%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET587^5 : 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 : 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 : Wed Sep 30 08:22:58 AM UTC 2026
% Result : Theorem 8.08s 3.30s
% Output : Refutation 7.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 6
% Syntax : Number of formulae : 99 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 506 ( 105 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 818 ( 205 ~; 176 |; 54 &; 363 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 132 ( 80 ^; 47 !; 0 ?; 132 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% 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(sk8_decl,type,
sk8: a ).
thf(sk9_decl,type,
sk9: a ).
thf(sk10_decl,type,
sk10: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( A @ B ) ) )
= ( ^ [B: a] : $false ) )
!= ( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
~ ( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: a] :
~ ( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: a] :
~ ( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 ) )
& ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(15,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(7,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(35,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16,13]) ).
thf(36,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
( ( sk1 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk4 ))]]) ).
thf(73,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk4 )
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,11]) ).
thf(74,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk4 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[74:[]]) ).
thf(17,plain,
( ~ ( sk2 @ sk4 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(84,plain,
( ( sk1 @ sk3 )
| ~ $true
| ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[75,17]) ).
thf(85,plain,
( ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(86,plain,
sk1 @ sk3,
inference(pattern_uni,[status(thm)],[85:[]]) ).
thf(106,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[86,13]) ).
thf(107,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( sk3 ))]]) ).
thf(138,plain,
( ( sk2 @ sk3 )
| ( ( ( ^ [A: a] : $false )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,5]) ).
thf(139,plain,
( ( sk2 @ sk3 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
( ( sk2 @ sk3 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[139:[]]) ).
thf(151,plain,
( ( ( sk2 @ sk3 )
| ( sk1 @ sk8 ) )
& ( ( sk2 @ sk3 )
| ~ ( sk2 @ sk8 ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(152,plain,
( ( sk2 @ sk3 )
| ( sk1 @ sk8 ) ),
inference(cnfConj,[status(thm)],[151]) ).
thf(12,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(21,plain,
( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ~ ( sk2 @ sk3 ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(22,plain,
( ( ( sk1 @ sk5 )
| ~ ( sk2 @ sk3 ) )
& ( ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
( ( sk1 @ sk5 )
| ~ ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(176,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk5 )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,23]) ).
thf(177,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk5 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[177:[]]) ).
thf(191,plain,
( ( sk1 @ sk5 )
| ( ( sk1 @ sk8 )
!= ( sk1 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[178]) ).
thf(194,plain,
( ( sk1 @ sk5 )
| ( sk8 != sk5 ) ),
inference(simp,[status(thm)],[191]) ).
thf(32,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( ( ^ [B: a] : $false )
!= ( ^ [B: a] : $false ) )
| ~ ( sk2 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,12]) ).
thf(33,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[33:[]]) ).
thf(24,plain,
( ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(111,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ sk3 )
| ~ $true
| ~ ( sk2 @ sk3 )
| ( ( sk2 @ A )
!= ( sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[34,24]) ).
thf(112,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ sk3 )
| ( ( sk2 @ A )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( sk5 ))]]) ).
thf(165,plain,
( ( sk1 @ sk8 )
| ~ ( sk1 @ sk5 )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,113]) ).
thf(166,plain,
( ( sk1 @ sk8 )
| ~ ( sk1 @ sk5 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
( ( sk1 @ sk8 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[166:[]]) ).
thf(247,plain,
( ( sk8 != sk5 )
| ( sk1 @ sk8 )
| ~ $true
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[194,167]) ).
thf(248,plain,
( ( sk8 != sk5 )
| ( sk1 @ sk8 )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk5 ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
( ( sk8 != sk5 )
| ( sk1 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[248:[]]) ).
thf(153,plain,
( ( sk2 @ sk3 )
| ~ ( sk2 @ sk8 ) ),
inference(cnfConj,[status(thm)],[151]) ).
thf(25,plain,
( ~ ( sk2 @ sk3 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(27,plain,
( ~ ( sk2 @ sk3 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[25]) ).
thf(162,plain,
( ( sk1 @ sk8 )
| ~ $true
| ( sk5 != sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,27]) ).
thf(163,plain,
( ( sk1 @ sk8 )
| ( sk5 != sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
( ( sk1 @ sk8 )
| ( sk5 != sk3 ) ),
inference(pattern_uni,[status(thm)],[163:[]]) ).
thf(183,plain,
! [A: a] :
( ( sk1 @ sk5 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk8 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[178,13]) ).
