%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 : Sun Sep 27 06:57:52 AM UTC 2026
% Result : Theorem 22.88s 7.44s
% Output : Refutation 23.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 295 ( 54 equ; 0 cnn)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 827 ( 104 ~; 128 |; 68 &; 520 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 43 ( 0 ^; 32 !; 9 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(aRewritingSystem0_decl,type,
aRewritingSystem0: $i > $o ).
thf(sdtmndtplgtdt0_decl,type,
sdtmndtplgtdt0: $i > $i > $i > $o ).
thf(aReductOfIn0_decl,type,
aReductOfIn0: $i > $i > $i > $o ).
thf(sdtmndtasgtdt0_decl,type,
sdtmndtasgtdt0: $i > $i > $i > $o ).
thf(xx_decl,type,
xx: $i ).
thf(xy_decl,type,
xy: $i ).
thf(xR_decl,type,
xR: $i ).
thf(xz_decl,type,
xz: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( xy @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xy @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(1,conjecture,
( ( ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
& ( ( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xy @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) ) ) )
| ( xy = xz ) )
& ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
& ( ( ( xy @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xy @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ) ) )
| ( xx = xy ) ) )
=> ( ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
| ( xz @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xz @ aReductOfIn0 ) ) )
| ( xx = xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
& ( ( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xy @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) ) ) )
| ( xy = xz ) )
& ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
& ( ( ( xy @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xy @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ) ) )
| ( xx = xy ) ) )
=> ( ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
| ( xz @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xz @ aReductOfIn0 ) ) )
| ( xx = xz ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ( ( ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
& ( ( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xy @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) ) ) )
| ( xy = xz ) )
& ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
& ( ( ( xy @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xy @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ) ) )
| ( xx = xy ) ) )
=> ( ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
| ( xz @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xx @ ( xz @ aReductOfIn0 ) ) )
| ( xx = xz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
& ~ ( xz @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
& ( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ~ ( xR @ ( xx @ ( xz @ aReductOfIn0 ) ) )
& ( xx != xz )
& ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
& ( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
| ( xy = xz ) )
& ( ( xz @ ( xR @ ( sk2 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) )
| ( xy = xz ) )
& ( ( xR @ ( xy @ ( sk2 @ aReductOfIn0 ) ) )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) )
| ( xy = xz ) )
& ( ( sk2 @ aElement0 )
| ( xR @ ( xy @ ( xz @ aReductOfIn0 ) ) )
| ( xy = xz ) )
& ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
& ( ( xy @ ( xR @ ( xx @ sdtmndtplgtdt0 ) ) )
| ( xx = xy ) )
& ( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) )
& ( ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) )
& ( ( sk1 @ aElement0 )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(21,plain,
( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(35,plain,
( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xy = xx ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(11,axiom,
( ( xz @ aElement0 )
& ( xy @ aElement0 )
& ( xR @ aRewritingSystem0 )
& ( xx @ aElement0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).
thf(61,plain,
( ( xz @ aElement0 )
& ( xy @ aElement0 )
& ( xR @ aRewritingSystem0 )
& ( xx @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(62,plain,
( ( xz @ aElement0 )
& ( xy @ aElement0 )
& ( xR @ aRewritingSystem0 )
& ( xx @ aElement0 ) ),
inference(cnf,[status(esa)],[61]) ).
thf(65,plain,
xy @ aElement0,
inference(cnfConj,[status(thm)],[62]) ).
thf(23,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(71,plain,
! [A: $i] :
( ( ( xy @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,23]) ).
thf(72,plain,
! [A: $i] :
( ( ( xy @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
( ~ ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( xy ))]]) ).
thf(16,plain,
( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
| ( xy = xz ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(32,plain,
( ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
| ( xz = xy ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(19,plain,
xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(22,plain,
~ ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(67,plain,
( ( ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
!= ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,22]) ).
thf(68,plain,
( ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) )
!= ( xy @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
( ( xz != xy )
| ( xR != xR )
| ( xx != xx ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
xz != xy,
inference(simp,[status(thm)],[69]) ).
thf(98,plain,
xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ),
inference(simplifyReflect,[status(thm)],[32,70]) ).
thf(99,plain,
( ~ $true
| ~ ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ) ),
inference(rewrite,[status(thm)],[73,98]) ).
thf(100,plain,
~ ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(245,plain,
( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| $false
| ( xy = xx ) ),
inference(rewrite,[status(thm)],[35,100]) ).
thf(246,plain,
( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ( xy = xx ) ),
inference(simp,[status(thm)],[245]) ).
thf(24,plain,
xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(80,plain,
( ( ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
!= ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,22]) ).
thf(81,plain,
( ( xz @ ( xR @ ( xy @ sdtmndtasgtdt0 ) ) )
!= ( xz @ ( xR @ ( xx @ sdtmndtasgtdt0 ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
( ( xz != xz )
| ( xR != xR )
| ( xy != xx ) ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
xy != xx,
inference(simp,[status(thm)],[82]) ).
