%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ108^5 : 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 08:20:47 AM UTC 2026
% Result : Theorem 13.00s 5.19s
% Output : Refutation 13.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 97 ( 39 unt; 0 typ; 5 def)
% Number of atoms : 263 ( 106 equ; 9 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1000 ( 136 ~; 109 |; 12 &; 721 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 6 ^; 58 !; 0 ?; 68 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i ).
thf(cCKB_E2_decl,type,
cCKB_E2: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(cCKB_E2_def,definition,
( cCKB_E2
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( ( C @ A )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ! [C: $i > $o] :
( ( ( C @ A )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ B ) )
=> ! [C: $i > $o] :
( ( ( C @ ( s @ A ) )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ ( s @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: $i > $o] :
( ( ( B @ sk1 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ ( s @ C ) ) ) ) )
=> ( B @ A ) )
=> ! [B: $i > $o] :
( ( ( B @ ( s @ sk1 ) )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ ( s @ C ) ) ) ) )
=> ( B @ ( s @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( s @ ( s @ B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ( ( ( A @ ( s @ sk1 ) )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( s @ ( s @ B ) ) ) ) )
=> ( A @ ( s @ sk2 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( cCKB_E2 @ A @ B )
=> ( cCKB_E2 @ ( s @ A ) @ ( s @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_L35000) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( cCKB_E2 @ A @ B )
=> ( cCKB_E2 @ ( s @ A ) @ ( s @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: $i > $o] :
( ( ( C @ A )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ B ) )
=> ! [C: $i > $o] :
( ( ( C @ ( s @ A ) )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ ( s @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i > $o] :
( ( ~ ( A @ sk1 )
| ( A @ ( sk3 @ A ) )
| ( A @ sk2 ) )
& ( ~ ( A @ sk1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
| ( A @ sk2 ) )
& ( sk4 @ ( s @ sk1 ) )
& ( ~ ( sk4 @ B )
| ( sk4 @ ( s @ ( s @ B ) ) ) )
& ~ ( sk4 @ ( s @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
sk4 @ ( s @ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk4 @ ( s @ ( s @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk4 @ ( s @ ( s @ A ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(111,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,14]) ).
thf(112,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
sk4 @ ( s @ ( s @ ( s @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( s @ sk1 ))]]) ).
thf(236,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ sk1 ) ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,14]) ).
thf(237,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ sk1 ) ) ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( s @ ( s @ ( s @ sk1 ) ) ))]]) ).
thf(265,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[238,14]) ).
thf(266,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ))]]) ).
thf(350,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[267,14]) ).
thf(351,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(352,plain,
sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$thf( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ))]]) ).
thf(7,plain,
~ ( sk4 @ ( s @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(379,plain,
( ~ $true
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[352,7]) ).
thf(380,plain,
( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ),
inference(simp,[status(thm)],[379]) ).
thf(385,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) )
!= ( s @ sk2 ) ),
inference(simp,[status(thm)],[380]) ).
thf(17,plain,
( ~ $true
| ( ( sk4 @ ( s @ sk2 ) )
!= ( sk4 @ ( s @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(18,plain,
( ( sk4 @ ( s @ sk2 ) )
!= ( sk4 @ ( s @ sk1 ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
( ( s @ sk2 )
!= ( s @ sk1 ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
sk2 != sk1,
inference(simp,[status(thm)],[19]) ).
thf(376,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[352,14]) ).
thf(377,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(378,plain,
sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ))]]) ).
thf(496,plain,
( ~ $true
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[378,7]) ).
thf(497,plain,
( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(507,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) )
!= ( s @ sk2 ) ),
inference(simp,[status(thm)],[497]) ).
thf(9,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ( A @ ( sk3 @ A ) )
| ( A @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
| ( A @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(120,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ sk1 )
| ~ $true
| ( B @ sk2 )
| ( ( sk4 @ ( s @ ( s @ A ) ) )
!= ( B @ ( s @ ( s @ ( sk3 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(121,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk4 @ A )
| ~ ( B @ sk1 )
| ( B @ sk2 )
| ( ( sk4 @ ( s @ ( s @ A ) ) )
!= ( B @ ( s @ ( s @ ( sk3 @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(131,plain,
( ~ ( sk4 @ ( sk3 @ sk4 ) )
| ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 ) ),
inference(pre_uni,[status(thm)],[121:[bind(A,$thf( sk3 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(300,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 )
| ~ $true
| ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 )
| ( ( A @ ( sk3 @ A ) )
!= ( sk4 @ ( sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,131]) ).
