%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU854^5 : 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 : n026.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 9.80s 3.66s
% Output : Refutation 8.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 88 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 497 ( 81 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 942 ( 206 ~; 228 |; 49 &; 427 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 25 ^; 59 !; 0 ?; 88 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% 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 > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) ) )
= ( ( ^ [D: a] :
( ( ( C @ D )
& ~ ( A @ D ) )
| ( B @ D ) ) )
= C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ! [C: a] :
( ( sk1 @ C )
=> ( B @ C ) )
& ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) )
=> ( ( ! [C: a] :
( ( sk1 @ C )
=> ( A @ C ) ) )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( sk1 @ C ) )
| ( A @ C ) ) )
= B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
~ ( ( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
& ! [B: a] :
( ( sk2 @ B )
=> ( A @ B ) ) )
=> ( ( ! [B: a] :
( ( sk1 @ B )
=> ( sk2 @ B ) ) )
= ( ( ^ [B: a] :
( ( ( A @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) ) )
= A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
~ ( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) ) )
= ( ( ^ [D: a] :
( ( ( C @ D )
& ~ ( A @ D ) )
| ( B @ D ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM34_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) ) )
= ( ( ^ [D: a] :
( ( ( C @ D )
& ~ ( A @ D ) )
| ( B @ D ) ) )
= C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) ) )
= ( ( ^ [D: a] :
( ( ( C @ D )
& ~ ( A @ D ) )
| ( B @ D ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: a,A: a] :
( ( ~ ( sk1 @ A )
| ( sk3 @ A ) )
& ( ~ ( sk2 @ B )
| ( sk3 @ B ) )
& ( ( ! [C: a] :
( ( sk1 @ C )
=> ( sk2 @ C ) ) )
!= ( ( ^ [C: a] :
( ( ( sk3 @ C )
& ~ ( sk1 @ C ) )
| ( sk2 @ C ) ) )
= sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
= sk3 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
( ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
( ( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 )
| ( sk1 @ sk4 ) )
& ( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 )
| ~ ( sk2 @ sk4 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(16,plain,
( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(19,plain,
( ( ( ( ( sk3 @ sk6 )
& ~ ( sk1 @ sk6 ) )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 ) ),
inference(func_ext,[status(esa)],[16]) ).
thf(22,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ( $true
& ~ ( sk1 @ sk6 ) )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5,19]) ).
thf(23,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
( ~ ( sk1 @ sk6 )
| ( ( ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk6 ))]]) ).
thf(11,plain,
( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
= sk3 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(13,plain,
( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
= sk3 )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) ) )
= sk3 )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(52,plain,
! [B: a,A: a] :
( ( ( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) )
= ( sk3 @ B ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(15,plain,
( ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= sk3 )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
( ( ( ( ( sk3 @ sk5 )
& ~ ( sk1 @ sk5 ) )
| ( sk2 @ sk5 ) )
!= ( sk3 @ sk5 ) )
| ( sk1 @ sk4 ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(70,plain,
( ( sk1 @ sk4 )
| ( ( sk3 @ sk5 )
& ~ ( sk1 @ sk5 ) )
| ( sk2 @ sk5 )
| ( sk3 @ sk5 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(84,plain,
( ( ( sk1 @ sk4 )
| ( sk3 @ sk5 )
| ( sk2 @ sk5 )
| ( sk3 @ sk5 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk3 @ sk5 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(85,plain,
( ( sk1 @ sk4 )
| ( sk3 @ sk5 )
| ( sk2 @ sk5 )
| ( sk3 @ sk5 ) ),
inference(cnfConj,[status(thm)],[84]) ).
thf(87,plain,
( ( sk1 @ sk4 )
| ( sk3 @ sk5 )
| ( sk2 @ sk5 ) ),
inference(simp,[status(thm)],[85]) ).
thf(69,plain,
( ( sk1 @ sk4 )
| ~ ( ( ( sk3 @ sk5 )
& ~ ( sk1 @ sk5 ) )
| ( sk2 @ sk5 ) )
| ~ ( sk3 @ sk5 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(80,plain,
( ( ( sk1 @ sk4 )
| ~ ( sk3 @ sk5 )
| ( sk1 @ sk5 )
| ~ ( sk3 @ sk5 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk5 )
| ~ ( sk3 @ sk5 ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(81,plain,
( ( sk1 @ sk4 )
| ~ ( sk3 @ sk5 )
| ( sk1 @ sk5 )
| ~ ( sk3 @ sk5 ) ),
inference(cnfConj,[status(thm)],[80]) ).
thf(83,plain,
( ( sk1 @ sk4 )
| ~ ( sk3 @ sk5 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[81]) ).
thf(131,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( sk1 @ sk4 )
| ~ $true
| ( sk1 @ sk5 )
| ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[87,83]) ).
thf(132,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[132:[]]) ).
thf(6,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(82,plain,
( ( sk1 @ sk4 )
| ~ ( sk2 @ sk5 )
| ~ ( sk3 @ sk5 ) ),
inference(cnfConj,[status(thm)],[80]) ).
thf(121,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk5 )
| ~ $true
| ( ( sk3 @ A )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8,82]) ).
thf(122,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk5 )
| ( ( sk3 @ A )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
( ~ ( sk2 @ sk5 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk5 ))]]) ).
thf(125,plain,
( ~ ( sk2 @ sk5 )
| ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[123]) ).
thf(193,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk5 )
| ~ $true
| ( sk1 @ sk4 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[133,125]) ).
thf(194,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk5 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[194:[]]) ).
thf(251,plain,
( ( sk1 @ sk4 )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[195]) ).