thf(247,plain,
xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ),
inference(simplifyReflect,[status(thm)],[246,83]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ aElement0 )
& ( C @ aElement0 )
& ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ( ( ( D @ ( B @ ( C @ sdtmndtplgtdt0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) ) )
=> ( D @ ( B @ ( A @ sdtmndtplgtdt0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
thf(59,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ aElement0 )
& ( C @ aElement0 )
& ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ( ( ( D @ ( B @ ( C @ sdtmndtplgtdt0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) ) )
=> ( D @ ( B @ ( A @ sdtmndtplgtdt0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( D @ ( B @ ( C @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( D @ aElement0 )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[59]) ).
thf(27,plain,
( ( sk1 @ aElement0 )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(36,plain,
( ( sk1 @ aElement0 )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xy = xx ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(124,plain,
( ( sk1 @ aElement0 )
| $false
| ( xy = xx ) ),
inference(rewrite,[status(thm)],[36,100]) ).
thf(125,plain,
( ( sk1 @ aElement0 )
| ( xy = xx ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
sk1 @ aElement0,
inference(simplifyReflect,[status(thm)],[125,83]) ).
thf(127,plain,
! [A: $i] :
( ( ( sk1 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[126,23]) ).
thf(128,plain,
! [A: $i] :
( ( ( sk1 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( A @ aReductOfIn0 ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
( ~ ( xz @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( sk1 ))]]) ).
thf(28,plain,
( ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xx = xy ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(34,plain,
( ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) )
| ( xR @ ( xx @ ( xy @ aReductOfIn0 ) ) )
| ( xy = xx ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(226,plain,
( ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) )
| $false
| ( xy = xx ) ),
inference(rewrite,[status(thm)],[34,100]) ).
thf(227,plain,
( ( xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ) )
| ( xy = xx ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
xR @ ( xx @ ( sk1 @ aReductOfIn0 ) ),
inference(simplifyReflect,[status(thm)],[227,83]) ).
thf(229,plain,
( ~ ( xz @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[129,228]) ).
thf(230,plain,
~ ( xz @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(2126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
!= ( xz @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) ) )
| ~ $true
| ~ ( D @ ( B @ ( C @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( D @ aElement0 )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[60,230]) ).
thf(2127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
!= ( xz @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) ) )
| ~ ( D @ ( B @ ( C @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( D @ aElement0 )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[2126]) ).
thf(2128,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( xz @ aElement0 )
| ~ ( A @ aElement0 )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( sk1 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[2127:[bind(A,$thf( sk1 )),bind(B,$thf( xR )),bind(C,$thf( C )),bind(D,$thf( xz ))]]) ).
thf(2197,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( xz @ aElement0 )
| ~ ( A @ aElement0 )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( sk1 @ aElement0 ) ),
inference(simp,[status(thm)],[2128]) ).
thf(64,plain,
xR @ aRewritingSystem0,
inference(cnfConj,[status(thm)],[62]) ).
thf(66,plain,
xz @ aElement0,
inference(cnfConj,[status(thm)],[62]) ).
thf(2308,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( A @ aElement0 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2197,64,66,126]) ).
thf(2309,plain,
! [A: $i] :
( ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[2308]) ).
thf(2340,plain,
! [A: $i] :
( ( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
!= ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[247,2309]) ).
thf(2341,plain,
! [A: $i] :
( ( ( xy @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
!= ( A @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) ) )
| ~ ( xz @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[2340]) ).
thf(2342,plain,
( ~ ( xz @ ( xR @ ( xy @ sdtmndtplgtdt0 ) ) )
| ~ ( xy @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[2341:[bind(A,$thf( xy ))]]) ).
thf(2414,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2342,65,98]) ).
thf(2415,plain,
$false,
inference(simp,[status(thm)],[2414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.51 % Computer : n013.cluster.edu
% 0.23/0.51 % Model : x86_64 x86_64
% 0.23/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.51 % Memory : 8046.5625MB
% 0.23/0.51 % OS : Linux 6.8.0-71-generic
% 0.23/0.51 % CPULimit : 300
% 0.23/0.51 % WCLimit : 300
% 0.23/0.51 % DateTime : Sat Sep 26 23:21:01 UTC 2026
% 0.27/0.51 % CPUTime :
% 0.27/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.42/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.64 % [INFO] Parsing done (289ms).
% 1.96/1.66 % [INFO] Running in sequential loop mode.
% 2.99/2.26 % [INFO] eprover registered as external prover.
% 2.99/2.27 % [INFO] Scanning for conjecture ...
% 3.21/2.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/2.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.41/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.62/2.54 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.62/2.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.62/2.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.62/2.56 % [INFO] Problem is first-order (TPTP FOF).
% 3.62/2.57 % [INFO] Type checking passed.
% 3.62/2.57 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 22.88/7.43 % [INFO] Killing All external provers ...
% 22.88/7.44 % Time passed: 6713ms (effective reasoning time: 5765ms)
% 22.88/7.44 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 22.88/7.44 % Axioms used in derivation (2): m__349, mTCTrans
% 22.88/7.44 % No. of inferences in proof: 64
% 22.88/7.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6713 ms resp. 5765 ms w/o parsing
% 23.37/7.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.37/7.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------