%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n010.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 08:53:42 AM UTC 2026
% Result : Theorem 38.44s 9.25s
% Output : Refutation 30.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 22 unt; 0 typ; 13 def)
% Number of atoms : 447 ( 135 equ; 0 cnn)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 1594 ( 205 ~; 176 |; 76 &;1034 @)
% ( 0 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 17 con; 0-2 aty)
% Number of variables : 181 ( 0 ^; 126 !; 42 ?; 181 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) )
& ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
!= C )
| ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= D ) ) ) ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
!= A ) ) ) )
| ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
= C )
& ( F @ ssList ) )
& ( E @ ssItem ) )
& ( D @ ssItem ) ) )
& ( ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( nil @ ( D @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B )
| ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
!= C ) ) ) ) )
| ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
!= A ) ) ) )
| ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( F @ ( nil @ ( D @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= sk1 )
& ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
= A )
& ( F @ ssList ) )
& ( E @ ssItem ) )
& ( D @ ssItem ) ) ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) )
| ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
= B )
& ( E @ ssList ) )
& ( D @ ssItem ) )
& ( C @ ssItem ) ) )
& ( ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( nil @ ( C @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
!= A )
| ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
!= B ) ) ) ) )
| ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) )
| ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( E @ ( nil @ ( C @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
= sk1 )
& ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
= sk2 )
& ( E @ ssList ) )
& ( D @ ssItem ) )
& ( C @ ssItem ) ) ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssItem ) )
& ( B @ ssItem ) ) )
& ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( nil @ ( B @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
!= sk3 )
| ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= A ) ) ) ) )
| ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( nil @ ( B @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
= sk1 )
& ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
= sk2 )
& ( D @ ssList ) )
& ( C @ ssItem ) )
& ( B @ ssItem ) ) ) )
| ( sk1 != sk3 )
| ( sk2 != A ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( nil @ ( A @ cons ) @ ( nil @ ( sk6 @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( A @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk3 )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( B @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk3 )
| ( ( B @ ( nil @ ( A @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
!= sk4 ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( A @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
!= sk3 )
| ( ( A @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
!= sk4 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( nil @ ( A @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( A @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
!= sk2 ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) )
& ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
!= C )
| ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= D ) ) ) ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) )
& ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
!= C )
| ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= D ) ) ) ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) )
& ( ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
!= C )
| ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= D ) ) ) ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
!= B ) ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( F @ cons ) @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( sk14 @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
= sk2 )
| sk5 )
& ( ( sk14 @ ssList )
| sk5 )
& ( ( sk13 @ ssItem )
| sk5 )
& ( ( sk12 @ ssItem )
| sk5 )
& ( ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
!= sk4 )
| ~ ( F @ ssList )
| ~ ( E @ ssItem )
| ~ ( D @ ssItem )
| sk5 )
& ( ~ sk5
| ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
= sk3 ) )
& ( ~ sk5
| ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
= sk4 ) )
& ( ~ sk5
| ( sk11 @ ssList ) )
& ( ~ sk5
| ( sk10 @ ssItem ) )
& ( ~ sk5
| ( sk9 @ ssItem ) )
& ( ~ sk5
| ( ( sk8 @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ app ) @ app ) )
= sk2 ) )
& ( ~ sk5
| ( sk8 @ ssList ) )
& ( ~ sk5
| ( sk7 @ ssItem ) )
& ( ~ sk5
| ( sk6 @ ssItem ) )
& ( ~ sk5
| ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(101,plain,
( ( ( sk14 @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
= sk2 )
| sk5 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(121,plain,
( sk5
| ( ( sk14 @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 ) ),
inference(simp,[status(thm)],[124]) ).
thf(108,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(129,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[108]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[125,129]) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
!= ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5
| ( sk2 != sk2 )
| sk5 ),
inference(paramod_ordered,[status(thm)],[121,612]) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( nil @ ( sk13 @ cons ) @ ( nil @ ( sk12 @ cons ) @ app ) @ app ) )
!= ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| sk5 ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
( ~ ( sk14 @ ssList )
| ~ ( sk13 @ ssItem )
| ~ ( sk12 @ ssItem )
| sk5 ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 )),bind(C,$thf( sk14 ))]]) ).
thf(113,plain,
( ( sk12 @ ssItem )
| sk5 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(100,plain,
( ~ sk5
| ( sk11 @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(116,plain,
( ~ sk5
| ( sk9 @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(115,plain,
( ~ sk5
| ( sk10 @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(109,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
= sk4 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(123,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
= sk4 ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(580,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
= sk2 ) ),
inference(rewrite,[status(thm)],[123,129]) ).
thf(114,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
= sk3 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(126,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(106,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(122,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[106]) ).
thf(590,plain,
( ~ sk5
| ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[126,122]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk5
| ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk5
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
!= ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) ) )
| ~ sk5
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( sk1 != sk1 )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 )
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[590,127]) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk11 @ ( nil @ ( sk9 @ cons ) @ ( nil @ ( sk10 @ cons ) @ app ) @ app ) )
!= ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 )
| ~ sk5 ),
inference(simp,[status(thm)],[843]) ).
