%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP012^5 : 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 : n006.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 : Wed Sep 30 08:05:12 AM UTC 2026
% Result : Theorem 56.92s 13.84s
% Output : CNFRefutation 56.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 753 ( 31 ~; 29 |; 7 &; 675 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_sort2,type,
tp__ty_2Einteger_2Eint: $tType ).
thf(decl_25,type,
arr: del > del > del ).
thf(decl_26,type,
mem: $i > del > $o ).
thf(decl_27,type,
ap: $i > $i > $i ).
thf(decl_29,type,
p: $i > $o ).
thf(decl_1314,type,
ty_2Einteger_2Eint: del ).
thf(decl_1315,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
thf(decl_1316,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
thf(decl_1335,type,
c_2Einteger_2Eint__divides: $i ).
thf(decl_1350,type,
c_2Einteger_2Eint__neg: $i ).
thf(decl_1358,type,
c_2Einteger_2Eint__sub: $i ).
thf(decl_1378,type,
esk1_0: tp__ty_2Einteger_2Eint ).
thf(decl_1379,type,
esk2_0: tp__ty_2Einteger_2Eint ).
thf(decl_1380,type,
esk3_0: tp__ty_2Einteger_2Eint ).
thf(ap_tp,axiom,
! [X3: del,X4: del,X5: $i] :
( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ X3 )
=> ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',ap_tp) ).
thf(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/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',mem_c_2Einteger_2Eint__sub) ).
thf(stp_inj_mem_ty_2Einteger_2Eint,axiom,
! [X17556: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X17556 ) @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',stp_inj_mem_ty_2Einteger_2Eint) ).
thf(mem_c_2Einteger_2Eint__neg,axiom,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',mem_c_2Einteger_2Eint__neg) ).
thf(stp_iso_mem_ty_2Einteger_2Eint,axiom,
! [X17557: $i] :
( ( mem @ X17557 @ ty_2Einteger_2Eint )
=> ( X17557
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X17557 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',stp_iso_mem_ty_2Einteger_2Eint) ).
thf(conj_thm_2Einteger_2EINT__NEG__SUB,axiom,
! [X17845: tp__ty_2Einteger_2Eint,X17846: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17845 ) ) @ ( inj__ty_2Einteger_2Eint @ X17846 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17846 ) ) @ ( inj__ty_2Einteger_2Eint @ X17845 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',conj_thm_2Einteger_2EINT__NEG__SUB) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
! [X18159: tp__ty_2Einteger_2Eint,X18160: tp__ty_2Einteger_2Eint,X18161: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( inj__ty_2Einteger_2Eint @ X18160 ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X18161 ) ) @ ( inj__ty_2Einteger_2Eint @ X18160 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( inj__ty_2Einteger_2Eint @ X18161 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',conj_thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
! [X18154: tp__ty_2Einteger_2Eint,X18155: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18154 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X18155 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18154 ) ) @ ( inj__ty_2Einteger_2Eint @ X18155 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X18154 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X18155 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18154 ) ) @ ( inj__ty_2Einteger_2Eint @ X18155 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',conj_thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__LSUB,axiom,
! [X18156: tp__ty_2Einteger_2Eint,X18157: tp__ty_2Einteger_2Eint,X18158: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18156 ) ) @ ( inj__ty_2Einteger_2Eint @ X18157 ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18156 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X18157 ) ) @ ( inj__ty_2Einteger_2Eint @ X18158 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18156 ) ) @ ( inj__ty_2Einteger_2Eint @ X18158 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p',conj_thm_2Einteger_2EINT__DIVIDES__LSUB) ).
thf(c_0_9,plain,
! [X19516: del,X19517: del,X19518: $i,X19519: $i] :
( ~ ( mem @ X19518 @ ( arr @ X19516 @ X19517 ) )
| ~ ( mem @ X19519 @ X19516 )
| ( mem @ ( ap @ X19518 @ X19519 ) @ X19517 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
thf(c_0_10,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
| ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,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]) ).
thf(c_0_12,plain,
! [X20179: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X20179 ) @ ty_2Einteger_2Eint ),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Einteger_2Eint]) ).
thf(c_0_13,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__sub @ X2 ) @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) )
| ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,plain,
! [X17555: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X17555 ) @ ty_2Einteger_2Eint ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__neg]) ).
thf(c_0_16,plain,
! [X17555: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
! [X20180: $i] :
( ~ ( mem @ X20180 @ ty_2Einteger_2Eint )
| ( X20180
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X20180 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_ty_2Einteger_2Eint])])]) ).
