%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU969^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n008.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 08:29:40 AM UTC 2026
% Result : Theorem 16.23s 4.82s
% Output : Refutation 15.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 138 ( 11 unt; 0 typ; 8 def)
% Number of atoms : 596 ( 179 equ; 18 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1325 ( 269 ~; 293 |; 31 &; 699 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 138 ( 60 ^; 72 !; 0 ?; 138 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c1_decl,type,
c1: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(cCKB6_BLACK_decl,type,
cCKB6_BLACK: $i > $i > $o ).
thf(cCKB6_NUM_decl,type,
cCKB6_NUM: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: ( $i > $i > $o ) > $i ).
thf(sk4_decl,type,
sk4: ( $i > $i > $o ) > $i ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk6_decl,type,
sk6: $i > $o ).
thf(sk7_decl,type,
sk7: $i > $o ).
thf(cCKB6_BLACK_def,definition,
( cCKB6_BLACK
= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ).
thf(cCKB6_NUM_def,definition,
( cCKB6_NUM
= ( ^ [A: $i] :
! [B: $i > $o] :
( ( ( B @ c1 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ C ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ A @ B ) )
=> ( ! [C: $i > $o] :
( ( ( C @ c1 )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ D ) ) ) )
=> ( C @ A ) )
& ! [C: $i > $o] :
( ( ( C @ c1 )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ D ) ) ) )
=> ( C @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: $i > $i > $o] :
( ( ( B @ c1 @ c1 )
& ! [C: $i,D: $i] :
( ( B @ C @ D )
=> ( ( B @ ( s @ ( s @ C ) ) @ D )
& ( B @ ( s @ C ) @ ( s @ D ) ) ) ) )
=> ( B @ sk1 @ A ) )
=> ( ! [B: $i > $o] :
( ( ( B @ c1 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ C ) ) ) )
=> ( B @ sk1 ) )
& ! [B: $i > $o] :
( ( ( B @ c1 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ C ) ) ) )
=> ( B @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ! [C: $i] :
( ( A @ B @ C )
=> ( ( A @ ( s @ ( s @ B ) ) @ C )
& ( A @ ( s @ B ) @ ( s @ C ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ( ( A @ ( sk3 @ A ) @ B )
=> ( ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ B )
& ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ B ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $o] :
~ ( ( ( A @ c1 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( s @ B ) ) ) )
=> ( A @ sk1 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $o] :
~ ( ( ( A @ c1 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( s @ B ) ) ) )
=> ( A @ sk2 ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( cCKB6_BLACK @ A @ B )
=> ( ( cCKB6_NUM @ A )
& ( cCKB6_NUM @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L6000_pme) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( cCKB6_BLACK @ A @ B )
=> ( ( cCKB6_NUM @ A )
& ( cCKB6_NUM @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ A @ B ) )
=> ( ! [C: $i > $o] :
( ( ( C @ c1 )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ D ) ) ) )
=> ( C @ A ) )
& ! [C: $i > $o] :
( ( ( C @ c1 )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ D ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i,A: $i > $i > $o] :
( ( ~ ( A @ c1 @ c1 )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 ) )
& ( ~ ( A @ c1 @ c1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ ( sk4 @ A ) )
| ~ ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ ( sk4 @ A ) ) )
| ( A @ sk1 @ sk2 ) )
& ( ( sk6 @ c1 )
| ~ sk5 )
& ( ~ ( sk6 @ B )
| ( sk6 @ ( s @ B ) )
| ~ sk5 )
& ( ~ ( sk6 @ sk1 )
| ~ sk5 )
& ( sk5
| ( sk7 @ c1 ) )
& ( sk5
| ~ ( sk7 @ C )
| ( sk7 @ ( s @ C ) ) )
& ( sk5
| ~ ( sk7 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( sk5
| ( sk7 @ c1 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [A: $i > $i > $o] :
( ~ ( A @ c1 @ c1 )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(175,plain,
! [A: $i > $i > $o] :
( sk5
| ~ $true
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( sk7 @ c1 )
!= ( A @ c1 @ c1 ) ) ),
inference(paramod_ordered,[status(thm)],[10,6]) ).