thf(301,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 )
| ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 )
| ( ( A @ ( sk3 @ A ) )
!= ( sk4 @ ( sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(319,plain,
( ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 )
| ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 ) ),
inference(pre_uni,[status(thm)],[301:[bind(A,$thf( sk4 ))]]) ).
thf(335,plain,
( ~ ( sk4 @ sk1 )
| ( sk4 @ sk2 ) ),
inference(simp,[status(thm)],[319]) ).
thf(420,plain,
( ~ ( sk4 @ sk1 )
| ~ $true
| ( ( sk4 @ ( s @ sk2 ) )
!= ( sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[335,7]) ).
thf(421,plain,
( ~ ( sk4 @ sk1 )
| ( ( sk4 @ ( s @ sk2 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(429,plain,
( ~ ( sk4 @ sk1 )
| ( ( s @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[421]) ).
thf(268,plain,
( ~ $true
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,7]) ).
thf(269,plain,
( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(274,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) )
!= ( s @ sk2 ) ),
inference(simp,[status(thm)],[269]) ).
thf(285,plain,
( ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[274]) ).
thf(25,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 )
| ( ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
!= ( A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(43,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 )
| ( ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
!= ( A @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[25:[]]) ).
thf(44,plain,
! [A: $i > $o] :
( ( A @ sk2 )
| ~ ( A @ sk1 )
| ( ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
!= ( A @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[43:[]]) ).
thf(21,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
| ( A @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5,8]) ).
thf(22,plain,
! [A: $i > $o] :
( ~ ( A @ ( s @ ( s @ ( sk3 @ A ) ) ) )
| ( A @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(35,plain,
! [A: $i > $o] :
( ( ( s @ ( s @ ( sk3 @ A ) ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i @ ( s @ ( s @ ( sk3 @ A ) ) ) ) ) ) ) )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk1 ) ) ),
inference(replace_leibeq,[status(thm)],[22:[bind(A,$thf( (=) @ $i @ ( s @ ( s @ ( sk3 @ A ) ) ) ))]]) ).
thf(37,plain,
! [A: $i > $o] :
( ( ( s @ ( s @ ( sk3 @ A ) ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i @ ( s @ ( s @ ( sk3 @ A ) ) ) ) ) ) ) )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk1 ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(472,plain,
! [A: $i > $o] :
( ( ( s @ ( s @ ( sk3 @ A ) ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i @ ( s @ ( s @ ( sk3 @ A ) ) ) ) ) ) ) )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk2 )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[37,5]) ).
thf(473,plain,
! [A: $i > $o] :
( ( ( s @ ( s @ ( sk3 @ A ) ) )
!= sk1 )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
!= ( s @ ( s @ ( sk3 @ ( (=) @ $i @ ( s @ ( s @ ( sk3 @ A ) ) ) ) ) ) ) )
| ( ( s @ ( s @ ( sk3 @ A ) ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[472]) ).
thf(239,plain,
( ~ $true
| ( ( sk4 @ ( s @ ( s @ ( s @ sk1 ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[113,7]) ).
thf(240,plain,
( ( sk4 @ ( s @ ( s @ ( s @ sk1 ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(249,plain,
( ( s @ ( s @ ( s @ sk1 ) ) )
!= ( s @ sk2 ) ),
inference(simp,[status(thm)],[240]) ).
thf(445,plain,
( ~ $true
| ( ( s @ sk2 )
!= sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5,429]) ).
thf(446,plain,
( ( ( s @ sk2 )
!= sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(468,plain,
( ( ( s @ sk2 )
!= sk2 )
| ( ( s @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[446]) ).
thf(389,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[385]) ).
thf(10,plain,
( ( sk1 != sk1 )
| ( sk1
= ( sk3 @ ( (=) @ $i @ sk1 ) ) )
| ( sk1 = sk2 ) ),
inference(replace_leibeq,[status(thm)],[9:[bind(A,$thf( (=) @ $i @ sk1 ))]]) ).
thf(12,plain,
( ( sk1 != sk1 )
| ( ( sk3 @ ( (=) @ $i @ sk1 ) )
= sk1 )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
( ( ( sk3 @ ( (=) @ $i @ sk1 ) )
= sk1 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[12]) ).