thf(c_0_18,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X2 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
thf(c_0_19,plain,
! [X17555: tp__ty_2Einteger_2Eint,X2: $i] :
( ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ X2 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
thf(c_0_20,plain,
! [X2: $i] :
( ( X2
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X2 ) ) )
| ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
! [X17555: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ty_2Einteger_2Eint ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
thf(c_0_22,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) @ ty_2Einteger_2Eint ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
thf(c_0_23,plain,
! [X19434: tp__ty_2Einteger_2Eint,X19435: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X19434 ) ) @ ( inj__ty_2Einteger_2Eint @ X19435 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X19435 ) ) @ ( inj__ty_2Einteger_2Eint @ X19434 ) ) ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Einteger_2EINT__NEG__SUB]) ).
thf(c_0_24,negated_conjecture,
~ ! [X18159: tp__ty_2Einteger_2Eint,X18160: tp__ty_2Einteger_2Eint,X18161: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( inj__ty_2Einteger_2Eint @ X18160 ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X18161 ) ) @ ( inj__ty_2Einteger_2Eint @ X18160 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X18159 ) ) @ ( inj__ty_2Einteger_2Eint @ X18161 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Einteger_2EINT__DIVIDES__RSUB]) ).
thf(c_0_25,plain,
! [X19420: tp__ty_2Einteger_2Eint,X19421: tp__ty_2Einteger_2Eint] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19420 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X19421 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG])])]) ).
thf(c_0_26,plain,
! [X17555: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
thf(c_0_28,plain,
! [X17556: tp__ty_2Einteger_2Eint,X17555: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
! [X19422: tp__ty_2Einteger_2Eint,X19423: tp__ty_2Einteger_2Eint,X19424: tp__ty_2Einteger_2Eint] :
( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X19423 ) ) @ ( inj__ty_2Einteger_2Eint @ X19424 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( inj__ty_2Einteger_2Eint @ X19424 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( inj__ty_2Einteger_2Eint @ X19423 ) ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( inj__ty_2Einteger_2Eint @ X19424 ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X19423 ) ) @ ( inj__ty_2Einteger_2Eint @ X19424 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X19422 ) ) @ ( inj__ty_2Einteger_2Eint @ X19423 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__LSUB])])])]) ).
thf(c_0_30,negated_conjecture,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) )
& ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_31,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,plain,
! [X17556: tp__ty_2Einteger_2Eint,X17555: tp__ty_2Einteger_2Eint] :
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_27]) ).
thf(c_0_33,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint,X17558: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_34,negated_conjecture,
p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17558: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_36,plain,
! [X17555: tp__ty_2Einteger_2Eint,X17558: tp__ty_2Einteger_2Eint,X17556: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17558 ) ) @ ( inj__ty_2Einteger_2Eint @ X17556 ) ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_32]) ).
thf(c_0_37,negated_conjecture,
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
! [X17555: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_39,negated_conjecture,
! [X17555: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
thf(c_0_40,negated_conjecture,
p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
thf(c_0_41,negated_conjecture,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,negated_conjecture,
p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_43,negated_conjecture,
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP012^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:25:57 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 4.26/4.34 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.Bi2hJAk9zf/E---3.1_1189798.p
% 56.92/13.84 % Version: 3.5.1-ho
% 56.92/13.84 % Preprocessing class: HMLLSMLLSSLNSFA.
% 56.92/13.84 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 56.92/13.84 % Starting new_bool_8 with 1192s (4) cores
% 56.92/13.84 % Starting post_as_ho5 with 596s (2) cores
% 56.92/13.84 % Starting new_bool_9 with 298s (1) cores
% 56.92/13.84 % Starting new_bool_3 with 298s (1) cores
% 56.92/13.84 % new_bool_8 with pid 1189833 completed with status 0
% 56.92/13.84 % Result found by new_bool_8
% 56.92/13.84 % Preprocessing class: HMLLSMLLSSLNSFA.
% 56.92/13.84 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 56.92/13.84 % Starting new_bool_8 with 1192s (4) cores
% 56.92/13.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 56.92/13.84 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 56.92/13.84 % Search class: HGHSM-FSLM32-DSFFFFNN
% 56.92/13.84 % partial match(2): FGHSM-FSLM32-DFFFFFNN
% 56.92/13.84 % Scheduled 13 strats onto 4 cores with 1192 seconds (1192 total)
% 56.92/13.84 % Starting SubtermCWHack with 108s (1) cores
% 56.92/13.84 % Starting new_bool_8 with 120s (1) cores
% 56.92/13.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 56.92/13.84 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 56.92/13.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1189846 completed with status 0
% 56.92/13.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 56.92/13.84 % Preprocessing class: HMLLSMLLSSLNSFA.