thf(256,plain,
( ( sk1 @ sk4 )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[251]) ).
thf(263,plain,
! [A: a] :
( ( sk5 != sk4 )
| ~ $true
| ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[256,5]) ).
thf(264,plain,
! [A: a] :
( ( sk5 != sk4 )
| ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
( ( sk5 != sk4 )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( sk4 ))]]) ).
thf(21,plain,
( ~ ( sk2 @ sk4 )
| ( ( sk3 @ sk6 )
& ~ ( sk1 @ sk6 ) )
| ( sk2 @ sk6 )
| ( sk3 @ sk6 ) ),
inference(bool_ext,[status(thm)],[19]) ).
thf(32,plain,
( ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk6 )
| ( sk2 @ sk6 )
| ( sk3 @ sk6 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 )
| ( sk3 @ sk6 ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(33,plain,
( ~ ( sk2 @ sk4 )
| ( sk3 @ sk6 )
| ( sk2 @ sk6 )
| ( sk3 @ sk6 ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(35,plain,
( ~ ( sk2 @ sk4 )
| ( sk3 @ sk6 )
| ( sk2 @ sk6 ) ),
inference(simp,[status(thm)],[33]) ).
thf(36,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ( ( ( $true
& ~ ( sk1 @ sk6 ) )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[35,19]) ).
thf(37,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ( ( ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ( ( ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 ) )
!= ( sk3 @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[37:[]]) ).
thf(243,plain,
! [A: a] :
( ( sk1 @ sk4 )
| ( ( ^ [B: a] :
( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) ) )
= sk3 )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,17]) ).
thf(244,plain,
! [A: a] :
( ( sk1 @ sk4 )
| ( ( ^ [B: a] :
( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) ) )
= sk3 )
| ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(245,plain,
( ( sk1 @ sk4 )
| ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
= sk3 )
| ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( sk5 ))]]) ).
thf(622,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( sk3 != sk3 )
| ( sk1 @ sk4 )
| ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[245,15]) ).
thf(623,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( ( sk3 @ A )
& ~ ( sk1 @ A ) )
| ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[622]) ).
thf(624,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[623:[]]) ).
thf(660,plain,
( ( sk1 @ sk4 )
| ~ $true
| ( sk1 @ sk4 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[624,125]) ).
thf(661,plain,
( ( sk1 @ sk4 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[660]) ).
thf(662,plain,
sk1 @ sk4,
inference(pattern_uni,[status(thm)],[661:[]]) ).
thf(330,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk1 @ sk6 )
| ( ( sk3 @ B )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 )
| ( ( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
| ( sk2 @ B ) )
!= ( ~ ( sk1 @ sk6 )
| ( sk2 @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,24]) ).
thf(406,plain,
! [B: a,A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk1 @ sk6 )
| ( ( sk3 @ B )
!= ( sk3 @ sk6 ) )
| ~ ( sk2 @ sk4 )
| ( ( ( sk3 @ B )
& ~ ( sk1 @ B ) )
!= ( ~ ( sk1 @ sk6 ) ) )
| ( ( sk2 @ B )
!= ( sk2 @ sk6 ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(20,plain,
( ~ ( sk2 @ sk4 )
| ~ ( ( ( sk3 @ sk6 )
& ~ ( sk1 @ sk6 ) )
| ( sk2 @ sk6 ) )
| ~ ( sk3 @ sk6 ) ),
inference(bool_ext,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk6 )
| ( sk1 @ sk6 )
| ~ ( sk3 @ sk6 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk6 )
| ~ ( sk3 @ sk6 ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(30,plain,
( ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk6 )
| ~ ( sk3 @ sk6 ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(45,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk6 )
| ~ $true
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[8,30]) ).
thf(46,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk6 )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
( ~ ( sk2 @ sk6 )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk6 ))]]) ).
thf(48,plain,
( ~ ( sk2 @ sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[47]) ).
thf(29,plain,
( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk6 )
| ( sk1 @ sk6 )
| ~ ( sk3 @ sk6 ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(31,plain,
( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(simp,[status(thm)],[29]) ).
thf(91,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ~ ( sk2 @ sk4 )
| ~ $true
| ( sk1 @ sk6 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[35,31]) ).
thf(92,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
( ~ ( sk2 @ sk4 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[92:[]]) ).
thf(152,plain,
( ~ ( sk2 @ sk4 )
| ( sk1 @ sk6 )
| ~ $true
| ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[93,48]) ).
thf(153,plain,
( ~ ( sk2 @ sk4 )
| ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk6 ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
( ~ ( sk2 @ sk4 )
| ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[153:[]]) ).
thf(49,plain,
( ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[48]) ).
thf(50,plain,
( ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
( ~ ( sk2 @ sk4 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[49]) ).
thf(893,plain,
$false,
inference(e,[status(thm)],[5,24,52,265,38,9,662,17,406,48,154,8,3,35,50,16,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU854^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.22 % Computer : n026.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:42:57 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (186ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.97/1.40 % [INFO] eprover registered as external prover.
% 1.97/1.41 % [INFO] Scanning for conjecture ...
% 1.97/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.13/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.13/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.54 % [INFO] Type checking passed.
% 2.13/1.55 % [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 ...
% 9.80/3.65 % External prover 'e' found a proof!
% 9.80/3.65 % [INFO] Killing All external provers ...
% 9.80/3.65 % Time passed: 3296ms (effective reasoning time: 2645ms)
% 9.80/3.65 % 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)>
% 9.80/3.65 % Axioms used in derivation (0):
% 9.80/3.65 % No. of inferences in proof: 84
% 9.80/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3296 ms resp. 2645 ms w/o parsing
% 8.84/3.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.84/3.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------