%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU855^5 : 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 08:29:29 AM UTC 2026
% Result : Theorem 11.73s 4.59s
% Output : Refutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 6
% Syntax : Number of formulae : 90 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 483 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 843 ( 174 ~; 146 |; 98 &; 389 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 142 ( 72 ^; 65 !; 0 ?; 142 :)
% ( 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 > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk9_decl,type,
sk9: 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] :
( ( A @ D )
& ( C @ D )
& ~ ( B @ D ) ) )
= ( ^ [D: a] : $false ) ) ) ) ) ) ).
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] :
( ( sk1 @ C )
& ( B @ C )
& ~ ( A @ C ) ) )
= ( ^ [C: a] : $false ) ) ) ) ) ) ).
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] :
( ( sk1 @ B )
& ( A @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[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 > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ! [D: a] :
( ( B @ D )
=> ( C @ D ) ) )
=> ( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) ) )
= ( ( ^ [D: a] :
( ( A @ D )
& ( C @ D )
& ~ ( B @ D ) ) )
= ( ^ [D: a] : $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM33_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] :
( ( A @ D )
& ( C @ D )
& ~ ( B @ D ) ) )
= ( ^ [D: a] : $false ) ) ) ),
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] :
( ( A @ D )
& ( C @ D )
& ~ ( B @ D ) ) )
= ( ^ [D: a] : $false ) ) ) ),
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] :
( ( sk1 @ C )
& ( sk3 @ C )
& ~ ( sk2 @ C ) ) )
= ( ^ [C: a] : $false ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
( ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
( ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk4 ) )
& ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk4 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(15,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
( ( ( sk1 @ sk5 )
& ( sk3 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( sk1 @ sk4 ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(19,plain,
( ( ( sk1 @ sk5 )
| ( sk1 @ sk4 ) )
& ( ( sk3 @ sk5 )
| ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk5 )
| ( sk1 @ sk4 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
( ( sk1 @ sk5 )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(11,plain,
( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(13,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(38,plain,
! [A: a] :
( ( sk1 @ sk4 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(39,plain,
! [A: a] :
( ( sk1 @ sk4 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
( ( sk1 @ sk4 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk5 ))]]) ).
thf(100,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk4 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(101,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[101:[]]) ).
thf(22,plain,
( ~ ( sk2 @ sk5 )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(149,plain,
( ( sk1 @ sk4 )
| ~ $true
| ( sk1 @ sk4 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[102,22]) ).
thf(150,plain,
( ( sk1 @ sk4 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
sk1 @ sk4,
inference(pattern_uni,[status(thm)],[150:[]]) ).
thf(173,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,17]) ).
thf(174,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(175,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( sk4 ))]]) ).
thf(188,plain,
( ( sk2 @ sk4 )
| ( ( ( ^ [A: a] : $false )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,9]) ).
thf(189,plain,
( ( sk2 @ sk4 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(190,plain,
( ( sk2 @ sk4 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[189:[]]) ).
thf(201,plain,
( ( ( sk2 @ sk4 )
| ( sk1 @ sk9 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk2 @ sk9 ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(202,plain,
( ( sk2 @ sk4 )
| ( sk1 @ sk9 ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(16,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(23,plain,
( ( ( sk1 @ sk6 )
& ( sk3 @ sk6 )
& ~ ( sk2 @ sk6 ) )
| ~ ( sk2 @ sk4 ) ),
inference(func_ext,[status(esa)],[16]) ).
thf(24,plain,
( ( ( sk1 @ sk6 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk3 @ sk6 )
| ~ ( sk2 @ sk4 ) )
& ( ~ ( sk2 @ sk6 )
| ~ ( sk2 @ sk4 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(27,plain,
( ~ ( sk2 @ sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
( ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(30,plain,
( ~ ( sk2 @ sk4 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[28]) ).
thf(232,plain,
( ( sk1 @ sk9 )
| ~ $true
| ( sk6 != sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[202,30]) ).
thf(233,plain,
( ( sk1 @ sk9 )
| ( sk6 != sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(234,plain,
( ( sk1 @ sk9 )
| ( sk6 != sk4 ) ),
inference(pattern_uni,[status(thm)],[233:[]]) ).
thf(209,plain,
( ( sk1 @ sk9 )
| ~ ( sk2 @ sk6 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[202,27]) ).
thf(210,plain,
( ( sk1 @ sk9 )
| ~ ( sk2 @ sk6 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
( ( sk1 @ sk9 )
| ~ ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[210:[]]) ).
thf(25,plain,
( ( sk1 @ sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(204,plain,
( ( sk1 @ sk9 )
| ( sk1 @ sk6 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[202,25]) ).