% 56.92/13.84 % Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 56.92/13.84 % Starting new_bool_8 with 1192s (4) cores
% 56.92/13.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 56.92/13.84 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 56.92/13.84 % Search class: HGHSM-FSLM32-DSFFFFNN
% 56.92/13.84 % partial match(2): FGHSM-FSLM32-DFFFFFNN
% 56.92/13.84 % Scheduled 13 strats onto 4 cores with 1192 seconds (1192 total)
% 56.92/13.84 % Starting SubtermCWHack with 108s (1) cores
% 56.92/13.84 % Starting new_bool_8 with 120s (1) cores
% 56.92/13.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 56.92/13.84 % Preprocessing time : 0.046 s
% 56.92/13.84 % Presaturation interreduction done
% 56.92/13.84
% 56.92/13.84 % Proof found!
% 56.92/13.84 % SZS status Theorem
% 56.92/13.84 % SZS output start CNFRefutation
% See solution above
% 56.92/13.84 % Parsed axioms : 9711
% 56.92/13.84 % Removed by relevancy pruning/SinE : 9252
% 56.92/13.84 % Initial clauses : 1964
% 56.92/13.84 % Removed in clause preprocessing : 992
% 56.92/13.84 % Initial clauses in saturation : 972
% 56.92/13.84 % Processed clauses : 5370
% 56.92/13.84 % ...of these trivial : 435
% 56.92/13.84 % ...subsumed : 456
% 56.92/13.84 % ...remaining for further processing : 4478
% 56.92/13.84 % Other redundant clauses eliminated : 102
% 56.92/13.84 % Clauses deleted for lack of memory : 0
% 56.92/13.84 % Backward-subsumed : 4
% 56.92/13.84 % Backward-rewritten : 86
% 56.92/13.84 % Generated clauses : 148490
% 56.92/13.84 % ...of the previous two non-redundant : 147122
% 56.92/13.84 % ...aggressively subsumed : 0
% 56.92/13.84 % Contextual simplify-reflections : 1
% 56.92/13.84 % Paramodulations : 148380
% 56.92/13.84 % Factorizations : 6
% 56.92/13.84 % NegExts : 0
% 56.92/13.84 % Equation resolutions : 111
% 56.92/13.84 % Disequality decompositions : 0
% 56.92/13.84 % Total rewrite steps : 3198
% 56.92/13.84 % ...of those cached : 2480
% 56.92/13.84 % Propositional unsat checks : 0
% 56.92/13.84 % Propositional check models : 0
% 56.92/13.84 % Propositional check unsatisfiable : 0
% 56.92/13.84 % Propositional clauses : 0
% 56.92/13.84 % Propositional clauses after purity: 0
% 56.92/13.84 % Propositional unsat core size : 0
% 56.92/13.84 % Propositional preprocessing time : 0.000
% 56.92/13.84 % Propositional encoding time : 0.000
% 56.92/13.84 % Propositional solver time : 0.000
% 56.92/13.84 % Success case prop preproc time : 0.000
% 56.92/13.84 % Success case prop encoding time : 0.000
% 56.92/13.84 % Success case prop solver time : 0.000
% 56.92/13.84 % Current number of processed clauses : 3442
% 56.92/13.84 % Positive orientable unit clauses : 1195
% 56.92/13.84 % Positive unorientable unit clauses: 5
% 56.92/13.84 % Negative unit clauses : 40
% 56.92/13.84 % Non-unit-clauses : 2202
% 56.92/13.84 % Current number of unprocessed clauses: 142457
% 56.92/13.84 % ...number of literals in the above : 434307
% 56.92/13.84 % Current number of archived formulas : 0
% 56.92/13.84 % Current number of archived clauses : 971
% 56.92/13.84 % Clause-clause subsumption calls (NU) : 464705
% 56.92/13.84 % Rec. Clause-clause subsumption calls : 231184
% 56.92/13.84 % Non-unit clause-clause subsumptions : 401
% 56.92/13.84 % Unit Clause-clause subsumption calls : 97677
% 56.92/13.84 % Rewrite failures with RHS unbound : 0
% 56.92/13.84 % BW rewrite match attempts : 112961
% 56.92/13.84 % BW rewrite match successes : 78
% 56.92/13.84 % Condensation attempts : 0
% 56.92/13.84 % Condensation successes : 0
% 56.92/13.84 % Termbank termtop insertions : 5357698
% 56.92/13.84 % Search garbage collected termcells : 271223
% 56.92/13.84
% 56.92/13.84 % -------------------------------------------------
% 56.92/13.84 % User time : 7.013 s
% 56.92/13.84 % System time : 0.234 s
% 56.92/13.84 % Total time : 7.247 s
% 56.92/13.84 % Maximum resident set size: 52448 pages
% 56.92/13.84
% 56.92/13.84 % -------------------------------------------------
% 56.92/13.84 % User time : 29.115 s
% 56.92/13.84 % System time : 0.693 s
% 56.92/13.84 % Total time : 29.808 s
% 56.92/13.84 % Maximum resident set size: 48384 pages
% 56.92/13.84 % E exiting
%------------------------------------------------------------------------------