thf(105,plain,
( ( sk3 @ ( (=) @ $i @ sk1 ) )
= sk1 ),
inference(simplifyReflect,[status(thm)],[13,20]) ).
thf(106,plain,
! [A: $i > $o] :
( ~ ( A @ sk1 )
| ~ ( A @ ( s @ ( s @ sk1 ) ) )
| ( A @ sk2 )
| ( ( sk3 @ ( (=) @ $i @ sk1 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,8]) ).
thf(107,plain,
( ( sk1 != sk1 )
| ( sk1
!= ( s @ ( s @ sk1 ) ) )
| ( sk1 = sk2 ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( (=) @ $i @ sk1 ))]]) ).
thf(108,plain,
( ( sk1 != sk1 )
| ( ( s @ ( s @ sk1 ) )
!= sk1 )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(109,plain,
( ( ( s @ ( s @ sk1 ) )
!= sk1 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[108]) ).
thf(110,plain,
( ( s @ ( s @ sk1 ) )
!= sk1 ),
inference(simplifyReflect,[status(thm)],[109,20]) ).
thf(256,plain,
( ( s @ ( s @ sk1 ) )
!= sk2 ),
inference(simp,[status(thm)],[249]) ).
thf(141,plain,
! [A: $i > $o] :
( ~ $true
| ( A @ ( sk3 @ A ) )
| ( A @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5,9]) ).
thf(142,plain,
! [A: $i > $o] :
( ( A @ ( sk3 @ A ) )
| ( A @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(186,plain,
( ( sk4
@ ( s
@ ( sk3
@ ^ [A: $i] : ( sk4 @ ( s @ A ) ) ) ) )
| ( sk4 @ ( s @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[142:[bind(A,$thf( ^ [B: $i] : ( sk4 @ ( s @ B ) ) ))]]) ).
thf(536,plain,
( ( sk4
@ ( s
@ ( sk3
@ ^ [A: $i] : ( sk4 @ ( s @ A ) ) ) ) )
| $false ),
inference(rewrite,[status(thm)],[186,7]) ).
thf(537,plain,
( sk4
@ ( s
@ ( sk3
@ ^ [A: $i] : ( sk4 @ ( s @ A ) ) ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(353,plain,
( ~ $true
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,7]) ).
thf(354,plain,
( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) )
!= ( sk4 @ ( s @ sk2 ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(360,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) )
!= ( s @ sk2 ) ),
inference(simp,[status(thm)],[354]) ).
thf(393,plain,
( ~ $true
| ( sk4 @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5,335]) ).
thf(394,plain,
( ( sk4 @ sk2 )
| ( ( sk4 @ ( s @ sk1 ) )
!= ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(434,plain,
( ( sk4 @ sk2 )
| ( ( s @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[394]) ).
thf(363,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[360]) ).
thf(493,plain,
! [A: $i] :
( ~ $true
| ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,14]) ).
thf(494,plain,
! [A: $i] :
( ( sk4 @ ( s @ ( s @ A ) ) )
| ( ( sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ) )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(495,plain,
sk4 @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) ) ))]]) ).
thf(510,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ sk1 ) ) ) ) ) ) ) ) ) )
!= sk2 ),
inference(simp,[status(thm)],[507]) ).
thf(720,plain,
$false,
inference(e,[status(thm)],[5,385,20,238,507,429,285,9,44,335,473,19,249,468,352,389,14,110,256,537,105,360,113,274,7,434,3,267,363,495,8,378,510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ108^5 : 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
% 0.10/0.22 % Computer : n008.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 13:24:24 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.99/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (169ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.39 % [INFO] eprover registered as external prover.
% 1.90/1.40 % [INFO] Scanning for conjecture ...
% 1.90/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.06/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.06/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.53 % [INFO] Type checking passed.
% 2.06/1.54 % [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 ...
% 13.00/5.19 % External prover 'e' found a proof!
% 13.00/5.19 % [INFO] Killing All external provers ...
% 13.00/5.19 % Time passed: 4821ms (effective reasoning time: 4197ms)
% 13.00/5.19 % 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)>
% 13.00/5.19 % Axioms used in derivation (0):
% 13.00/5.19 % No. of inferences in proof: 92
% 13.00/5.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4821 ms resp. 4197 ms w/o parsing
% 13.37/5.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.37/5.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------