thf(184,plain,
! [A: a] :
( ( sk1 @ sk5 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk8 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
( ( sk1 @ sk5 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( sk8 ))]]) ).
thf(256,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ( ( ( ^ [A: a] : $false )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[185,5]) ).
thf(257,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[257:[]]) ).
thf(274,plain,
( ( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ( sk1 @ sk9 ) )
& ( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ~ ( sk2 @ sk9 ) ) ),
inference(cnf,[status(esa)],[258]) ).
thf(275,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk8 )
| ( sk1 @ sk9 ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(168,plain,
( ( sk1 @ sk8 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,12]) ).
thf(169,plain,
( ( sk1 @ sk8 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
( ( sk1 @ sk8 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[169:[]]) ).
thf(452,plain,
( ( ( sk1 @ sk10 )
& ~ ( sk2 @ sk10 ) )
| ( sk1 @ sk8 ) ),
inference(func_ext,[status(esa)],[170]) ).
thf(462,plain,
( ( ( sk1 @ sk10 )
| ( sk1 @ sk8 ) )
& ( ~ ( sk2 @ sk10 )
| ( sk1 @ sk8 ) ) ),
inference(cnf,[status(esa)],[452]) ).
thf(463,plain,
( ( sk1 @ sk10 )
| ( sk1 @ sk8 ) ),
inference(cnfConj,[status(thm)],[462]) ).
thf(244,plain,
( ( sk8 != sk5 )
| ~ $true
| ~ ( sk2 @ sk3 )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[194,113]) ).
thf(245,plain,
( ( sk8 != sk5 )
| ~ ( sk2 @ sk3 )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk5 ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
( ( sk8 != sk5 )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[245:[]]) ).
thf(193,plain,
( ( sk1 @ sk5 )
| ( ( sk1 @ sk8 )
!= ( sk1 @ sk5 ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(28,plain,
! [B: a,A: a] :
( ~ ( ( sk1 @ B )
& ~ ( sk2 @ B ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[13]) ).
thf(41,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ( sk2 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[28]) ).
thf(316,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ $true
| ( sk5 != sk3 )
| ( ( sk2 @ B )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[41,27]) ).
thf(317,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ A )
| ( sk5 != sk3 )
| ( ( sk2 @ B )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [A: a] :
( ~ ( sk1 @ sk3 )
| ~ ( sk1 @ A )
| ( sk2 @ A )
| ( sk5 != sk3 ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(488,plain,
! [A: a] :
( ~ $true
| ~ ( sk1 @ A )
| ( sk2 @ A )
| ( sk5 != sk3 ) ),
inference(rewrite,[status(thm)],[318,86]) ).
thf(489,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[488]) ).
thf(26,plain,
( ~ ( sk2 @ sk3 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(171,plain,
( ( sk1 @ sk8 )
| ~ $true
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,26]) ).
thf(172,plain,
( ( sk1 @ sk8 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
( ( sk1 @ sk8 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[172:[]]) ).
thf(156,plain,
( ( sk1 @ sk8 )
| ~ ( sk2 @ sk5 )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[152,24]) ).
thf(157,plain,
( ( sk1 @ sk8 )
| ~ ( sk2 @ sk5 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
( ( sk1 @ sk8 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[157:[]]) ).
thf(729,plain,
$false,
inference(e,[status(thm)],[249,153,152,164,275,34,27,113,108,194,463,246,178,170,5,185,24,193,489,173,13,41,12,86,3,167,26,158,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587^5 : 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
% 0.10/0.21 % Computer : n009.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:38:15 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.96 % [INFO] Parsing done (178ms).
% 1.23/0.97 % [INFO] Running in sequential loop mode.
% 1.84/1.36 % [INFO] eprover registered as external prover.
% 1.84/1.37 % [INFO] Scanning for conjecture ...
% 2.06/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.50 % [INFO] Type checking passed.
% 2.22/1.51 % [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 ...
% 8.08/3.29 % External prover 'e' found a proof!
% 8.08/3.29 % [INFO] Killing All external provers ...
% 8.08/3.29 % Time passed: 2938ms (effective reasoning time: 2315ms)
% 8.08/3.29 % 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)>
% 8.08/3.29 % Axioms used in derivation (0):
% 8.08/3.29 % No. of inferences in proof: 94
% 8.08/3.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2938 ms resp. 2315 ms w/o parsing
% 7.42/3.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.42/3.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------