thf(205,plain,
( ( sk1 @ sk9 )
| ( sk1 @ sk6 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
( ( sk1 @ sk9 )
| ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[205:[]]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(246,plain,
! [A: a] :
( ( sk1 @ sk6 )
| ~ $true
| ( sk3 @ A )
| ( ( sk1 @ sk9 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[206,5]) ).
thf(247,plain,
! [A: a] :
( ( sk1 @ sk6 )
| ( sk3 @ A )
| ( ( sk1 @ sk9 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
( ( sk1 @ sk6 )
| ( sk3 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( sk9 ))]]) ).
thf(203,plain,
( ( sk2 @ sk4 )
| ~ ( sk2 @ sk9 ) ),
inference(cnfConj,[status(thm)],[201]) ).
thf(26,plain,
( ( sk3 @ sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[24]) ).
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(215,plain,
( ( sk1 @ sk9 )
| ( sk3 @ sk6 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[202,26]) ).
thf(216,plain,
( ( sk1 @ sk9 )
| ( sk3 @ sk6 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
( ( sk1 @ sk9 )
| ( sk3 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[216:[]]) ).
thf(254,plain,
( ( sk1 @ sk6 )
| ( ( sk1 @ sk9 )
!= ( sk1 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[206]) ).
thf(257,plain,
( ( sk1 @ sk6 )
| ( sk9 != sk6 ) ),
inference(simp,[status(thm)],[254]) ).
thf(44,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( ( ^ [B: a] : $false )
!= ( ^ [B: a] : $false ) )
| ~ ( sk2 @ sk4 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,16]) ).
thf(45,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk4 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[45:[]]) ).
thf(29,plain,
( ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(76,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( ( sk2 @ A )
!= ( sk2 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[46,29]) ).
thf(77,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ sk4 )
| ( ( sk2 @ A )
!= ( sk2 @ sk6 ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(78,plain,
( ~ ( sk1 @ sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( sk6 ))]]) ).
thf(170,plain,
! [A: a] :
( ~ $true
| ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,5]) ).
thf(171,plain,
! [A: a] :
( ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(172,plain,
sk3 @ sk4,
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( sk4 ))]]) ).
thf(243,plain,
! [A: a] :
( ( sk1 @ sk6 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk9 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[206,17]) ).
thf(244,plain,
! [A: a] :
( ( sk1 @ sk6 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( sk2 @ A )
| ( ( sk1 @ sk9 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(245,plain,
( ( sk1 @ sk6 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk3 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( sk9 ))]]) ).
thf(392,plain,
( ( sk9 != sk6 )
| ~ $true
| ~ ( sk2 @ sk4 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[257,78]) ).
thf(393,plain,
( ( sk9 != sk6 )
| ~ ( sk2 @ sk4 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(simp,[status(thm)],[392]) ).
thf(394,plain,
( ( sk9 != sk6 )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[393:[]]) ).
thf(224,plain,
( ( sk1 @ sk9 )
| ~ ( sk1 @ sk6 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[202,78]) ).
thf(225,plain,
( ( sk1 @ sk9 )
| ~ ( sk1 @ sk6 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
( ( sk1 @ sk9 )
| ~ ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[225:[]]) ).
thf(37,plain,
! [B: a,A: a] :
( ~ ( ( sk1 @ B )
& ( sk3 @ B )
& ~ ( sk2 @ B ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(50,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ~ ( sk3 @ B )
| ( sk2 @ B )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[37]) ).
thf(541,plain,
$false,
inference(e,[status(thm)],[234,211,206,248,9,17,27,175,203,26,8,217,5,202,25,257,46,78,29,172,245,394,226,3,50,16,151,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU855^5 : 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
% 0.10/0.22 % Computer : n009.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:40:15 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
% 1.17/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.69/1.27 % [INFO] Parsing done (269ms).
% 1.69/1.29 % [INFO] Running in sequential loop mode.
% 2.61/1.90 % [INFO] eprover registered as external prover.
% 2.83/1.91 % [INFO] Scanning for conjecture ...
% 2.83/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.12/2.10 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.12/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 3.12/2.10 % [INFO] Type checking passed.
% 3.12/2.11 % [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 ...
% 11.73/4.58 % External prover 'e' found a proof!
% 11.73/4.58 % [INFO] Killing All external provers ...
% 11.73/4.58 % Time passed: 4216ms (effective reasoning time: 3290ms)
% 11.73/4.59 % 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)>
% 11.73/4.59 % Axioms used in derivation (0):
% 11.73/4.59 % No. of inferences in proof: 85
% 11.73/4.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4216 ms resp. 3290 ms w/o parsing
% 11.12/4.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.12/4.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------