%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM013+4 : 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 : n009.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 188.38s 96.27s
% Output : Refutation 189.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 113 ( 19 unt; 0 typ; 6 def)
% Number of atoms : 669 ( 65 equ; 0 cnn)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 2209 ( 323 ~; 324 |; 129 &;1392 @)
% ( 2 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 210 ( 9 ^; 151 !; 44 ?; 210 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% 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(isTerminating0_decl,type,
isTerminating0: $i > $o ).
thf(iLess0_decl,type,
iLess0: $i > $i > $o ).
thf(aNormalFormOfIn0_decl,type,
aNormalFormOfIn0: $i > $i > $i > $o ).
thf(xR_decl,type,
xR: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ aElement0 )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( ( A @ ( B @ iLess0 ) )
=> ? [C: $i] :
( ( xR @ ( B @ ( C @ aNormalFormOfIn0 ) ) )
& ~ ? [D: $i] : ( xR @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( C @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [D: $i] :
( ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( xR @ ( B @ ( C @ aReductOfIn0 ) ) ) ) )
| ( B = C ) )
& ( C @ aElement0 ) ) ) )
=> ( ? [B: $i] : ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
| ? [B: $i] :
( ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
( ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
& ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
& ( ( ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk2 @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] : ( xR @ ( A @ ( B @ aReductOfIn0 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] : ( B @ ( A @ ( D @ aReductOfIn0 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( A @ ( B @ ( D @ sdtmndtplgtdt0 ) ) )
& ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ aElement0 )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( ( A @ ( B @ iLess0 ) )
=> ? [C: $i] :
( ( xR @ ( B @ ( C @ aNormalFormOfIn0 ) ) )
& ~ ? [D: $i] : ( xR @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( C @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [D: $i] :
( ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( xR @ ( B @ ( C @ aReductOfIn0 ) ) ) ) )
| ( B = C ) )
& ( C @ aElement0 ) ) ) )
=> ? [B: $i] :
( ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
| ( ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ aElement0 )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( ( A @ ( B @ iLess0 ) )
=> ? [C: $i] :
( ( xR @ ( B @ ( C @ aNormalFormOfIn0 ) ) )
& ~ ? [D: $i] : ( xR @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( C @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [D: $i] :
( ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( xR @ ( B @ ( C @ aReductOfIn0 ) ) ) ) )
| ( B = C ) )
& ( C @ aElement0 ) ) ) )
=> ? [B: $i] :
( ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
| ( ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i] :
( ( A @ aElement0 )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( ( A @ ( B @ iLess0 ) )
=> ? [C: $i] :
( ( xR @ ( B @ ( C @ aNormalFormOfIn0 ) ) )
& ~ ? [D: $i] : ( xR @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( C @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [D: $i] :
( ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( xR @ ( B @ ( C @ aReductOfIn0 ) ) ) ) )
| ( B = C ) )
& ( C @ aElement0 ) ) ) )
=> ? [B: $i] :
( ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
| ( ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
~ ! [A: $i] :
( ( A @ aElement0 )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( ( A @ ( B @ iLess0 ) )
=> ? [C: $i] :
( ( xR @ ( B @ ( C @ aNormalFormOfIn0 ) ) )
& ~ ? [D: $i] : ( xR @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( xR @ ( B @ sdtmndtasgtdt0 ) ) )
& ( ( ( C @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( ? [D: $i] :
( ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( B @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( xR @ ( B @ ( C @ aReductOfIn0 ) ) ) ) )
| ( B = C ) )
& ( C @ aElement0 ) ) ) )
=> ( ? [B: $i] : ( xR @ ( A @ ( B @ aNormalFormOfIn0 ) ) )
| ? [B: $i] :
( ~ ? [C: $i] : ( xR @ ( B @ ( C @ aReductOfIn0 ) ) )
& ( ( B @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [C: $i] :
( ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
& ( C @ aElement0 ) )
| ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ( A = B ) )
& ( B @ aElement0 ) ) ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( xR @ ( sk1 @ ( E @ aNormalFormOfIn0 ) ) )
& ( ( xR @ ( C @ ( C @ sk4 @ aReductOfIn0 ) ) )
| ~ ( C @ ( xR @ ( sk1 @ sdtmndtasgtdt0 ) ) )
| ~ ( C @ aElement0 ) )
& ( ( xR @ ( C @ ( C @ sk4 @ aReductOfIn0 ) ) )
| ~ ( C @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ aElement0 ) )
& ( ( xR @ ( C @ ( C @ sk4 @ aReductOfIn0 ) ) )
| ~ ( C @ ( xR @ ( D @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( sk1 @ ( D @ aReductOfIn0 ) ) )
| ~ ( D @ aElement0 )
| ~ ( C @ aElement0 ) )
& ( ( xR @ ( C @ ( C @ sk4 @ aReductOfIn0 ) ) )
| ~ ( xR @ ( sk1 @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 ) )
& ( ( xR @ ( C @ ( C @ sk4 @ aReductOfIn0 ) ) )
| ( sk1 != C )
| ~ ( C @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ~ ( xR @ ( A @ sk2 @ ( B @ aReductOfIn0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( A @ sk2 @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( A @ sk2 @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ( A
= ( A @ sk2 ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( A @ sk2 @ ( xR @ ( A @ sk3 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( A @ ( A @ sk2 @ aReductOfIn0 ) ) )
| ( A
= ( A @ sk2 ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( xR @ ( A @ ( A @ sk3 @ aReductOfIn0 ) ) )
| ( xR @ ( A @ ( A @ sk2 @ aReductOfIn0 ) ) )
| ( A
= ( A @ sk2 ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( A @ sk3 @ aElement0 )
| ( xR @ ( A @ ( A @ sk2 @ aReductOfIn0 ) ) )
| ( A
= ( A @ sk2 ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( ( A @ sk2 @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) )
& ( sk1 @ aElement0 ) ),
inference(cnf,[status(esa)],[18]) ).
