%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV261^5 : 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 : n020.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 08:37:05 AM UTC 2026
% Result : Theorem 10.18s 3.70s
% Output : Refutation 9.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 105 ( 12 unt; 0 typ; 9 def)
% Number of atoms : 770 ( 213 equ; 0 cnn)
% Maximal formula atoms : 55 ( 7 avg)
% Number of connectives : 766 ( 212 ~; 295 |; 81 &; 154 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 295 ( 189 ^; 74 !; 23 ?; 295 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: a > $o ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk6_decl,type,
sk6: ( a > $o ) > $o ).
thf(sk7_decl,type,
sk7: a > $o ).
thf(sk8_decl,type,
sk8: a > $o ).
thf(sk9_decl,type,
sk9: a > $o ).
thf(sk10_decl,type,
sk10: a > $o ).
thf(sk18_decl,type,
sk18: a ).
thf(sk19_decl,type,
sk19: a ).
thf(sk21_decl,type,
sk21: a ).
thf(sk22_decl,type,
sk22: a > $o ).
thf(sk23_decl,type,
sk23: a > $o ).
thf(sk24_decl,type,
sk24: a ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a > $o] :
~ ( ( A
= ( ^ [B: a] : $true ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: ( a > $o ) > $o] :
~ ! [B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : $true ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: a > $o] :
~ ( ( ! [B: a > $o] :
( ( sk6 @ B )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : $true ) ) ) )
& ( A
= ( ^ [B: a] :
? [C: a > $o] :
( ( sk6 @ C )
& ( C @ B ) ) ) ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: a > $o] :
~ ! [B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : $true ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : $true ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ( ( sk8
= ( ^ [C: a] : $false ) )
| ( sk8
= ( ^ [C: a] : $true ) ) )
& ( ( A
= ( ^ [C: a] : $false ) )
| ( A
= ( ^ [C: a] : $true ) ) )
& ( B
= ( ^ [C: a] :
( ( sk8 @ C )
& ( A @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : $true ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: a > $o] :
~ ( ( ( ( sk8
= ( ^ [B: a] : $false ) )
| ( sk8
= ( ^ [B: a] : $true ) ) )
& ( ( sk9
= ( ^ [B: a] : $false ) )
| ( sk9
= ( ^ [B: a] : $true ) ) )
& ( A
= ( ^ [B: a] :
( ( sk8 @ B )
& ( sk9 @ B ) ) ) ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: a > $o] :
( ( sk6 @ A )
& ( A @ sk21 ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[A: a > $o] :
( ( sk6 @ A )
& ( A @ sk21 ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : ~ $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : ~ $false ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : ~ $false ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : ~ $false ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cINDISCRETE_TOPOLOGY_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : ~ $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : ~ $false ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : ~ $false ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : ~ $false ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : ~ $false ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : ~ $false ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) )
& ! [A: a > $o] :
( ( A
= ( ^ [B: a] : $true ) )
=> ( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) ) ) )
& ! [A: ( a > $o ) > $o,B: a > $o] :
( ( ! [C: a > $o] :
( ( A @ C )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) )
& ( B
= ( ^ [C: a] :
? [D: a > $o] :
( ( A @ D )
& ( D @ C ) ) ) ) )
=> ( ( B
= ( ^ [C: a] : $false ) )
| ( B
= ( ^ [C: a] : $true ) ) ) )
& ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ( ( A
= ( ^ [D: a] : $false ) )
| ( A
= ( ^ [D: a] : $true ) ) )
& ( ( B
= ( ^ [D: a] : $false ) )
| ( B
= ( ^ [D: a] : $true ) ) )
& ( C
= ( ^ [D: a] :
( ( A @ D )
& ( B @ D ) ) ) ) )
=> ( ( C
= ( ^ [D: a] : $false ) )
| ( C
= ( ^ [D: a] : $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a > $o] :
( ( ( sk2
= ( ^ [B: a] : $false ) )
| ~ sk1 )
& ( ( sk2
!= ( ^ [B: a] : $false ) )
| ~ sk1 )
& ( ( sk2
!= ( ^ [B: a] : $true ) )
| ~ sk1 )
& ( sk1
| ( sk4
= ( ^ [B: a] : $true ) )
| ~ sk3 )
& ( sk1
| ( sk4
!= ( ^ [B: a] : $false ) )
| ~ sk3 )
& ( sk1
| ( sk4
!= ( ^ [B: a] : $true ) )
| ~ sk3 )
& ( sk1
| sk3
| ~ ( sk6 @ A )
| ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| ~ sk5 )
& ( sk1
| sk3
| ( sk7
= ( ^ [B: a] :
? [C: a > $o] :
( ( sk6 @ C )
& ( C @ B ) ) ) )
| ~ sk5 )
& ( sk1
| sk3
| ( sk7
!= ( ^ [B: a] : $false ) )
| ~ sk5 )
& ( sk1
| sk3
| ( sk7
!= ( ^ [B: a] : $true ) )
| ~ sk5 )
& ( sk1
| sk3
| sk5
| ( sk8
= ( ^ [B: a] : $false ) )
| ( sk8
= ( ^ [B: a] : $true ) ) )
& ( sk1
| sk3
| sk5
| ( sk9
= ( ^ [B: a] : $false ) )
| ( sk9
= ( ^ [B: a] : $true ) ) )
& ( sk1
| sk3
| sk5
| ( sk10
= ( ^ [B: a] :
( ( sk8 @ B )
& ( sk9 @ B ) ) ) ) )
& ( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [B: a] : $false ) ) )
& ( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [B: a] : $true ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( sk1
| sk3
| ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[10]) ).
