%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 06:57:53 AM UTC 2026
% Result : Theorem 56.25s 20.06s
% Output : Refutation 56.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 7 def)
% Number of atoms : 343 ( 40 equ; 0 cnn)
% Maximal formula atoms : 96 ( 10 avg)
% Number of connectives : 1155 ( 106 ~; 164 |; 126 &; 749 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 81 ( 12 ^; 33 !; 29 ?; 81 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% 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(isLocallyConfluent0_decl,type,
isLocallyConfluent0: $i > $o ).
thf(isTerminating0_decl,type,
isTerminating0: $i > $o ).
thf(iLess0_decl,type,
iLess0: $i > $i > $o ).
thf(aNormalFormOfIn0_decl,type,
aNormalFormOfIn0: $i > $i > $i > $o ).
thf(xw_decl,type,
xw: $i ).
thf(xR_decl,type,
xR: $i ).
thf(xu_decl,type,
xu: $i ).
thf(xv_decl,type,
xv: $i ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk26_decl,type,
sk26: $i > $i > $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i > $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xu @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xv @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( D @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( A @ ( D @ aReductOfIn0 ) ) ) ) )
| ( A = D ) )
& ( D @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( B @ ( D @ aReductOfIn0 ) ) ) ) )
| ( B = D ) )
& ( D @ aElement0 ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( C @ ( B @ ( A @ sk26 ) ) @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( C @ ( B @ ( A @ sk26 ) ) @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) ) ) ) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ isTerminating0 )
& ( A @ aRewritingSystem0 ) )
=> ! [B: $i] :
( ( B @ aElement0 )
=> ? [C: $i] : ( A @ ( B @ ( C @ aNormalFormOfIn0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
thf(153,plain,
! [A: $i] :
( ( ( A @ isTerminating0 )
& ( A @ aRewritingSystem0 ) )
=> ! [B: $i] :
( ( B @ aElement0 )
=> ? [C: $i] : ( A @ ( B @ ( C @ aNormalFormOfIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( B @ sk19 ) @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(cnf,[status(esa)],[153]) ).
thf(1,conjecture,
? [A: $i] :
( ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) )
| ( ~ ? [B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( ( A @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
| ( A @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
| ( xw = A ) )
& ( A @ aElement0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) )
| ( ~ ? [B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( ( A @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
| ( A @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
| ( xw = A ) )
& ( A @ aElement0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ? [A: $i] :
( ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) )
| ( ~ ? [B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( ( A @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
| ( A @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
| ( xw = A ) )
& ( A @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
~ ( ? [A: $i] : ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) )
| ? [A: $i] :
( ~ ? [B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( ( A @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
| ( A @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
| ( xw = A ) )
& ( A @ aElement0 ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( xR @ ( xw @ ( C @ aNormalFormOfIn0 ) ) )
& ( ( xR @ ( A @ ( A @ sk1 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk1 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk1 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xw @ ( B @ aReductOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk1 @ aReductOfIn0 ) ) )
| ~ ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk1 @ aReductOfIn0 ) ) )
| ( xw != A )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(31,plain,
! [A: $i] :
~ ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(34,plain,
! [A: $i] :
~ ( xR @ ( xw @ ( A @ aNormalFormOfIn0 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(30940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk19 ) @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( xw @ ( C @ aNormalFormOfIn0 ) ) ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(paramod_ordered,[status(thm)],[154,34]) ).
thf(30941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk19 ) @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( xw @ ( C @ aNormalFormOfIn0 ) ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ isTerminating0 )
| ~ ( A @ aRewritingSystem0 ) ),
inference(simp,[status(thm)],[30940]) ).
thf(30942,plain,
( ~ ( xw @ aElement0 )
| ~ ( xR @ isTerminating0 )
| ~ ( xR @ aRewritingSystem0 ) ),
inference(pattern_uni,[status(thm)],[30941:[bind(A,$thf( xR )),bind(B,$thf( xw )),bind(C,$thf( xR @ ( xw @ sk19 ) ))]]) ).
thf(17,axiom,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( ( ( xw @ ( xR @ ( xv @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xv @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xv @ ( xw @ aReductOfIn0 ) ) ) ) )
| ( xv = xw ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( ( ( xw @ ( xR @ ( xu @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xu @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xu @ ( xw @ aReductOfIn0 ) ) ) ) )
| ( xu = xw ) )
& ( xw @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
thf(155,plain,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( ( ( xw @ ( xR @ ( xv @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xv @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xv @ ( xw @ aReductOfIn0 ) ) ) ) )
| ( xv = xw ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( ( ( xw @ ( xR @ ( xu @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xw @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xu @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xu @ ( xw @ aReductOfIn0 ) ) ) ) )
| ( xu = xw ) )
& ( xw @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(156,plain,
( ( xw @ ( xR @ ( xv @ sdtmndtasgtdt0 ) ) )
& ( ( xw @ ( xR @ ( xv @ sdtmndtplgtdt0 ) ) )
| ( xv = xw ) )
& ( ( xw @ ( xR @ ( sk21 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xv @ ( xw @ aReductOfIn0 ) ) )
| ( xv = xw ) )
& ( ( xR @ ( xv @ ( sk21 @ aReductOfIn0 ) ) )
| ( xR @ ( xv @ ( xw @ aReductOfIn0 ) ) )
| ( xv = xw ) )
& ( ( sk21 @ aElement0 )
| ( xR @ ( xv @ ( xw @ aReductOfIn0 ) ) )
| ( xv = xw ) )
& ( xw @ ( xR @ ( xu @ sdtmndtasgtdt0 ) ) )
& ( ( xw @ ( xR @ ( xu @ sdtmndtplgtdt0 ) ) )
| ( xu = xw ) )
& ( ( xw @ ( xR @ ( sk20 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xu @ ( xw @ aReductOfIn0 ) ) )
| ( xu = xw ) )
& ( ( xR @ ( xu @ ( sk20 @ aReductOfIn0 ) ) )
| ( xR @ ( xu @ ( xw @ aReductOfIn0 ) ) )
| ( xu = xw ) )
& ( ( sk20 @ aElement0 )
| ( xR @ ( xu @ ( xw @ aReductOfIn0 ) ) )
| ( xu = xw ) )
& ( xw @ aElement0 ) ),
inference(cnf,[status(esa)],[155]) ).