thf(176,plain,
! [A: $i > $i > $o] :
( sk5
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( sk7 @ c1 )
!= ( A @ c1 @ c1 ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(254,plain,
( sk5
| ( sk7
@ ( sk4
@ ^ [A: $i] : sk7 ) )
| ( sk7 @ sk2 ) ),
inference(pre_uni,[status(thm)],[176:[bind(A,$thf( ^ [B: $i] : sk7 ))]]) ).
thf(5,plain,
! [A: $i] :
( sk5
| ~ ( sk7 @ A )
| ( sk7 @ ( s @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
! [A: $i] :
( sk5
| ~ ( sk7 @ A )
| ( sk7 @ ( s @ A ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(595,plain,
! [A: $i] :
( sk5
| ( sk7 @ sk2 )
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7
@ ( sk4
@ ^ [B: $i] : sk7 ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[254,15]) ).
thf(596,plain,
! [A: $i] :
( sk5
| ( sk7 @ sk2 )
| ( sk7 @ ( s @ A ) )
| ( ( sk7
@ ( sk4
@ ^ [B: $i] : sk7 ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(597,plain,
( sk5
| ( sk7 @ sk2 )
| ( sk7
@ ( s
@ ( sk4
@ ^ [A: $i] : sk7 ) ) ) ),
inference(pattern_uni,[status(thm)],[596:[bind(A,$thf( sk4 @ ^ [B: $i] : sk7 ))]]) ).
thf(12,plain,
( ( sk6 @ c1 )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: $i] :
( ~ ( sk6 @ A )
| ( sk6 @ ( s @ A ) )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(20,plain,
! [A: $i] :
( ~ ( sk6 @ A )
| ( sk6 @ ( s @ A ) )
| ~ sk5 ),
inference(simp,[status(thm)],[11]) ).
thf(846,plain,
! [A: $i] :
( ~ sk5
| ~ $true
| ( sk6 @ ( s @ A ) )
| ~ sk5
| ( ( sk6 @ c1 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(847,plain,
! [A: $i] :
( ~ sk5
| ( sk6 @ ( s @ A ) )
| ( ( sk6 @ c1 )
!= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[846]) ).
thf(848,plain,
( ~ sk5
| ( sk6 @ ( s @ c1 ) ) ),
inference(pattern_uni,[status(thm)],[847:[bind(A,$thf( c1 ))]]) ).
thf(896,plain,
! [A: $i] :
( ~ sk5
| ~ $true
| ( sk6 @ ( s @ A ) )
| ~ sk5
| ( ( sk6 @ ( s @ c1 ) )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[848,20]) ).
thf(897,plain,
! [A: $i] :
( ~ sk5
| ( sk6 @ ( s @ A ) )
| ( ( sk6 @ ( s @ c1 ) )
!= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[896]) ).
thf(898,plain,
( ~ sk5
| ( sk6 @ ( s @ ( s @ c1 ) ) ) ),
inference(pattern_uni,[status(thm)],[897:[bind(A,$thf( s @ c1 ))]]) ).
thf(949,plain,
! [A: $i] :
( ~ sk5
| ~ $true
| ( sk6 @ ( s @ A ) )
| ~ sk5
| ( ( sk6 @ ( s @ ( s @ c1 ) ) )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[898,20]) ).
thf(950,plain,
! [A: $i] :
( ~ sk5
| ( sk6 @ ( s @ A ) )
| ( ( sk6 @ ( s @ ( s @ c1 ) ) )
!= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[949]) ).
thf(951,plain,
( ~ sk5
| ( sk6 @ ( s @ ( s @ ( s @ c1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[950:[bind(A,$thf( s @ ( s @ c1 ) ))]]) ).
