%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO264^5 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:45:30 AM UTC 2026
% Result : Theorem 52.92s 12.68s
% Output : Refutation 43.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of formulae : 125 ( 36 unt; 0 typ; 5 def)
% Number of atoms : 438 ( 97 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1258 ( 318 ~; 238 |; 28 &; 674 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 317 ( 91 ^; 207 !; 14 ?; 317 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk6_decl,type,
sk6: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( E @ A )
| ( F @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) )
& ! [G: $i] :
( ( F @ G )
= ( ~ ( D @ G ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i > $o] :
? [D: $i > $o,E: $i > $o] :
( ( ( D @ sk1 )
| ( E @ sk1 ) )
& ( ( C @ A )
| ( E @ A ) )
& ( ( D @ B )
| ~ ( C @ B ) )
& ! [F: $i] :
( ( E @ F )
= ( ~ ( C @ F ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i > $o] :
? [C: $i > $o,D: $i > $o] :
( ( ( C @ sk1 )
| ( D @ sk1 ) )
& ( ( B @ sk2 )
| ( D @ sk2 ) )
& ( ( C @ A )
| ~ ( B @ A ) )
& ! [E: $i] :
( ( D @ E )
= ( ~ ( B @ E ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ? [B: $i > $o,C: $i > $o] :
( ( ( B @ sk1 )
| ( C @ sk1 ) )
& ( ( A @ sk2 )
| ( C @ sk2 ) )
& ( ( B @ sk3 )
| ~ ( A @ sk3 ) )
& ! [D: $i] :
( ( C @ D )
= ( ~ ( A @ D ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i > $o,B: $i > $o] :
@+[C: $i] :
( ( A @ C )
!= ( ~ ( sk4 @ C ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( E @ A )
| ( F @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) )
& ! [G: $i] :
( ( F @ G )
= ( ~ ( D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM125C) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( E @ A )
| ( F @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) )
& ! [G: $i] :
( ( F @ G )
= ( ~ ( D @ G ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i,C: $i,D: $i > $o] :
? [E: $i > $o,F: $i > $o] :
( ( ( E @ A )
| ( F @ A ) )
& ( ( D @ B )
| ( F @ B ) )
& ( ( E @ C )
| ~ ( D @ C ) )
& ! [G: $i] :
( ( F @ G )
= ( ~ ( D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i > $o] :
( ( ~ ( A @ sk1 )
| ~ ( sk5 @ B @ A ) )
& ( ~ ( B @ sk1 )
| ~ ( sk5 @ B @ A ) )
& ( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ~ ( A @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) )
& ( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ( sk4 @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) )
& ( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ~ ( A @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) )
& ( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ~ ( sk5 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(32,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [C: $i] :
~ ( B @ C ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(38,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [C: $i] :
~ ( B @ C ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(39,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [C: $i] :
~ ( B @ C ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(6,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(17,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(27,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ~ ( sk5
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(28,plain,
! [B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ~ ( sk5
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ),
inference(simp,[status(thm)],[27]) ).
thf(36,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( sk5 @ A
@ ^ [B: $i] : $true ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [C: $i] : $true ))]]) ).
thf(46,plain,
! [A: $i > $o] :
~ ( sk5 @ A
@ ^ [B: $i] : $true ),
inference(simp,[status(thm)],[36]) ).
thf(87,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk5
@ ^ [D: $i] :
~ ( B @ D )
@ A )
| ~ $true
| ( ( B @ sk1 )
!= ( sk5 @ C
@ ^ [D: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[28,46]) ).
thf(88,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk5
@ ^ [D: $i] :
~ ( B @ D )
@ A )
| ( ( B @ sk1 )
!= ( sk5 @ C
@ ^ [D: $i] : $true ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(112,plain,
! [B: $i > $i > $o,A: $i > $o] :
~ ( sk5
@ ^ [C: $i] :
~ ( sk5 @ ( B @ C )
@ ^ [D: $i] : $true )
@ A ),
inference(pre_uni,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( sk5 @ ( D @ E ) @ ^ [F: $i] : $true ) )),bind(C,$thf( D @ sk1 ))]]) ).
thf(134,plain,
! [B: $i > $i > $o,A: $i > $o] :
~ ( sk5
@ ^ [C: $i] :
~ ( sk5 @ ( B @ C )
@ ^ [D: $i] : $true )
@ A ),
inference(simp,[status(thm)],[112]) ).