thf(19,plain,
( sk1
| ( sk4
= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(33,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| sk1
| ~ sk3 ),
inference(lifteq,[status(thm)],[19]) ).
thf(12,plain,
( ( sk2
= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(27,plain,
( ( sk2
= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[12]) ).
thf(18,plain,
( ( sk2
!= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(29,plain,
( ( sk2
!= ( ^ [A: a] : $false ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[18]) ).
thf(37,plain,
( ~ sk1
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ~ sk1
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27,29]) ).
thf(38,plain,
( ~ sk1
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[38:[]]) ).
thf(71,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| $false
| ~ sk3 ),
inference(rewrite,[status(thm)],[33,39]) ).
thf(72,plain,
( ( sk4
= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(simp,[status(thm)],[71]) ).
thf(11,plain,
( sk1
| ( sk4
!= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(31,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| sk1
| ~ sk3 ),
inference(lifteq,[status(thm)],[11]) ).
thf(42,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| $false
| ~ sk3 ),
inference(rewrite,[status(thm)],[31,39]) ).
thf(43,plain,
( ( sk4
!= ( ^ [A: a] : $true ) )
| ~ sk3 ),
inference(simp,[status(thm)],[42]) ).
thf(80,plain,
( ~ sk3
| ( ( ^ [A: a] : $true )
!= ( ^ [A: a] : $true ) )
| ~ sk3
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[72,43]) ).
thf(81,plain,
( ~ sk3
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[81:[]]) ).
thf(144,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| $false
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[21,82,39]) ).
thf(145,plain,
( ( sk7
= ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| ~ sk5 ),
inference(simp,[status(thm)],[144]) ).
thf(146,plain,
! [A: a] :
( ( ( sk7 @ A )
= ( ? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) ) )
| ~ sk5 ),
inference(func_ext,[status(esa)],[145]) ).
thf(17,plain,
( sk1
| sk3
| ( sk7
!= ( ^ [A: a] : $false ) )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(26,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[17]) ).
thf(449,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| $false
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[26,82,39]) ).
thf(450,plain,
( ( sk7
!= ( ^ [A: a] : $false ) )
| ~ sk5 ),
inference(simp,[status(thm)],[449]) ).
thf(451,plain,
( ( sk7 @ sk21 )
| ~ sk5 ),
inference(func_ext,[status(esa)],[450]) ).
thf(480,plain,
! [A: a] :
( ~ sk5
| ? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) )
| ~ sk5
| ( ( sk7 @ A )
!= ( sk7 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[146,451]) ).
thf(481,plain,
! [A: a] :
( ~ sk5
| ? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) )
| ( ( sk7 @ A )
!= ( sk7 @ sk21 ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(482,plain,
( ~ sk5
| ? [A: a > $o] :
( ( sk6 @ A )
& ( A @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( sk21 ))]]) ).
thf(503,plain,
( ( ~ sk5
| ( sk6 @ sk22 ) )
& ( ~ sk5
| ( sk22 @ sk21 ) ) ),
inference(cnf,[status(esa)],[482]) ).