thf(9,plain,
( ~ ( sk6 @ sk1 )
| ~ sk5 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(1427,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( sk6 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[951,9]) ).
thf(1428,plain,
( ~ sk5
| ( ( sk6 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1462,plain,
( ~ sk5
| ( ( s @ ( s @ ( s @ c1 ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1428]) ).
thf(253,plain,
( sk5
| ( sk7
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) ) )
| ( sk7 @ sk1 ) ),
inference(pre_uni,[status(thm)],[176:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk7 @ B ) ))]]) ).
thf(429,plain,
! [A: $i] :
( sk5
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ c1 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,15]) ).
thf(430,plain,
! [A: $i] :
( sk5
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ c1 )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(431,plain,
( sk5
| ( sk7 @ ( s @ c1 ) ) ),
inference(pattern_uni,[status(thm)],[430:[bind(A,$thf( c1 ))]]) ).
thf(7,plain,
( sk5
| ~ ( sk7 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(478,plain,
( sk5
| sk5
| ~ $true
| ( ( sk7 @ ( s @ c1 ) )
!= ( sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[431,7]) ).
thf(479,plain,
( sk5
| ( ( sk7 @ ( s @ c1 ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[478]) ).
thf(493,plain,
( sk5
| ( ( s @ c1 )
!= sk2 ) ),
inference(simp,[status(thm)],[479]) ).
thf(21,plain,
( sk5
| sk5
| ~ $true
| ( ( sk7 @ sk2 )
!= ( sk7 @ c1 ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(22,plain,
( sk5
| ( ( sk7 @ sk2 )
!= ( sk7 @ c1 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( sk5
| ( sk2 != c1 ) ),
inference(simp,[status(thm)],[22]) ).
thf(956,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( sk6 @ ( s @ ( s @ c1 ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[898,9]) ).
thf(957,plain,
( ~ sk5
| ( ( sk6 @ ( s @ ( s @ c1 ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[956]) ).
thf(975,plain,
( ~ sk5
| ( ( s @ ( s @ c1 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[957]) ).
thf(995,plain,
( ( sk2 != c1 )
| ~ $true
| ( ( s @ ( s @ c1 ) )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,975]) ).
thf(996,plain,
( ( sk2 != c1 )
| ( ( s @ ( s @ c1 ) )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[995]) ).
thf(997,plain,
( ( sk2 != c1 )
| ( ( s @ ( s @ c1 ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[996:[]]) ).
thf(8,plain,
! [A: $i > $i > $o] :
( ~ ( A @ c1 @ c1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ ( sk4 @ A ) )
| ~ ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ ( sk4 @ A ) ) )
| ( A @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
( ( c1 != c1 )
| ( ( s @ ( s @ ( sk3 @ ( (=) @ $i ) ) ) )
!= ( sk4 @ ( (=) @ $i ) ) )
| ( ( s @ ( sk3 @ ( (=) @ $i ) ) )
!= ( s @ ( sk4 @ ( (=) @ $i ) ) ) )
| ( sk1 = sk2 ) ),
inference(replace_andrewseq,[status(thm)],[8:[bind(A,$thf( (=) @ $i ))]]) ).
thf(16,plain,
( ( c1 != c1 )
| ( ( sk4 @ ( (=) @ $i ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i ) ) ) ) )
| ( ( s @ ( sk4 @ ( (=) @ $i ) ) )
!= ( s @ ( sk3 @ ( (=) @ $i ) ) ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(17,plain,
( ( ( sk4 @ ( (=) @ $i ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i ) ) ) ) )
| ( ( s @ ( sk4 @ ( (=) @ $i ) ) )
!= ( s @ ( sk3 @ ( (=) @ $i ) ) ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[16]) ).
thf(148,plain,
( ( sk2 != c1 )
| ( sk6 @ c1 )
| ~ $true
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,12]) ).
thf(149,plain,
( ( sk2 != c1 )
| ( sk6 @ c1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
( ( sk2 != c1 )
| ( sk6 @ c1 ) ),
inference(pattern_uni,[status(thm)],[149:[]]) ).
