
( mem(X25,ty_2Einteger_2Eint)
=> ! [X26] :
( mem(X26,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),X25))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,X24),ap(ap(c_2Einteger_2Eint__sub,X26),X25)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,X24),X26)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Einteger_2EINT__DIVIDES__RSUB]) ).
fof(c_0_16,plain,
! [X29,X30,X31,X32] :
( mem(ap(X31,X32),X30)
| ~ mem(X32,X29)
| ~ mem(X31,arr(X29,X30)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
fof(c_0_17,plain,
! [X33,X34] :
( ( ~ mem(X33,bool)
| ~ mem(X34,bool)
| X33 = X34
| p(X34)
| p(X33) )
& ( ~ mem(X33,bool)
| ~ mem(X34,bool)
| X33 = X34
| ~ p(X34)
| ~ p(X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])])]) ).
fof(c_0_18,negated_conjecture,
( ( p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0))) )
& ( ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0))) )
& p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk10_0))
& mem(esk11_0,ty_2Einteger_2Eint)
& mem(esk10_0,ty_2Einteger_2Eint)
& mem(esk9_0,ty_2Einteger_2Eint) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_19,plain,
( ~ mem(X4,X2)
| ~ mem(X1,arr(X2,X3))
| mem(ap(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
mem(c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__divides]) ).
fof(c_0_21,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
cnf(c_0_22,plain,
( ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| mem(ap(c_2Einteger_2Eint__divides,X1),arr(ty_2Einteger_2Eint,bool)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
~ p(c_2Ebool_2EF),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( ~ mem(X1,bool)
| ~ mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| ~ p(X1)
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| X1 = ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__divides,X1),X2),bool) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
mem(esk9_0,ty_2Einteger_2Eint),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( ~ mem(X1,bool)
| ~ mem(X2,bool)
| X1 = X2
| p(X2)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_31,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( ~ mem(X1,bool)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| ~ p(X1)
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| X1 = ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_33,plain,
( ~ mem(X1,bool)
| p(X1)
| X1 = c_2Ebool_2EF ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( ~ mem(X1,bool)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| X1 = c_2Ebool_2EF
| X1 = ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
mem(c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__sub]) ).
cnf(c_0_36,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_37,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| mem(ap(c_2Einteger_2Eint__sub,X1),arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
fof(c_0_38,plain,
! [X93,X94,X95] :
( ( ~ mem(X93,ty_2Einteger_2Eint)
| ~ mem(X94,ty_2Einteger_2Eint)
| ~ mem(X95,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X93),X94))
| p(ap(ap(c_2Einteger_2Eint__divides,X93),ap(ap(c_2Einteger_2Eint__add,X95),X94)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X93),X95)) )
& ( ~ mem(X93,ty_2Einteger_2Eint)
| ~ mem(X94,ty_2Einteger_2Eint)
| ~ mem(X95,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X93),X94))
| p(ap(ap(c_2Einteger_2Eint__divides,X93),X95))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X93),ap(ap(c_2Einteger_2Eint__add,X95),X94))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__RADD])])])])]) ).
fof(c_0_39,plain,
! [X91,X92] :
( ap(ap(c_2Einteger_2Eint__sub,X91),X92) = ap(ap(c_2Einteger_2Eint__add,X91),ap(c_2Einteger_2Eint__neg,X92))
| ~ mem(X92,ty_2Einteger_2Eint)
| ~ mem(X91,ty_2Einteger_2Eint) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Einteger_2Eint__sub])])])]) ).
cnf(c_0_40,plain,
mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__neg]) ).
cnf(c_0_41,plain,
p(c_2Ebool_2ET),
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
cnf(c_0_42,plain,
mem(c_2Ebool_2ET,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
cnf(c_0_43,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X1),X2))
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_44,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__sub,X1),X2),ty_2Einteger_2Eint) ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
mem(esk10_0,ty_2Einteger_2Eint),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,negated_conjecture,
mem(esk11_0,ty_2Einteger_2Eint),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_47,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X3,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),X3))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),X2))
| p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(ap(c_2Einteger_2Eint__add,X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,plain,
( ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__sub,X1),X2) = ap(ap(c_2Einteger_2Eint__add,X1),ap(c_2Einteger_2Eint__neg,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| mem(ap(c_2Einteger_2Eint__neg,X1),ty_2Einteger_2Eint) ),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_50,plain,
( ~ mem(X1,bool)
| ~ p(X1)
| X1 = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_42])]) ).
cnf(c_0_51,negated_conjecture,
p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X1),X2))
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_53,negated_conjecture,
( ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,plain,
( ~ mem(X3,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),X2))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Einteger_2Eint__neg,X3)))
| p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(ap(c_2Einteger_2Eint__sub,X2),X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
fof(c_0_55,plain,
! [X96,X97] :
( ( ~ mem(X96,ty_2Einteger_2Eint)
| ~ mem(X97,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X96)),X97))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X96),X97)) )
& ( ~ mem(X96,ty_2Einteger_2Eint)
| ~ mem(X97,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X96),X97))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X96)),X97)) )
& ( ~ mem(X96,ty_2Einteger_2Eint)
| ~ mem(X97,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X96),ap(c_2Einteger_2Eint__neg,X97)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X96),X97)) )
& ( ~ mem(X96,ty_2Einteger_2Eint)
| ~ mem(X97,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X96),X97))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X96),ap(c_2Einteger_2Eint__neg,X97))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG])])])])]) ).