thf(26,plain,
! [A: $i] :
( ( A @ sk2 @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ( A
= ( A @ sk2 ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(44,plain,
! [A: $i] :
( ( A @ sk2 @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 )
| ( ( A @ sk2 )
= A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(22,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ( sk1 != A )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(41,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 )
| ( sk1 != A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(42,plain,
( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
| ~ ( sk1 @ aElement0 ) ),
inference(simp,[status(thm)],[41]) ).
thf(28,plain,
sk1 @ aElement0,
inference(cnfConj,[status(thm)],[19]) ).
thf(128,plain,
( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[42,28]) ).
thf(129,plain,
xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ),
inference(simp,[status(thm)],[128]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( sk1 @ ( B @ aReductOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( sk1 @ ( B @ aReductOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[25]) ).
thf(494,plain,
! [B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ ( B @ aReductOfIn0 ) ) ) )
| ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[129,36]) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ ( B @ aReductOfIn0 ) ) ) )
| ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[494]) ).
thf(496,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ sk4 @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( A )),bind(B,$thf( sk1 @ sk4 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
=> ( C @ aElement0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
=> ( C @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ aElement0 )
| ~ ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[102]) ).
thf(29494,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) )
| ( C @ aElement0 )
| ~ $true
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[129,103]) ).
thf(29495,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) )
| ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[29494]) ).
thf(29496,plain,
( ( sk1 @ sk4 @ aElement0 )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( sk1 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[29495:[bind(A,$thf( sk1 )),bind(B,$thf( xR )),bind(C,$thf( sk1 @ sk4 ))]]) ).
thf(16,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 @ aRewritingSystem0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__587) ).
thf(110,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 @ aRewritingSystem0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( xR @ isTerminating0 )
& ( ( A @ ( B @ iLess0 ) )
| ~ ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ iLess0 ) )
| ~ ( B @ ( xR @ ( C @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ iLess0 ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) )
& ( xR @ aRewritingSystem0 ) ),
inference(cnf,[status(esa)],[110]) ).
thf(112,plain,
xR @ aRewritingSystem0,
inference(cnfConj,[status(thm)],[111]) ).
thf(29766,plain,
( ( sk1 @ sk4 @ aElement0 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[29496,112,28]) ).
thf(29767,plain,
sk1 @ sk4 @ aElement0,
inference(simp,[status(thm)],[29766]) ).
thf(72607,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(rewrite,[status(thm)],[496,29767]) ).
thf(72608,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[72607]) ).