thf(327,plain,
( sk5
| ( sk7 @ sk1 )
| ( ( sk7
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) ) )
!= ( sk7 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[253]) ).
thf(336,plain,
( sk5
| ( sk7 @ sk1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) )
!= sk1 ) ),
inference(simp,[status(thm)],[327]) ).
thf(187,plain,
! [A: $i > $i > $o] :
( ~ sk5
| ~ $true
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( sk6 @ c1 )
!= ( A @ c1 @ c1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,6]) ).
thf(188,plain,
! [A: $i > $i > $o] :
( ~ sk5
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( sk6 @ c1 )
!= ( A @ c1 @ c1 ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(242,plain,
( ~ sk5
| ( sk6
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) ) )
| ( sk6 @ sk1 ) ),
inference(pre_uni,[status(thm)],[188:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk6 @ B ) ))]]) ).
thf(145,plain,
( ( sk2 != c1 )
| ~ ( sk6 @ sk1 )
| ~ $true
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,9]) ).
thf(146,plain,
( ( sk2 != c1 )
| ~ ( sk6 @ sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
( ( sk2 != c1 )
| ~ ( sk6 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[146:[]]) ).
thf(345,plain,
( ~ sk5
| ( sk6 @ sk1 )
| ( sk2 != c1 )
| ~ $true
| ( ( sk6
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[242,147]) ).
thf(346,plain,
( ~ sk5
| ( sk6 @ sk1 )
| ( sk2 != c1 )
| ( ( sk6
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(375,plain,
( ( sk6 @ sk1 )
| ~ sk5
| ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 ) ),
inference(simp,[status(thm)],[346]) ).
thf(544,plain,
( ~ sk5
| ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ~ $true
| ~ sk5
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[375,9]) ).
thf(545,plain,
( ~ sk5
| ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[544]) ).
thf(546,plain,
( ~ sk5
| ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[545:[]]) ).
thf(579,plain,
( ( sk2 != c1 )
| ~ $true
| ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,546]) ).
thf(580,plain,
( ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[579]) ).
thf(581,plain,
( ( sk2 != c1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[580:[]]) ).
thf(13,plain,
( ( c1 != c1 )
| ( ( sk3 @ ( (=) @ $i ) )
= ( sk4 @ ( (=) @ $i ) ) )
| ( sk1 = sk2 ) ),
inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ $i ))]]) ).
thf(18,plain,
( ( c1 != c1 )
| ( ( sk4 @ ( (=) @ $i ) )
= ( sk3 @ ( (=) @ $i ) ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(19,plain,
( ( ( sk4 @ ( (=) @ $i ) )
= ( sk3 @ ( (=) @ $i ) ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[18]) ).
thf(486,plain,
! [A: $i] :
( sk5
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ c1 ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[431,15]) ).
thf(487,plain,
! [A: $i] :
( sk5
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ c1 ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[486]) ).
thf(488,plain,
( sk5
| ( sk7 @ ( s @ ( s @ c1 ) ) ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( s @ c1 ))]]) ).
thf(510,plain,
( sk5
| sk5
| ~ $true
| ( ( sk7 @ ( s @ ( s @ c1 ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[488,7]) ).
thf(511,plain,
( sk5
| ( ( sk7 @ ( s @ ( s @ c1 ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(533,plain,
( sk5
| ( ( s @ ( s @ c1 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[511]) ).
thf(243,plain,
( ~ sk5
| ( sk6
@ ( sk4
@ ^ [A: $i] : sk6 ) )
| ( sk6 @ sk2 ) ),
inference(pre_uni,[status(thm)],[188:[bind(A,$thf( ^ [B: $i] : sk6 ))]]) ).