thf(504,plain,
( ~ sk5
| ( sk6 @ sk22 ) ),
inference(cnfConj,[status(thm)],[503]) ).
thf(14,plain,
( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [A: a] : $true ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(22,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[14]) ).
thf(409,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[22,82,39]) ).
thf(410,plain,
( ( sk10
!= ( ^ [A: a] : $true ) )
| sk5 ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
( ~ ( sk10 @ sk18 )
| sk5 ),
inference(func_ext,[status(esa)],[410]) ).
thf(13,plain,
( sk1
| sk3
| sk5
| ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(25,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[13]) ).
thf(406,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[25,82,39]) ).
thf(407,plain,
( ( sk8
= ( ^ [A: a] : $false ) )
| ( sk8
= ( ^ [A: a] : $true ) )
| sk5 ),
inference(simp,[status(thm)],[406]) ).
thf(454,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ sk5
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[145,450]) ).
thf(455,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk7 != sk7 ) ),
inference(simp,[status(thm)],[454]) ).
thf(456,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[455:[]]) ).
thf(477,plain,
! [A: a] :
( ~ sk5
| ? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) )
| ~ sk5
| ( ( sk7 @ sk21 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[451,146]) ).
thf(478,plain,
! [A: a] :
( ~ sk5
| ? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) )
| ( ( sk7 @ sk21 )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[477]) ).
thf(479,plain,
( ~ sk5
| ? [A: a > $o] :
( ( sk6 @ A )
& ( A @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( sk21 ))]]) ).
thf(514,plain,
( ( ~ sk5
| ( sk6 @ sk23 ) )
& ( ~ sk5
| ( sk23 @ sk21 ) ) ),
inference(cnf,[status(esa)],[479]) ).
thf(515,plain,
( ~ sk5
| ( sk6 @ sk23 ) ),
inference(cnfConj,[status(thm)],[514]) ).
thf(9,plain,
( sk1
| sk3
| sk5
| ( sk10
= ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(24,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[9]) ).
thf(45,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| $false
| sk3
| sk5 ),
inference(rewrite,[status(thm)],[24,39]) ).
thf(46,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk3
| sk5 ),
inference(simp,[status(thm)],[45]) ).
thf(85,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| $false
| sk5 ),
inference(rewrite,[status(thm)],[46,82]) ).
thf(86,plain,
( ( ( ^ [A: a] :
( ( sk8 @ A )
& ( sk9 @ A ) ) )
= sk10 )
| sk5 ),
inference(simp,[status(thm)],[85]) ).
thf(5,plain,
! [A: a > $o] :
( sk1
| sk3
| ~ ( sk6 @ A )
| ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(20,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| sk1
| sk3
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(lifteq,[status(thm)],[5]) ).
thf(49,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| $false
| sk3
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(rewrite,[status(thm)],[20,39]) ).
thf(50,plain,
! [A: a > $o] :
( ( A
= ( ^ [B: a] : $false ) )
| ( A
= ( ^ [B: a] : $true ) )
| sk3
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ( A @ C )
| sk3
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(func_ext,[status(esa)],[50]) ).
thf(87,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ( A @ C )
| $false
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(rewrite,[status(thm)],[51,82]) ).
thf(88,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ( A @ C )
| ~ ( sk6 @ A )
| ~ sk5 ),
inference(simp,[status(thm)],[87]) ).
thf(100,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk6 @ A )
| ~ sk5
| ( ( A @ C )
!= ( ~ ( A @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[88]) ).
thf(127,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk6 @ A )
| ~ sk5
| ( ( A @ C )
!= ( ~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(6,plain,
( sk1
| sk3
| ( sk7
!= ( ^ [A: a] : $true ) )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(23,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| sk1
| sk3
| ~ sk5 ),
inference(lifteq,[status(thm)],[6]) ).
thf(414,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| $false
| $false
| ~ sk5 ),
inference(rewrite,[status(thm)],[23,82,39]) ).
thf(415,plain,
( ( sk7
!= ( ^ [A: a] : $true ) )
| ~ sk5 ),
inference(simp,[status(thm)],[414]) ).
thf(416,plain,
( ~ ( sk7 @ sk19 )
| ~ sk5 ),
inference(func_ext,[status(esa)],[415]) ).
thf(469,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( sk7 @ sk21 )
!= ( sk7 @ sk19 ) ) ),
inference(paramod_ordered,[status(thm)],[451,416]) ).