cnf(c_0_56,negated_conjecture,
( ~ mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk10_0),bool)
| ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk10_0) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| p(ap(ap(c_2Einteger_2Eint__divides,X1),esk11_0))
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,X1),esk11_0) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_58,negated_conjecture,
( ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(c_2Einteger_2Eint__neg,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46]),c_0_28]),c_0_45])]) ).
cnf(c_0_59,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),X2))
| p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Einteger_2Eint__neg,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk10_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_27]),c_0_45]),c_0_28])]) ).
cnf(c_0_61,negated_conjecture,
( p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_57,c_0_28]) ).
cnf(c_0_62,negated_conjecture,
~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0)),
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_58,c_0_59]),c_0_60]),c_0_41]),c_0_45]),c_0_28])]) ).
cnf(c_0_63,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
cnf(c_0_64,negated_conjecture,
ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0) = c_2Ebool_2EF,
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_65,plain,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
inference(fof_simplification,[status(thm)],[ax_neg_p]) ).
cnf(c_0_66,plain,
( ~ mem(X1,bool)
| X1 = c_2Ebool_2ET
| X1 = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_67,plain,
( ~ mem(X1,bool)
| mem(ap(c_2Ebool_2E_7E,X1),bool) ),
inference(spm,[status(thm)],[c_0_19,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_64]),c_0_31]) ).
fof(c_0_69,plain,
! [X56] :
( ( ~ mem(X56,bool)
| p(ap(c_2Ebool_2E_7E,X56))
| p(X56) )
& ( ~ mem(X56,bool)
| ~ p(X56)
| ~ p(ap(c_2Ebool_2E_7E,X56)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
cnf(c_0_70,plain,
( ~ mem(X1,bool)
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0),ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_27,c_0_68]) ).
cnf(c_0_72,plain,
( ~ mem(X1,bool)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_73,plain,
( ~ mem(X1,bool)
| c_2Ebool_2EF != c_2Ebool_2ET
| ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2ET ),
inference(ef,[status(thm)],[c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| ap(ap(c_2Einteger_2Eint__divides,X1),X2) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_75,plain,
( ~ mem(X1,bool)
| ~ p(X1)
| c_2Ebool_2EF != c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_41])]) ).
cnf(c_0_76,negated_conjecture,
( ~ mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),esk11_0))
| ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_77,negated_conjecture,
( ~ mem(X1,ty_2Einteger_2Eint)
| mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| ap(ap(c_2Einteger_2Eint__divides,X1),esk10_0) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_74,c_0_45]) ).
cnf(c_0_78,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_41]),c_0_42])]) ).
cnf(c_0_79,plain,
( ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X3,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),X3))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(ap(c_2Einteger_2Eint__add,X2),X3)))
| p(ap(ap(c_2Einteger_2Eint__divides,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_80,negated_conjecture,
( ~ mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool)
| ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) = c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_64]),c_0_31]) ).
cnf(c_0_81,negated_conjecture,
mem(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)),bool),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_28]),c_0_60]),c_0_78]) ).
cnf(c_0_82,plain,
( ~ mem(X3,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Einteger_2Eint__neg,X3)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X1),ap(ap(c_2Einteger_2Eint__sub,X2),X3)))
| p(ap(ap(c_2Einteger_2Eint__divides,X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_48]),c_0_49]) ).
cnf(c_0_83,negated_conjecture,
ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(ap(c_2Einteger_2Eint__sub,esk11_0),esk10_0)) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_84,negated_conjecture,
~ p(ap(ap(c_2Einteger_2Eint__divides,esk9_0),ap(c_2Einteger_2Eint__neg,esk10_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_64]),c_0_41]),c_0_46]),c_0_28]),c_0_45])]),c_0_31]) ).
cnf(c_0_85,negated_conjecture,
$false,
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_84,c_0_59]),c_0_60]),c_0_41]),c_0_45]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP012+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 21:45:40 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.95/0.78 % Version: 3.5.1
% 0.95/0.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.95/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.95/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.95/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.95/0.78 % Starting sh5l with 300s (1) cores
% 0.95/0.78 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 214810 completed with status 0
% 0.95/0.78 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.95/0.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.95/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.95/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.95/0.78 % No SInE strategy applied
% 0.95/0.78 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.95/0.78 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.95/0.78 % Starting SubtermCWHack with 151s (1) cores
% 0.95/0.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.95/0.78 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.95/0.78 % Starting G-E--_302_C18_F1_URBAN_S0Y with 151s (1) cores
% 0.95/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 146s (1) cores
% 0.95/0.78 % G-E--_302_C18_F1_URBAN_S0Y with pid 214817 completed with status 0
% 0.95/0.78 % Result found by G-E--_302_C18_F1_URBAN_S0Y
% 0.95/0.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.95/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.95/0.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.95/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.95/0.78 % No SInE strategy applied
% 0.95/0.78 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.95/0.78 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.95/0.78 % Starting SubtermCWHack with 151s (1) cores
% 0.95/0.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.95/0.78 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.95/0.78 % Starting G-E--_302_C18_F1_URBAN_S0Y with 151s (1) cores
% 0.95/0.78 % Preprocessing time : 0.005 s
% 0.95/0.78
% 0.95/0.78 % Proof found!