thf(167,plain,
! [A: $i > $o] :
~ ( sk5
@ ^ [B: $i] : ~ $false
@ A ),
inference(rewrite,[status(thm)],[134,46]) ).
thf(168,plain,
! [A: $i > $o] :
~ ( sk5
@ ^ [B: $i] : $true
@ A ),
inference(simp,[status(thm)],[167]) ).
thf(577,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk5 @ A
@ ^ [D: $i] :
~ ( B @ D ) )
| ~ $true
| ( ( B @ sk1 )
!= ( sk5
@ ^ [D: $i] : $true
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[39,168]) ).
thf(578,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk5 @ A
@ ^ [D: $i] :
~ ( B @ D ) )
| ( ( B @ sk1 )
!= ( sk5
@ ^ [D: $i] : $true
@ C ) ) ),
inference(simp,[status(thm)],[577]) ).
thf(601,plain,
! [B: $i > $i > $o,A: $i > $o] :
~ ( sk5 @ A
@ ^ [C: $i] :
~ ( sk5
@ ^ [D: $i] : $true
@ ( B @ C ) ) ),
inference(pre_uni,[status(thm)],[578:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( sk5 @ ^ [F: $i] : $true @ ( E @ E ) ) )),bind(C,$thf( E @ sk1 ))]]) ).
thf(638,plain,
! [B: $i > $i > $o,A: $i > $o] :
~ ( sk5 @ A
@ ^ [C: $i] :
~ ( sk5
@ ^ [D: $i] : $true
@ ( B @ C ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(877,plain,
! [A: $i > $o] :
~ ( sk5 @ A
@ ^ [B: $i] : ~ $false ),
inference(rewrite,[status(thm)],[638,168]) ).
thf(878,plain,
! [A: $i > $o] :
~ ( sk5 @ A
@ ^ [B: $i] : $true ),
inference(simp,[status(thm)],[877]) ).
thf(7,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ~ ( A @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ~ ( A @ sk3 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
! [C: $i > $i > $o,B: $i > $i > $o,A: $i > $o] :
( ~ ( sk5 @ ( B @ sk1 ) @ ( C @ sk1 ) )
| ~ ( sk5
@ ^ [D: $i] : ( sk5 @ ( B @ D ) @ ( C @ D ) )
@ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( sk5 @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(29,plain,
! [C: $i > $i > $o,B: $i > $i > $o,A: $i > $o] :
( ~ ( sk5 @ ( B @ sk1 ) @ ( C @ sk1 ) )
| ~ ( sk5
@ ^ [D: $i] : ( sk5 @ ( B @ D ) @ ( C @ D ) )
@ A ) ),
inference(simp,[status(thm)],[18]) ).
thf(111,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [C: $i] :
~ ~ ( B @ C )
@ A ) ),
inference(prim_subst,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(132,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [C: $i] :
~ ~ ( B @ C )
@ A ) ),
inference(cnf,[status(esa)],[111]) ).
thf(133,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ B @ A ) ),
inference(simp,[status(thm)],[132]) ).
thf(9,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ( sk4 @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ( sk4 @ sk3 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(10,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(655,plain,
! [A: $i > $o] :
( ( sk4 @ sk3 )
| ~ ~ ( sk4 @ sk2 )
| ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ A ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ~ ( sk4 @ C ) ))]]) ).
thf(821,plain,
! [A: $i > $o] :
( ( sk4 @ sk3 )
| ( sk4 @ sk2 )
| ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ A ) ),
inference(cnf,[status(esa)],[655]) ).
thf(1361,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk3 )
| ( sk4 @ sk2 )
| ~ $true
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ A )
!= ( sk5 @ B
@ ^ [C: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[821,878]) ).
thf(1362,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk3 )
| ( sk4 @ sk2 )
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ A )
!= ( sk5 @ B
@ ^ [C: $i] : $true ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1363,plain,
( ( sk4 @ sk3 )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( ^ [C: $i] : $true )),bind(B,$thf( ^ [C: $i] : ~ ( sk4 @ C ) ))]]) ).
thf(1727,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ~ $true
| ( ( sk4 @ sk3 )
!= ( A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1363,14]) ).