thf(42,plain,
! [A: $i > $i > $o] :
( ~ ( A @ c1 @ c1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ ( sk4 @ A ) ) )
!= ( A @ c1 @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(76,plain,
! [A: $i > $i > $o] :
( ~ ( A @ c1 @ c1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ ( sk4 @ A ) ) )
!= ( A @ c1 @ c1 ) ) ),
inference(pre_uni,[status(thm)],[42:[]]) ).
thf(77,plain,
! [A: $i > $i > $o] :
( ( A @ sk1 @ sk2 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) @ ( sk4 @ A ) )
| ~ ( A @ c1 @ c1 )
| ( ( A @ ( s @ ( sk3 @ A ) ) @ ( s @ ( sk4 @ A ) ) )
!= ( A @ c1 @ c1 ) ) ),
inference(pre_uni,[status(thm)],[76:[]]) ).
thf(518,plain,
! [A: $i] :
( sk5
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ c1 ) ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[488,15]) ).
thf(519,plain,
! [A: $i] :
( sk5
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ c1 ) ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
( sk5
| ( sk7 @ ( s @ ( s @ ( s @ c1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( s @ ( s @ c1 ) ))]]) ).
thf(666,plain,
! [A: $i] :
( sk5
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[520,15]) ).
thf(667,plain,
! [A: $i] :
( sk5
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(668,plain,
( sk5
| ( sk7 @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( s @ ( s @ ( s @ c1 ) ) ))]]) ).
thf(696,plain,
( sk5
| sk5
| ~ $true
| ( ( sk7 @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[668,7]) ).
thf(697,plain,
( sk5
| ( ( sk7 @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[696]) ).
thf(706,plain,
( sk5
| ( ( s @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[697]) ).
thf(351,plain,
( ~ sk5
| ( sk6 @ sk1 )
| ~ $true
| ~ sk5
| ( ( sk6
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[242,9]) ).
thf(352,plain,
( ~ sk5
| ( sk6 @ sk1 )
| ( ( sk6
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) ) )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[351]) ).
thf(369,plain,
( ( sk6 @ sk1 )
| ~ sk5
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 ) ),
inference(simp,[status(thm)],[352]) ).
thf(785,plain,
( ~ sk5
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ~ $true
| ~ sk5
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[369,9]) ).
thf(786,plain,
( ~ sk5
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[785]) ).
thf(787,plain,
( ~ sk5
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk6 @ A ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[786:[]]) ).
thf(24,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( sk6 @ sk1 )
!= ( sk6 @ c1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(25,plain,
( ~ sk5
| ( ( sk6 @ sk1 )
!= ( sk6 @ c1 ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(26,plain,
( ~ sk5
| ( sk1 != c1 ) ),
inference(simp,[status(thm)],[25]) ).
thf(157,plain,
( ( sk2 != c1 )
| ~ $true
| ( sk1 != c1 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,26]) ).
thf(158,plain,
( ( sk2 != c1 )
| ( sk1 != c1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
( ( sk2 != c1 )
| ( sk1 != c1 ) ),
inference(pattern_uni,[status(thm)],[158:[]]) ).
thf(658,plain,
( sk5
| sk5
| ~ $true
| ( ( sk7 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[520,7]) ).
thf(659,plain,
( sk5
| ( ( sk7 @ ( s @ ( s @ ( s @ c1 ) ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(681,plain,
( sk5
| ( ( s @ ( s @ ( s @ c1 ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[659]) ).
thf(432,plain,
! [A: $i] :
( sk5
| ( sk7 @ sk1 )
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7
@ ( sk3
@ ^ [B: $i,C: $i] : ( sk7 @ B ) ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[253,15]) ).
thf(433,plain,
! [A: $i] :
( sk5
| ( sk7 @ sk1 )
| ( sk7 @ ( s @ A ) )
| ( ( sk7
@ ( sk3
@ ^ [B: $i,C: $i] : ( sk7 @ B ) ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(434,plain,
( sk5
| ( sk7 @ sk1 )
| ( sk7
@ ( s
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[433:[bind(A,$thf( sk3 @ ^ [B: $i] : ^ [C: $i] : ( sk7 @ B ) ))]]) ).