thf(30,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
<=> ( ~ ? [D: $i] : ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
& ( C @ aElement0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ! [C: $i] :
( ( ( ~ ? [D: $i] : ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
& ( C @ aElement0 ) )
=> ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) ) )
& ( ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
=> ( ~ ? [D: $i] : ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
& ( C @ aElement0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ( ! [C: $i] :
( ( ~ ? [D: $i] : ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
& ( C @ aElement0 ) )
=> ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) ) )
& ! [C: $i] :
( ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
=> ( ~ ? [D: $i] : ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
& ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
& ( C @ aElement0 ) ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( E @ aNormalFormOfIn0 ) ) )
| ( B @ ( E @ ( A @ ( B @ ( E @ sk5 ) ) @ aReductOfIn0 ) ) )
| ~ ( E @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
| ~ ( E @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ~ ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( C @ ( B @ ( A @ sdtmndtasgtdt0 ) ) )
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( C @ aElement0 )
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ aReductOfIn0 ) ) )
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
!= ( C @ ( B @ ( D @ aNormalFormOfIn0 ) ) ) )
| ~ ( C @ ( D @ ( E @ aReductOfIn0 ) ) )
| ~ $true
| ~ ( C @ aRewritingSystem0 )
| ~ ( B @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[30,51]) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
!= ( C @ ( B @ ( D @ aNormalFormOfIn0 ) ) ) )
| ~ ( C @ ( D @ ( E @ aReductOfIn0 ) ) )
| ~ ( C @ aRewritingSystem0 )
| ~ ( B @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( B @ aElement0 )
| ~ ( sk1 @ ( B @ iLess0 ) )
| ~ ( B @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( xR )),bind(D,$thf( F @ sk2 ))]]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( sk1 @ ( B @ iLess0 ) )
| ~ ( B @ aElement0 ) ),
inference(simp,[status(thm)],[263]) ).
thf(1538,plain,
! [B: $i,A: $i] :
( ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ $true
| ~ ( sk1 @ ( B @ iLess0 ) )
| ~ ( B @ aElement0 ) ),
inference(rewrite,[status(thm)],[268,112]) ).
thf(1539,plain,
! [B: $i,A: $i] :
( ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( sk1 @ ( B @ iLess0 ) )
| ~ ( B @ aElement0 ) ),
inference(simp,[status(thm)],[1538]) ).
thf(29864,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( B @ aElement0 ) )
| ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( sk1 @ ( B @ iLess0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29767,1539]) ).
thf(29865,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( B @ aElement0 ) )
| ~ ( xR @ ( B @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( sk1 @ ( B @ iLess0 ) ) ),
inference(simp,[status(thm)],[29864]) ).
thf(29866,plain,
! [A: $i] :
( ~ ( xR @ ( sk1 @ sk4 @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(pattern_uni,[status(thm)],[29865:[bind(A,$thf( A )),bind(B,$thf( sk1 @ sk4 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aElement0 )
& ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ( ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
<=> ( ? [D: $i] :
( ( C @ ( B @ ( D @ sdtmndtplgtdt0 ) ) )
& ( B @ ( A @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aElement0 )
& ( B @ aRewritingSystem0 )
& ( A @ aElement0 ) )
=> ( ( ( ? [D: $i] :
( ( C @ ( B @ ( D @ sdtmndtplgtdt0 ) ) )
& ( B @ ( A @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) )
=> ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) ) )
& ( ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
=> ( ? [D: $i] :
( ( C @ ( B @ ( D @ sdtmndtplgtdt0 ) ) )
& ( B @ ( A @ ( D @ aReductOfIn0 ) ) )
& ( D @ aElement0 ) )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ ( B @ ( D @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ ( A @ ( D @ aReductOfIn0 ) ) )
| ~ ( D @ aElement0 )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( C @ ( B @ ( A @ ( B @ ( C @ sk16 ) ) @ sdtmndtplgtdt0 ) ) )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( B @ ( A @ ( A @ ( B @ ( C @ sk16 ) ) @ aReductOfIn0 ) ) )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) )
& ( ( A @ ( B @ ( C @ sk16 ) ) @ aElement0 )
| ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ ( A @ ( C @ aReductOfIn0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(25609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) )
| ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[129,97]) ).
thf(25610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( A @ ( C @ aReductOfIn0 ) ) ) )
| ( C @ ( B @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[25609]) ).
thf(25611,plain,
( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ sk4 @ aElement0 )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( sk1 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[25610:[bind(A,$thf( sk1 )),bind(B,$thf( xR )),bind(C,$thf( sk1 @ sk4 ))]]) ).
thf(29236,plain,
( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ sk4 @ aElement0 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[25611,112,28]) ).
thf(29237,plain,
( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(simp,[status(thm)],[29236]) ).
thf(29776,plain,
( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[29237,29767]) ).
thf(29777,plain,
sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ),
inference(simp,[status(thm)],[29776]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ iLess0 ) )
| ~ ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[111]) ).
thf(33329,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
!= ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) ) )
| ( A @ ( B @ iLess0 ) )
| ~ $true
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[29777,113]) ).
thf(33330,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk4 @ ( xR @ ( sk1 @ sdtmndtplgtdt0 ) ) )
!= ( B @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) ) )
| ( A @ ( B @ iLess0 ) )
| ~ ( B @ aElement0 )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[33329]) ).