thf(1728,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( B @ sk2 )
| ( ( sk4 @ sk3 )
!= ( A @ sk3 ) ) ),
inference(simp,[status(thm)],[1727]) ).
thf(1762,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( A @ ( sk6 @ A @ sk4 ) )
!= ( ~ ( sk4 @ ( sk6 @ A @ sk4 ) ) ) )
| ( sk5 @ A @ sk4 )
| ~ ( A @ sk2 ) ),
inference(pre_uni,[status(thm)],[1728:[bind(A,$thf( sk4 )),bind(B,$thf( B ))]]) ).
thf(1764,plain,
( ~ ~ ( sk4 @ sk2 )
| ( sk5
@ ^ [A: $i] :
~ ( sk4 @ A )
@ sk4 )
| ( sk4 @ sk2 ) ),
inference(pre_uni,[status(thm)],[1762:[bind(A,$thf( ^ [B: $i] : ~ ( sk4 @ B ) ))]]) ).
thf(1934,plain,
( ( sk4 @ sk2 )
| ( sk5
@ ^ [A: $i] :
~ ( sk4 @ A )
@ sk4 )
| ( sk4 @ sk2 ) ),
inference(cnf,[status(esa)],[1764]) ).
thf(1935,plain,
( ( sk4 @ sk2 )
| ( sk5
@ ^ [A: $i] :
~ ( sk4 @ A )
@ sk4 ) ),
inference(simp,[status(thm)],[1934]) ).
thf(2020,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ( B @ sk1 )
| ~ $true
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ sk4 )
!= ( sk5
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[1935,28]) ).
thf(2021,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ( B @ sk1 )
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ sk4 )
!= ( sk5
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ),
inference(simp,[status(thm)],[2020]) ).
thf(2022,plain,
( ( sk4 @ sk2 )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2021:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(2300,plain,
( ( sk4 @ sk1 )
| ( ( sk4 @ sk2 )
!= ( sk4 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2022]) ).
thf(2322,plain,
( ( sk4 @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2300]) ).
thf(2666,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk2 != sk1 )
| ~ $true
| ~ ( sk5 @ B @ A )
| ( ( sk4 @ sk1 )
!= ( B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2322,133]) ).
thf(2667,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk2 != sk1 )
| ~ ( sk5 @ B @ A )
| ( ( sk4 @ sk1 )
!= ( B @ sk1 ) ) ),
inference(simp,[status(thm)],[2666]) ).
thf(2734,plain,
! [A: $i > $o] :
( ( sk2 != sk1 )
| ~ ( sk5 @ sk4 @ A ) ),
inference(pre_uni,[status(thm)],[2667:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(725,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 )
| ~ $true
| ( ( sk5 @ B @ A )
!= ( sk5
@ ^ [D: $i] : $true
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,168]) ).
thf(726,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ~ ( B @ sk2 )
| ( sk4 @ sk3 )
| ( ( sk5 @ B @ A )
!= ( sk5
@ ^ [D: $i] : $true
@ C ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(727,plain,
! [A: $i > $o] :
( ~ ~ ( sk4
@ ( sk6
@ ^ [B: $i] : $true
@ A ) )
| ~ $true
| ( sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $true )),bind(C,$thf( A ))]]) ).
thf(857,plain,
! [A: $i > $o] :
( ( sk4
@ ( sk6
@ ^ [B: $i] : $true
@ A ) )
| ~ $true
| ( sk4 @ sk3 ) ),
inference(cnf,[status(esa)],[727]) ).
thf(858,plain,
! [A: $i > $o] :
( ( sk4
@ ( sk6
@ ^ [B: $i] : $true
@ A ) )
| ( sk4 @ sk3 ) ),
inference(simp,[status(thm)],[857]) ).
thf(1491,plain,
( ( sk4 @ sk2 )
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1363]) ).
thf(1505,plain,
( ( sk4 @ sk2 )
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[1491]) ).
thf(1506,plain,
( ( sk4 @ sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[1491]) ).
thf(1513,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk3 != sk2 )
| ~ $true
| ~ ( sk5 @ B @ A )
| ( ( sk4 @ sk2 )
!= ( B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1506,133]) ).
thf(1514,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk3 != sk2 )
| ~ ( sk5 @ B @ A )
| ( ( sk4 @ sk2 )
!= ( B @ sk1 ) ) ),
inference(simp,[status(thm)],[1513]) ).