thf(845,plain,
( ~ ( sk11 @ ssList )
| ~ ( sk10 @ ssItem )
| ~ ( sk9 @ ssItem )
| ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
!= sk2 )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[844:[bind(A,$thf( sk9 )),bind(B,$thf( sk10 )),bind(C,$thf( sk11 ))]]) ).
thf(1268,plain,
( ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
!= ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) ) )
| ~ ( sk11 @ ssList )
| ~ ( sk10 @ ssItem )
| ~ ( sk9 @ ssItem )
| ( sk2 != sk2 )
| ~ sk5
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[580,845]) ).
thf(1269,plain,
( ( ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) )
!= ( sk11 @ ( nil @ ( sk10 @ cons ) @ ( nil @ ( sk9 @ cons ) @ app ) @ app ) ) )
| ~ ( sk11 @ ssList )
| ~ ( sk10 @ ssItem )
| ~ ( sk9 @ ssItem )
| ~ sk5 ),
inference(simp,[status(thm)],[1268]) ).
thf(1270,plain,
( ~ ( sk11 @ ssList )
| ~ ( sk10 @ ssItem )
| ~ ( sk9 @ ssItem )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[1269:[]]) ).
thf(1322,plain,
( ( ( sk10 @ ssItem )
!= ( sk10 @ ssItem ) )
| ~ ( sk11 @ ssList )
| ~ $true
| ~ ( sk9 @ ssItem )
| ~ sk5
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[115,1270]) ).
thf(1323,plain,
( ( ( sk10 @ ssItem )
!= ( sk10 @ ssItem ) )
| ~ ( sk11 @ ssList )
| ~ ( sk9 @ ssItem )
| ~ sk5 ),
inference(simp,[status(thm)],[1322]) ).
thf(1324,plain,
( ~ ( sk11 @ ssList )
| ~ ( sk9 @ ssItem )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[1323:[]]) ).
thf(2004,plain,
( ( ( sk9 @ ssItem )
!= ( sk9 @ ssItem ) )
| ~ ( sk11 @ ssList )
| ~ $true
| ~ sk5
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[116,1324]) ).
thf(2005,plain,
( ( ( sk9 @ ssItem )
!= ( sk9 @ ssItem ) )
| ~ ( sk11 @ ssList )
| ~ sk5 ),
inference(simp,[status(thm)],[2004]) ).
thf(2006,plain,
( ~ ( sk11 @ ssList )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[2005:[]]) ).
thf(2069,plain,
( ( ( sk11 @ ssList )
!= ( sk11 @ ssList ) )
| ~ $true
| ~ sk5
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[100,2006]) ).
thf(2070,plain,
( ( ( sk11 @ ssList )
!= ( sk11 @ ssList ) )
| ~ sk5 ),
inference(simp,[status(thm)],[2069]) ).
thf(2071,plain,
~ sk5,
inference(pattern_uni,[status(thm)],[2070:[]]) ).
thf(2129,plain,
( ( sk12 @ ssItem )
| $false ),
inference(rewrite,[status(thm)],[113,2071]) ).
thf(2130,plain,
sk12 @ ssItem,
inference(simp,[status(thm)],[2129]) ).
thf(110,plain,
( ( sk13 @ ssItem )
| sk5 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(2119,plain,
( ( sk13 @ ssItem )
| $false ),
inference(rewrite,[status(thm)],[110,2071]) ).
thf(2120,plain,
sk13 @ ssItem,
inference(simp,[status(thm)],[2119]) ).
thf(111,plain,
( ( sk14 @ ssList )
| sk5 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(2139,plain,
( ( sk14 @ ssList )
| $false ),
inference(rewrite,[status(thm)],[111,2071]) ).
thf(2140,plain,
sk14 @ ssList,
inference(simp,[status(thm)],[2139]) ).
thf(8832,plain,
( ~ $true
| ~ $true
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[656,2130,2071,2120,2140]) ).
thf(8833,plain,
$false,
inference(simp,[status(thm)],[8832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n010.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 13:00:24 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 1.31/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.29/1.63 % [INFO] Parsing done (416ms).
% 2.29/1.65 % [INFO] Running in sequential loop mode.
% 3.26/2.25 % [INFO] eprover registered as external prover.
% 3.26/2.26 % [INFO] Scanning for conjecture ...
% 3.67/2.49 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 4.08/2.65 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 4.58/2.82 % [INFO] Problem is first-order (TPTP FOF).
% 4.58/2.86 % [INFO] Type checking passed.
% 4.58/2.87 % [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 ...
% 38.44/9.24 % [INFO] Killing All external provers ...
% 38.44/9.25 % Time passed: 8647ms (effective reasoning time: 7582ms)
% 38.44/9.25 % 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)>
% 38.44/9.25 % Axioms used in derivation (0):
% 38.44/9.25 % No. of inferences in proof: 54
% 38.44/9.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8647 ms resp. 7582 ms w/o parsing
% 30.45/9.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.45/9.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------