%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU856^5 : 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 : n006.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 08:29:29 AM UTC 2026
% Result : Theorem 11.42s 3.83s
% Output : Refutation 10.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 87 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 581 ( 156 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 940 ( 239 ~; 262 |; 51 &; 388 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 30 ^; 32 !; 0 ?; 64 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk7_decl,type,
sk7: a ).
thf(sk8_decl,type,
sk8: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ( sk1 = A )
!= ( ( ^ [B: a] :
( ( ( A @ B )
& ~ ( sk1 @ B ) )
| ( ( sk1 @ B )
& ~ ( A @ B ) ) ) )
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM46_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1 = sk2 )
!= ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
!= ( sk1 = sk2 ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
| ( sk1 = sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(7,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 != sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
( ( ( sk2 @ sk5 )
& ~ ( sk1 @ sk5 ) )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(13,plain,
( ( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) )
& ( ( sk2 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) )
& ( ~ ( sk1 @ sk5 )
| ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) )
& ( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(37,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(18,plain,
! [B: a,A: a] :
( ~ ( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(28,plain,
! [B: a,A: a] :
( ( ~ ( sk2 @ A )
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) )
& ( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(29,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(6,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= sk1 )
| ( sk2
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(11,plain,
( ( ( ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 ) ),
inference(func_ext,[status(esa)],[6]) ).
thf(55,plain,
( ( sk2 @ sk4 )
| ~ ( ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
| ~ ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(63,plain,
( ( ( sk2 @ sk4 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(65,plain,
( ( sk2 @ sk4 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(66,plain,
( ( sk2 @ sk4 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 ) ),
inference(simp,[status(thm)],[65]) ).
thf(88,plain,
( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[66]) ).
thf(89,plain,
( ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(56,plain,
( ( sk2 @ sk4 )
| ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
| ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(67,plain,
( ( ( sk2 @ sk4 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ( sk2 @ sk4 )
| ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk1 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(68,plain,
( ( sk2 @ sk4 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(72,plain,
( ( sk2 @ sk4 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[68]) ).
thf(113,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[72]) ).
thf(118,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[113]) ).
thf(297,plain,
! [B: a,A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ~ $true
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[118,29]) ).
thf(298,plain,
! [B: a,A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ sk3 )
| ( ( sk2 @ A )
= ( sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( sk3 ))]]) ).
thf(367,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ A )
= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(500,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ A )
| ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ A )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[367,118]) ).
thf(501,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ A )
| ( ( sk2 @ A )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[500]) ).
thf(502,plain,
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( sk3 ))]]) ).
thf(564,plain,
( ( sk1 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[502]) ).
thf(90,plain,
( ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[88]) ).
thf(585,plain,
( ( sk4 != sk3 )
| ( sk2 @ sk3 )
| ~ $true
| ( sk4 != sk3 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[564,90]) ).
thf(586,plain,
( ( sk4 != sk3 )
| ( sk2 @ sk3 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[585]) ).
thf(587,plain,
( ( sk4 != sk3 )
| ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[586:[]]) ).
thf(17,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(31,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk6 )
| ~ ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(581,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk6 )
| ~ $true
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[564,31]) ).
thf(582,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk6 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[581]) ).
thf(602,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk6 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[582]) ).
thf(896,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ $true
| ( sk6 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[587,602]) ).
thf(897,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk6 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[896]) ).
thf(937,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk6 != sk3 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[897]) ).
thf(939,plain,
( ( sk4 != sk3 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[937]) ).
thf(22,plain,
( ( sk2 = sk1 )
| ( sk1
!= ( ^ [A: a] : $false ) )
| ( sk2
!= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,6]) ).
thf(23,plain,
( ( sk2 = sk1 )
| ( sk1
!= ( ^ [A: a] : $false ) )
| ( sk2
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[22:[]]) ).
thf(347,plain,
! [B: a,A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ~ $true
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[72,29]) ).
thf(348,plain,
! [B: a,A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 )
| ( ( sk2 @ A )
= ( sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( sk4 ))]]) ).
thf(362,plain,
! [A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 )
| ( ( sk2 @ A )
= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(827,plain,
! [A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 )
| ( sk1 @ A )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( ( sk2 @ A )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[362,72]) ).
thf(828,plain,
! [A: a] :
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 )
| ( sk1 @ A )
| ( ( sk2 @ A )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[827]) ).
thf(829,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[828:[bind(A,$thf( sk4 ))]]) ).
thf(861,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[829]) ).
thf(245,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[37]) ).
thf(248,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk1 @ sk6 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[245]) ).
thf(117,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(38,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( sk1 @ A ) )
| ( sk1 @ sk7 )
| ( sk2 @ sk8 ) ),
inference(func_ext,[status(esa)],[23]) ).
thf(596,plain,
( ( sk4 != sk3 )
| ( ( ( ( sk2 @ sk3 )
& ~ $true )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[564,11]) ).
thf(597,plain,
( ( sk4 != sk3 )
| ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(598,plain,
( ( sk4 != sk3 )
| ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[597:[]]) ).
thf(32,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(33,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(34,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(1323,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 )
| ( ( $true
& ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[564,598]) ).
thf(1324,plain,
( ( sk4 != sk3 )
| ( ( ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[1323]) ).
thf(1325,plain,
( ( sk4 != sk3 )
| ( ( ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1324:[]]) ).
thf(588,plain,
( ( sk4 != sk3 )
| ~ $true
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[564,17]) ).
thf(589,plain,
( ( sk4 != sk3 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[588]) ).
thf(604,plain,
( ( sk4 != sk3 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[589]) ).
thf(909,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 )
| ~ $true
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[587,604]) ).
thf(910,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(924,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[910]) ).
thf(943,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[924]) ).
thf(35,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[33]) ).
thf(36,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ~ ( sk2 @ sk6 )
| ~ ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(30,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(1551,plain,
$false,
inference(e,[status(thm)],[10,37,29,89,9,939,31,23,564,5,861,14,587,6,248,117,38,598,17,32,34,66,1325,943,3,35,11,72,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU856^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n006.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 14:39:54 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (185ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.04/1.40 % [INFO] eprover registered as external prover.
% 2.04/1.41 % [INFO] Scanning for conjecture ...
% 2.04/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.54 % [INFO] Type checking passed.
% 2.23/1.54 % [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 ...
% 11.42/3.83 % External prover 'e' found a proof!
% 11.42/3.83 % [INFO] Killing All external provers ...
% 11.42/3.83 % Time passed: 3480ms (effective reasoning time: 2829ms)
% 11.42/3.83 % 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)>
% 11.42/3.83 % Axioms used in derivation (0):
% 11.42/3.83 % No. of inferences in proof: 85
% 11.42/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3480 ms resp. 2829 ms w/o parsing
% 10.23/3.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.23/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------