thf(33331,plain,
( ( sk1 @ ( sk1 @ sk4 @ iLess0 ) )
| ~ ( sk1 @ sk4 @ aElement0 )
| ~ ( sk1 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[33330:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk4 ))]]) ).
thf(36660,plain,
( ( sk1 @ ( sk1 @ sk4 @ iLess0 ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[33331,29767,28]) ).
thf(36661,plain,
sk1 @ ( sk1 @ sk4 @ iLess0 ),
inference(simp,[status(thm)],[36660]) ).
thf(36664,plain,
! [A: $i] :
( ~ ( xR @ ( sk1 @ sk4 @ sk2 @ ( A @ aReductOfIn0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[29866,36661]) ).
thf(36665,plain,
! [A: $i] :
~ ( xR @ ( sk1 @ sk4 @ sk2 @ ( A @ aReductOfIn0 ) ) ),
inference(simp,[status(thm)],[36664]) ).
thf(72629,plain,
! [B: $i,A: $i] :
( ( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ sk4 @ sk2 @ ( B @ aReductOfIn0 ) ) ) )
| ~ $true
| ~ ( A @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[72608,36665]) ).
thf(72630,plain,
! [B: $i,A: $i] :
( ( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ sk4 @ sk2 @ ( B @ aReductOfIn0 ) ) ) )
| ~ ( A @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[72629]) ).
thf(72631,plain,
( ~ ( sk1 @ sk4 @ sk2 @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk1 @ sk4 @ sk2 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[72630:[bind(A,$thf( sk1 @ sk4 @ sk2 )),bind(B,$thf( sk1 @ sk4 @ sk2 @ sk4 ))]]) ).
thf(33,plain,
! [A: $i] :
( ( A @ sk2 @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(29840,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ( A @ sk2 @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29767,33]) ).
thf(29841,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ( A @ sk2 @ aElement0 )
| ~ ( sk1 @ ( A @ iLess0 ) ) ),
inference(simp,[status(thm)],[29840]) ).
thf(29842,plain,
( ( sk1 @ sk4 @ sk2 @ aElement0 )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(pattern_uni,[status(thm)],[29841:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(36666,plain,
( ( sk1 @ sk4 @ sk2 @ aElement0 )
| ~ $true ),
inference(rewrite,[status(thm)],[29842,36661]) ).
thf(36667,plain,
sk1 @ sk4 @ sk2 @ aElement0,
inference(simp,[status(thm)],[36666]) ).
thf(72968,plain,
( ~ ( sk1 @ sk4 @ sk2 @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[72631,36667]) ).
thf(72969,plain,
~ ( sk1 @ sk4 @ sk2 @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) ),
inference(simp,[status(thm)],[72968]) ).
thf(72987,plain,
! [A: $i] :
( ( ( A @ sk2 @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
!= ( sk1 @ sk4 @ sk2 @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) ) )
| ~ $true
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 )
| ( ( A @ sk2 )
= A ) ),
inference(paramod_ordered,[status(thm)],[44,72969]) ).
thf(72988,plain,
! [A: $i] :
( ( ( A @ sk2 @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
!= ( sk1 @ sk4 @ sk2 @ ( xR @ ( sk1 @ sk4 @ sdtmndtplgtdt0 ) ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ ( A @ aElement0 )
| ( ( A @ sk2 )
= A ) ),
inference(simp,[status(thm)],[72987]) ).
thf(72989,plain,
( ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) )
| ~ ( sk1 @ sk4 @ aElement0 )
| ( ( sk1 @ sk4 @ sk2 )
= ( sk1 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[72988:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(118034,plain,
( ~ $true
| ~ $true
| ( ( sk1 @ sk4 @ sk2 )
= ( sk1 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[72989,36661,29767]) ).
thf(118035,plain,
( ( sk1 @ sk4 @ sk2 )
= ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[118034]) ).
thf(30012,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29767,30]) ).
thf(30013,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ( xR @ ( A @ ( A @ sk2 @ aNormalFormOfIn0 ) ) )
| ~ ( sk1 @ ( A @ iLess0 ) ) ),
inference(simp,[status(thm)],[30012]) ).
thf(30014,plain,
( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk2 @ aNormalFormOfIn0 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(pattern_uni,[status(thm)],[30013:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(24,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( xR @ ( sk1 @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(35,plain,
! [A: $i] :
( ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( xR @ ( sk1 @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[24]) ).
thf(306,plain,
! [A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ ( A @ aReductOfIn0 ) ) ) )
| ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[129,35]) ).