% 0.95/0.78 % SZS status Theorem
% 0.95/0.78 % SZS output start CNFRefutation
% See solution above
% 0.95/0.78 % Parsed axioms : 57
% 0.95/0.78 % Removed by relevancy pruning/SinE : 0
% 0.95/0.78 % Initial clauses : 352
% 0.95/0.78 % Removed in clause preprocessing : 249
% 0.95/0.78 % Initial clauses in saturation : 103
% 0.95/0.78 % Processed clauses : 649
% 0.95/0.78 % ...of these trivial : 4
% 0.95/0.78 % ...subsumed : 194
% 0.95/0.78 % ...remaining for further processing : 451
% 0.95/0.78 % Other redundant clauses eliminated : 3
% 0.95/0.78 % Clauses deleted for lack of memory : 0
% 0.95/0.78 % Backward-subsumed : 30
% 0.95/0.78 % Backward-rewritten : 54
% 0.95/0.78 % Generated clauses : 5233
% 0.95/0.78 % ...of the previous two non-redundant : 4921
% 0.95/0.78 % ...aggressively subsumed : 0
% 0.95/0.78 % Contextual simplify-reflections : 29
% 0.95/0.78 % Paramodulations : 5203
% 0.95/0.78 % Factorizations : 24
% 0.95/0.78 % NegExts : 0
% 0.95/0.78 % Equation resolutions : 4
% 0.95/0.78 % Disequality decompositions : 0
% 0.95/0.78 % Total rewrite steps : 1963
% 0.95/0.78 % ...of those cached : 1942
% 0.95/0.78 % Propositional unsat checks : 0
% 0.95/0.78 % Propositional check models : 0
% 0.95/0.78 % Propositional check unsatisfiable : 0
% 0.95/0.78 % Propositional clauses : 0
% 0.95/0.78 % Propositional clauses after purity: 0
% 0.95/0.78 % Propositional unsat core size : 0
% 0.95/0.78 % Propositional preprocessing time : 0.000
% 0.95/0.78 % Propositional encoding time : 0.000
% 0.95/0.78 % Propositional solver time : 0.000
% 0.95/0.78 % Success case prop preproc time : 0.000
% 0.95/0.78 % Success case prop encoding time : 0.000
% 0.95/0.78 % Success case prop solver time : 0.000
% 0.95/0.78 % Current number of processed clauses : 364
% 0.95/0.78 % Positive orientable unit clauses : 24
% 0.95/0.78 % Positive unorientable unit clauses: 0
% 0.95/0.78 % Negative unit clauses : 3
% 0.95/0.78 % Non-unit-clauses : 337
% 0.95/0.78 % Current number of unprocessed clauses: 4232
% 0.95/0.78 % ...number of literals in the above : 29970
% 0.95/0.78 % Current number of archived formulas : 0
% 0.95/0.78 % Current number of archived clauses : 86
% 0.95/0.78 % Clause-clause subsumption calls (NU) : 19986
% 0.95/0.78 % Rec. Clause-clause subsumption calls : 2924
% 0.95/0.78 % Non-unit clause-clause subsumptions : 206
% 0.95/0.78 % Unit Clause-clause subsumption calls : 421
% 0.95/0.78 % Rewrite failures with RHS unbound : 0
% 0.95/0.78 % BW rewrite match attempts : 17
% 0.95/0.78 % BW rewrite match successes : 9
% 0.95/0.78 % Condensation attempts : 0
% 0.95/0.78 % Condensation successes : 0
% 0.95/0.78 % Termbank termtop insertions : 176618
% 0.95/0.78 % Search garbage collected termcells : 4095
% 0.95/0.78
% 0.95/0.78 % -------------------------------------------------
% 0.95/0.78 % User time : 0.206 s
% 0.95/0.78 % System time : 0.010 s
% 0.95/0.78 % Total time : 0.216 s
% 0.95/0.78 % Maximum resident set size: 4440 pages
% 0.95/0.78
% 0.95/0.78 % -------------------------------------------------
% 0.95/0.78 % User time : 0.951 s
% 0.95/0.78 % System time : 0.043 s
% 0.95/0.78 % Total time : 0.994 s
% 0.95/0.78 % Maximum resident set size: 4864 pages
% 0.95/0.78 % E exiting
%------------------------------------------------------------------------------