thf(163,plain,
xw @ aElement0,
inference(cnfConj,[status(thm)],[156]) ).
thf(8,axiom,
xR @ aRewritingSystem0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
thf(75,plain,
xR @ aRewritingSystem0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
( ( xR @ isTerminating0 )
& ! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) ) )
=> ( A @ ( B @ iLess0 ) ) ) )
& ( xR @ isLocallyConfluent0 )
& ! [A: $i,B: $i,C: $i] :
( ( ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( C @ aElement0 )
& ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ? [D: $i] :
( ( D @ ( xR @ ( C @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( C @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( C @ ( D @ aReductOfIn0 ) ) ) ) )
| ( C = D ) )
& ( D @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( B @ ( D @ aReductOfIn0 ) ) ) ) )
| ( B = D ) )
& ( D @ aElement0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
thf(201,plain,
( ( xR @ isTerminating0 )
& ! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) ) )
=> ( A @ ( B @ iLess0 ) ) ) )
& ( xR @ isLocallyConfluent0 )
& ! [A: $i,B: $i,C: $i] :
( ( ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( C @ aElement0 )
& ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ? [D: $i] :
( ( D @ ( xR @ ( C @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( C @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( C @ ( D @ aReductOfIn0 ) ) ) ) )
| ( C = D ) )
& ( D @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( D @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [E: $i] :
( ( D @ ( xR @ ( E @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( E @ aReductOfIn0 ) ) )
& ( E @ aElement0 ) )
| ( xR @ ( B @ ( D @ aReductOfIn0 ) ) ) ) )
| ( B = D ) )
& ( D @ aElement0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(202,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( xR @ isTerminating0 )
& ( ( D @ ( E @ iLess0 ) )
| ~ ( E @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
| ~ ( E @ aElement0 )
| ~ ( D @ aElement0 ) )
& ( ( D @ ( E @ iLess0 ) )
| ~ ( E @ ( xR @ ( F @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( D @ ( F @ aReductOfIn0 ) ) )
| ~ ( F @ aElement0 )
| ~ ( E @ aElement0 )
| ~ ( D @ aElement0 ) )
& ( ( D @ ( E @ iLess0 ) )
| ~ ( xR @ ( D @ ( E @ aReductOfIn0 ) ) )
| ~ ( E @ aElement0 )
| ~ ( D @ aElement0 ) )
& ( xR @ isLocallyConfluent0 )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( C @ sdtmndtasgtdt0 ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( A @ ( B @ ( C @ sk28 ) ) @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( C @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( C @ ( A @ ( B @ ( C @ sk28 ) ) @ aReductOfIn0 ) ) )
| ( xR @ ( C @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk28 ) ) @ aElement0 )
| ( xR @ ( C @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ( B
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ ( xR @ ( A @ ( B @ ( C @ sk27 ) ) @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( B @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( B
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( B @ ( A @ ( B @ ( C @ sk27 ) ) @ aReductOfIn0 ) ) )
| ( xR @ ( B @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( B
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk27 ) ) @ aElement0 )
| ( xR @ ( B @ ( A @ ( B @ ( C @ sk26 ) ) @ aReductOfIn0 ) ) )
| ( B
= ( A @ ( B @ ( C @ sk26 ) ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk26 ) ) @ aElement0 )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[201]) ).
thf(203,plain,
xR @ isTerminating0,
inference(cnfConj,[status(thm)],[202]) ).
thf(32492,plain,
( ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[30942,163,75,203]) ).
thf(32493,plain,
$false,
inference(simp,[status(thm)],[32492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 23:27:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.21 % [INFO] Parsing done (224ms).
% 1.45/1.22 % [INFO] Running in sequential loop mode.
% 2.14/1.62 % [INFO] eprover registered as external prover.
% 2.14/1.63 % [INFO] Scanning for conjecture ...
% 2.31/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.53/1.88 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.53/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.96 % [INFO] Type checking passed.
% 2.75/1.96 % [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 ...
% 56.25/20.05 % [INFO] Killing All external provers ...
% 56.25/20.05 % Time passed: 19505ms (effective reasoning time: 18825ms)
% 56.25/20.06 % 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)>
% 56.25/20.06 % Axioms used in derivation (4): mTermNF, m__799, m__656, m__656_01
% 56.25/20.06 % No. of inferences in proof: 25
% 56.25/20.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19505 ms resp. 18825 ms w/o parsing
% 56.25/20.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 56.25/20.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------