thf(307,plain,
! [A: $i] :
( ( ( xR @ ( sk1 @ ( sk1 @ sk4 @ aReductOfIn0 ) ) )
!= ( xR @ ( sk1 @ ( A @ aReductOfIn0 ) ) ) )
| ( xR @ ( A @ ( A @ sk4 @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk4 @ aReductOfIn0 ) ) )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( C @ ( D @ aReductOfIn0 ) ) ) )
| ~ $true
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[308,51]) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk4 @ aReductOfIn0 ) ) )
!= ( B @ ( C @ ( D @ aReductOfIn0 ) ) ) )
| ~ ( B @ ( A @ ( C @ aNormalFormOfIn0 ) ) )
| ~ ( B @ aRewritingSystem0 )
| ~ ( A @ aElement0 )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [A: $i] :
( ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ ( xR @ aRewritingSystem0 )
| ~ ( A @ aElement0 )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( A )),bind(B,$thf( xR )),bind(C,$thf( sk1 @ sk4 )),bind(D,$thf( sk1 @ sk4 @ sk4 ))]]) ).
thf(370,plain,
! [A: $i] :
( ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ $true
| ~ ( A @ aElement0 )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(rewrite,[status(thm)],[349,112]) ).
thf(371,plain,
! [A: $i] :
( ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ ( A @ aElement0 )
| ~ ( sk1 @ sk4 @ aElement0 ) ),
inference(simp,[status(thm)],[370]) ).
thf(29778,plain,
! [A: $i] :
( ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ ( A @ aElement0 )
| ~ $true ),
inference(rewrite,[status(thm)],[371,29767]) ).
thf(29779,plain,
! [A: $i] :
( ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[29778]) ).
thf(34271,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29767,29779]) ).
thf(34272,plain,
! [A: $i] :
( ( ( sk1 @ sk4 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ ( xR @ ( A @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) ) ),
inference(simp,[status(thm)],[34271]) ).
thf(34273,plain,
~ ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) ),
inference(pattern_uni,[status(thm)],[34272:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(35278,plain,
( ( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk2 @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) ) )
| ~ $true
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(paramod_ordered,[status(thm)],[30014,34273]) ).
thf(35279,plain,
( ( ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ sk2 @ aNormalFormOfIn0 ) ) )
!= ( xR @ ( sk1 @ sk4 @ ( sk1 @ sk4 @ aNormalFormOfIn0 ) ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(simp,[status(thm)],[35278]) ).
thf(35410,plain,
( ( xR != xR )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) )
| ( ( sk1 @ sk4 @ sk2 )
!= ( sk1 @ sk4 ) )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(simp,[status(thm)],[35279]) ).
thf(35478,plain,
( ( ( sk1 @ sk4 @ sk2 )
!= ( sk1 @ sk4 ) )
| ~ ( sk1 @ ( sk1 @ sk4 @ iLess0 ) ) ),
inference(simp,[status(thm)],[35410]) ).
thf(36662,plain,
( ( ( sk1 @ sk4 @ sk2 )
!= ( sk1 @ sk4 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[35478,36661]) ).
thf(36663,plain,
( ( sk1 @ sk4 @ sk2 )
!= ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[36662]) ).
thf(118036,plain,
$false,
inference(simplifyReflect,[status(thm)],[118035,36663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM013+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.14 % 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
% 0.20/5.47 % Computer : n009.cluster.edu
% 0.20/5.47 % Model : x86_64 x86_64
% 0.20/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.47 % Memory : 8046.5625MB
% 0.20/5.47 % OS : Linux 6.8.0-71-generic
% 0.20/5.47 % CPULimit : 300
% 0.20/5.47 % WCLimit : 300
% 0.20/5.47 % DateTime : Sat Sep 26 23:21:20 UTC 2026
% 0.20/5.47 % CPUTime :
% 0.20/5.48 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
% 1.03/6.06 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/6.28 % [INFO] Parsing done (209ms).
% 1.31/6.29 % [INFO] Running in sequential loop mode.
% 2.28/6.70 % [INFO] eprover registered as external prover.
% 2.28/6.71 % [INFO] Scanning for conjecture ...
% 2.28/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.87 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.69/6.92 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.69/6.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/6.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.69/6.97 % [INFO] Type checking passed.
% 2.69/6.97 % [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 ...
% 188.38/96.26 % [INFO] Killing All external provers ...
% 188.38/96.27 % Time passed: 90648ms (effective reasoning time: 89967ms)
% 188.38/96.27 % 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)>
% 188.38/96.27 % Axioms used in derivation (4): mReduct, m__587, mNFRDef, mTCDef
% 188.38/96.27 % No. of inferences in proof: 107
% 188.38/96.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 90648 ms resp. 89967 ms w/o parsing
% 189.16/96.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 189.16/96.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------