thf(470,plain,
( ~ sk5
| ( ( sk7 @ sk21 )
!= ( sk7 @ sk19 ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(496,plain,
( ~ sk5
| ( sk21 != sk19 ) ),
inference(simp,[status(thm)],[470]) ).
thf(7,plain,
( sk1
| sk3
| sk5
| ( sk10
!= ( ^ [A: a] : $false ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(28,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[7]) ).
thf(517,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[28,82,39]) ).
thf(518,plain,
( ( sk10
!= ( ^ [A: a] : $false ) )
| sk5 ),
inference(simp,[status(thm)],[517]) ).
thf(419,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) )
| ~ sk5
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[145,415]) ).
thf(420,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) )
| ( sk7 != sk7 ) ),
inference(simp,[status(thm)],[419]) ).
thf(421,plain,
( ~ sk5
| ( ( ^ [A: a] :
? [B: a > $o] :
( ( sk6 @ B )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[420:[]]) ).
thf(519,plain,
( ( sk10 @ sk24 )
| sk5 ),
inference(func_ext,[status(esa)],[518]) ).
thf(141,plain,
! [A: a] :
( ( ( ( sk8 @ A )
& ( sk9 @ A ) )
= ( sk10 @ A ) )
| sk5 ),
inference(func_ext,[status(esa)],[86]) ).
thf(505,plain,
( ~ sk5
| ( sk22 @ sk21 ) ),
inference(cnfConj,[status(thm)],[503]) ).
thf(223,plain,
! [F: a,E: a,D: a > $o,C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk6 @ A )
| ~ sk5
| ~ ( D @ E )
| ~ ( sk6 @ D )
| ~ $true
| ( ( D @ F )
!= ( ~ ( D @ E ) ) )
| ( ( A @ C )
!= sk5 ) ),
inference(paramod_ordered,[status(thm)],[88,127]) ).
thf(224,plain,
! [F: a,E: a,D: a > $o,C: a,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk6 @ A )
| ~ sk5
| ~ ( D @ E )
| ~ ( sk6 @ D )
| ( ( D @ F )
!= ( ~ ( D @ E ) ) )
| ( ( A @ C )
!= sk5 ) ),
inference(simp,[status(thm)],[223]) ).
thf(271,plain,
! [C: a,B: a,A: a > $o] :
( ~ sk5
| ~ ( sk6
@ ^ [D: a] : sk5 )
| ~ sk5
| ~ ( A @ B )
| ~ ( sk6 @ A )
| ( ( A @ C )
!= ( ~ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[224:[bind(A,$thf( ^ [G: a] : sk5 ))]]) ).
thf(290,plain,
! [C: a,B: a,A: a > $o] :
( ~ sk5
| ~ ( sk6
@ ^ [D: a] : sk5 )
| ~ ( A @ B )
| ~ ( sk6 @ A )
| ( ( A @ C )
!= ( ~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(16,plain,
( sk1
| sk3
| sk5
| ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| sk1
| sk3
| sk5 ),
inference(lifteq,[status(thm)],[16]) ).
thf(446,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| $false
| $false
| sk5 ),
inference(rewrite,[status(thm)],[30,82,39]) ).
thf(447,plain,
( ( sk9
= ( ^ [A: a] : $false ) )
| ( sk9
= ( ^ [A: a] : $true ) )
| sk5 ),
inference(simp,[status(thm)],[446]) ).
thf(994,plain,
$false,
inference(e,[status(thm)],[504,411,407,456,515,86,145,127,450,415,496,518,88,421,416,519,141,451,39,3,505,290,82,447,410,146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV261^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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 : n020.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 15:29:19 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (199ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.15/1.40 % [INFO] eprover registered as external prover.
% 2.15/1.41 % [INFO] Scanning for conjecture ...
% 2.36/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.36/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.36/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.57 % [INFO] Type checking passed.
% 2.36/1.57 % [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 ...
% 10.18/3.69 % External prover 'e' found a proof!
% 10.18/3.69 % [INFO] Killing All external provers ...
% 10.18/3.69 % Time passed: 3346ms (effective reasoning time: 2686ms)
% 10.18/3.70 % 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)>
% 10.18/3.70 % Axioms used in derivation (0):
% 10.18/3.70 % No. of inferences in proof: 96
% 10.18/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3346 ms resp. 2686 ms w/o parsing
% 9.51/3.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.51/3.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------