thf(1565,plain,
! [A: $i > $o] :
( ( sk3 != sk2 )
| ~ ( sk5
@ ^ [B: $i] : ( sk4 @ sk2 )
@ A ) ),
inference(pre_uni,[status(thm)],[1514:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk4 @ sk2 ) ))]]) ).
thf(591,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [C: $i] :
~ ~ ( B @ C ) ) ),
inference(prim_subst,[status(thm)],[39:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(631,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [C: $i] :
~ ~ ( B @ C ) ) ),
inference(cnf,[status(esa)],[591]) ).
thf(632,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ A @ B ) ),
inference(simp,[status(thm)],[631]) ).
thf(1550,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk3 != sk2 )
| ~ $true
| ~ ( sk5 @ A @ B )
| ( ( sk4 @ sk2 )
!= ( B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1506,632]) ).
thf(1551,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk3 != sk2 )
| ~ ( sk5 @ A @ B )
| ( ( sk4 @ sk2 )
!= ( B @ sk1 ) ) ),
inference(simp,[status(thm)],[1550]) ).
thf(1559,plain,
! [A: $i > $o] :
( ( sk3 != sk2 )
| ~ ( sk5 @ A
@ ^ [B: $i] : ( sk4 @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[1551:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( sk4 @ sk2 ) ))]]) ).
thf(1978,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ~ $true
| ( ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ sk4 )
!= ( sk5 @ A
@ ^ [B: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[1935,878]) ).
thf(1979,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ sk4 )
!= ( sk5 @ A
@ ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[1978]) ).
thf(2046,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( ^ [B: $i] :
~ ( sk4 @ B ) )
!= A )
| ( sk4
!= ( ^ [B: $i] : $true ) ) ),
inference(simp,[status(thm)],[1979]) ).
thf(2076,plain,
( ( sk4 @ sk2 )
| ( sk4
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[2046]) ).
thf(2423,plain,
( ~ ( sk4 @ sk7 )
| ( sk4 @ sk2 ) ),
inference(func_ext,[status(esa)],[2076]) ).
thf(2780,plain,
( ( sk4 @ sk2 )
| ~ $true
| ( sk4 @ sk2 )
| ( ( sk4 @ sk7 )
!= ( sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1363,2423]) ).
thf(2781,plain,
( ( sk4 @ sk2 )
| ( ( sk4 @ sk7 )
!= ( sk4 @ sk3 ) ) ),
inference(simp,[status(thm)],[2780]) ).
thf(2787,plain,
( ( sk4 @ sk2 )
| ( sk7 != sk3 ) ),
inference(simp,[status(thm)],[2781]) ).
thf(31,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ( ( sk5 @ B @ A )
!= ( A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(37,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( A @ sk1 )
| ( ( sk5 @ B @ A )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(16,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( ( B @ sk1 )
| ( C @ sk1 ) )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(22,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) )
& ( ~ ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(23,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(25,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(15,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ( ( sk5 @ B @ A )
!= ( B @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(21,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ( ( sk5 @ B @ A )
!= ( B @ sk1 ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(2006,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ~ ( A @ sk1 )
| ~ $true
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ sk4 )
!= ( sk5 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1935,8]) ).
thf(2007,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk4 @ sk2 )
| ~ ( A @ sk1 )
| ( ( sk5
@ ^ [C: $i] :
~ ( sk4 @ C )
@ sk4 )
!= ( sk5 @ B @ A ) ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2008,plain,
( ( sk4 @ sk2 )
| ~ ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2007:[bind(A,$thf( sk4 )),bind(B,$thf( ^ [C: $i] : ~ ( sk4 @ C ) ))]]) ).
thf(2139,plain,
( ( sk4 @ sk2 )
| ( sk4 @ sk2 )
| ~ $true
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1363,2008]) ).
thf(2140,plain,
( ( sk4 @ sk2 )
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[2139]) ).
thf(2166,plain,
( ( sk4 @ sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[2140]) ).
thf(2009,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ~ $true
| ( ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ sk4 )
!= ( sk5
@ ^ [B: $i] : $true
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[1935,168]) ).
thf(2010,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( sk5
@ ^ [B: $i] :
~ ( sk4 @ B )
@ sk4 )
!= ( sk5
@ ^ [B: $i] : $true
@ A ) ) ),
inference(simp,[status(thm)],[2009]) ).