thf(913,plain,
( ( sk2 != c1 )
| ~ $true
| ( sk6 @ ( s @ c1 ) )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,848]) ).
thf(914,plain,
( ( sk2 != c1 )
| ( sk6 @ ( s @ c1 ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[913]) ).
thf(915,plain,
( ( sk2 != c1 )
| ( sk6 @ ( s @ c1 ) ) ),
inference(pattern_uni,[status(thm)],[914:[]]) ).
thf(698,plain,
! [A: $i] :
( sk5
| sk5
| ~ $true
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[668,15]) ).
thf(699,plain,
! [A: $i] :
( sk5
| ( sk7 @ ( s @ A ) )
| ( ( sk7 @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) )
!= ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(700,plain,
( sk5
| ( sk7 @ ( s @ ( s @ ( s @ ( s @ ( s @ c1 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[699:[bind(A,$thf( s @ ( s @ ( s @ ( s @ c1 ) ) ) ))]]) ).
thf(903,plain,
( ~ sk5
| ~ $true
| ~ sk5
| ( ( sk6 @ ( s @ c1 ) )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[848,9]) ).
thf(904,plain,
( ~ sk5
| ( ( sk6 @ ( s @ c1 ) )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(927,plain,
( ~ sk5
| ( ( s @ c1 )
!= sk1 ) ),
inference(simp,[status(thm)],[904]) ).
thf(942,plain,
( ( sk2 != c1 )
| ~ $true
| ( ( s @ c1 )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,927]) ).
thf(943,plain,
( ( sk2 != c1 )
| ( ( s @ c1 )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[942]) ).
thf(944,plain,
( ( sk2 != c1 )
| ( ( s @ c1 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[943:[]]) ).
thf(966,plain,
( ( sk2 != c1 )
| ~ $true
| ( sk6 @ ( s @ ( s @ c1 ) ) )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[23,898]) ).
thf(967,plain,
( ( sk2 != c1 )
| ( sk6 @ ( s @ ( s @ c1 ) ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[966]) ).
thf(968,plain,
( ( sk2 != c1 )
| ( sk6 @ ( s @ ( s @ c1 ) ) ) ),
inference(pattern_uni,[status(thm)],[967:[]]) ).
thf(319,plain,
( sk5
| ( sk7 @ sk1 )
| sk5
| ~ $true
| ( ( sk7
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[253,7]) ).
thf(320,plain,
( sk5
| ( sk7 @ sk1 )
| ( ( sk7
@ ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(332,plain,
( sk5
| ( sk7 @ sk1 )
| ( ( sk3
@ ^ [A: $i,B: $i] : ( sk7 @ A ) )
!= sk2 ) ),
inference(simp,[status(thm)],[320]) ).
thf(2230,plain,
$false,
inference(e,[status(thm)],[597,898,1462,20,253,6,493,9,997,17,975,150,951,336,581,8,19,242,254,10,533,147,243,488,77,706,12,787,159,681,7,434,915,668,848,700,520,3,431,944,927,968,26,23,332,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU969^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.12/0.22 % Computer : n008.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 14:55:22 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (191ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.04/1.42 % [INFO] eprover registered as external prover.
% 2.04/1.42 % [INFO] Scanning for conjecture ...
% 2.23/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.57 % [INFO] Type checking passed.
% 2.23/1.58 % [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 ...
% 16.23/4.82 % External prover 'e' found a proof!
% 16.23/4.82 % [INFO] Killing All external provers ...
% 16.23/4.82 % Time passed: 4463ms (effective reasoning time: 3805ms)
% 16.23/4.82 % 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)>
% 16.23/4.82 % Axioms used in derivation (0):
% 16.23/4.82 % No. of inferences in proof: 130
% 16.23/4.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4463 ms resp. 3805 ms w/o parsing
% 15.20/4.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.20/4.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------