thf(2043,plain,
! [A: $i > $o] :
( ( sk4 @ sk2 )
| ( ( ^ [B: $i] :
~ ( sk4 @ B ) )
!= ( ^ [B: $i] : $true ) )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[2010]) ).
thf(2075,plain,
( ( sk4 @ sk2 )
| ( ( ^ [A: $i] :
~ ( sk4 @ A ) )
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[2043]) ).
thf(109,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
~ ( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(prim_subst,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(129,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
~ ( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(cnf,[status(esa)],[109]) ).
thf(130,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( B @ sk1 )
| ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
~ ( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(simp,[status(thm)],[129]) ).
thf(956,plain,
! [A: $i > $o] :
( ( sk4 @ sk3 )
| ( ( sk4
@ ( sk6
@ ^ [B: $i] : $true
@ A ) )
!= ( sk4 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[858]) ).
thf(959,plain,
! [A: $i > $o] :
( ( sk4 @ sk3 )
| ( ( sk4
@ ( sk6
@ ^ [B: $i] : $true
@ A ) )
!= ( sk4 @ sk3 ) ) ),
inference(simp,[status(thm)],[956]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ~ ( A @ sk3 )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( sk4 @ ( sk6 @ B @ A ) ) ) )
| ( sk5 @ B @ A )
| ~ ( sk4 @ sk2 )
| ~ ( A @ sk3 ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(2703,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk2 != sk1 )
| ~ $true
| ~ ( sk5 @ A @ B )
| ( ( sk4 @ sk1 )
!= ( B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2322,632]) ).
thf(2704,plain,
! [B: $i > $o,A: $i > $o] :
( ( sk2 != sk1 )
| ~ ( sk5 @ A @ B )
| ( ( sk4 @ sk1 )
!= ( B @ sk1 ) ) ),
inference(simp,[status(thm)],[2703]) ).
thf(2728,plain,
! [A: $i > $o] :
( ( sk2 != sk1 )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pre_uni,[status(thm)],[2704:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(34,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( ( B @ sk1 )
| ( C @ sk1 ) )
| ~ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(40,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ( ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) )
& ( ~ ( C @ sk1 )
| ~ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(41,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(43,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( B @ sk1 )
| ~ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(2705,plain,
( ( sk2 != sk1 )
| ( sk4 @ sk2 )
| ~ $true
| ( ( sk4 @ sk1 )
!= ( sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2322,2008]) ).
thf(2706,plain,
( ( sk2 != sk1 )
| ( sk4 @ sk2 )
| ( ( sk4 @ sk1 )
!= ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[2705]) ).
thf(2707,plain,
( ( sk2 != sk1 )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2706:[]]) ).
thf(24,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(26,plain,
! [C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( C @ sk1 )
| ~ ( sk5
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) )
@ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(960,plain,
! [A: $i > $o] :
( ( sk4 @ sk3 )
| ( ( sk6
@ ^ [B: $i] : $true
@ A )
!= sk3 ) ),
inference(simp,[status(thm)],[956]) ).
thf(7983,plain,
$false,
inference(e,[status(thm)],[878,14,29,133,6,13,2734,39,858,2322,8,1505,1565,1559,2787,1935,37,25,28,21,2076,2423,12,2166,2075,130,959,2022,3,1506,11,2728,43,2707,26,632,168,2008,1363,960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO264^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:44:52 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.05/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.05 % [INFO] Parsing done (188ms).
% 1.45/1.06 % [INFO] Running in sequential loop mode.
% 2.00/1.47 % [INFO] eprover registered as external prover.
% 2.00/1.48 % [INFO] Scanning for conjecture ...
% 2.21/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.38/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.38/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.38/1.62 % [INFO] Type checking passed.
% 2.38/1.62 % [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 ...
% 52.92/12.67 % External prover 'e' found a proof!
% 52.92/12.67 % [INFO] Killing All external provers ...
% 52.92/12.68 % Time passed: 12273ms (effective reasoning time: 11607ms)
% 52.92/12.68 % 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)>
% 52.92/12.68 % Axioms used in derivation (0):
% 52.92/12.68 % No. of inferences in proof: 120
% 52.92/12.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12273 ms resp. 11607 ms w/o parsing
% 43.59/12.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.59/12.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------