%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n007.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 08:37:07 AM UTC 2026
% Result : Theorem 11.66s 3.82s
% Output : Refutation 11.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 19 unt; 0 typ; 9 def)
% Number of atoms : 507 ( 283 equ; 65 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 712 ( 212 ~; 149 |; 55 &; 296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 85 ( 18 ^; 20 !; 41 ?; 85 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cONE_decl,type,
cONE: ( $i > $o ) > $o ).
thf(cSUCC_decl,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(cZERO_decl,type,
cZERO: ( $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(cONE_def,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(cSUCC_def,definition,
( cSUCC
= ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ) ).
thf(cZERO_def,definition,
( cZERO
= ( ^ [A: $i > $o] :
~ ? [B: $i] : ( A @ B ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( sk1
= ( (=) @ $i @ B ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ) ).
thf(1,conjecture,
( cONE
= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_pme) ).
thf(2,negated_conjecture,
( cONE
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ^ [A: $i > $o,B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o,B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(simp,[status(thm)],[4]) ).
thf(6,plain,
( ( ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) )
!= ( ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(10,plain,
( ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) )
| ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(16,plain,
! [A: $i] :
( ( ( sk1 @ sk5 )
| ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) ) )
& ( ( A = sk5 )
| ~ ( sk1 @ A )
| ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(18,plain,
! [A: $i] :
( ( A = sk5 )
| ~ ( sk1 @ A )
| ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(20,plain,
! [A: $i] :
( ( A = sk5 )
| ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(7,plain,
( ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(22,plain,
( ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(24,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(29,plain,
! [A: $i] :
( ( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk3 ) )
& ( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( A = sk3 )
| ~ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(30,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(39,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( $true
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[30,7]) ).
thf(40,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[40:[]]) ).
thf(68,plain,
! [A: $i] :
( ( ( sk2 @ A )
= ( sk3 = A ) )
| ( ( ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[41]) ).
thf(100,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( ( sk3 = A )
& ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( sk2 @ A )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[68,7]) ).
thf(101,plain,
( ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( ( sk3 = sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk3 ))]]) ).
thf(125,plain,
( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(136,plain,
( ( sk2 @ sk3 )
| ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( ( (=) @ $i @ sk3 )
= ( (=) @ $i @ sk3 ) ) )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[30,125]) ).
thf(137,plain,
( ( sk2 @ sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( sk2 @ sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[137:[]]) ).
thf(143,plain,
( ( ( sk2 @ sk3 )
| ( sk10 != sk3 ) )
& ( ( sk2 @ sk3 )
| ( sk2 @ sk10 ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(145,plain,
( ( sk2 @ sk3 )
| ( sk2 @ sk10 ) ),
inference(cnfConj,[status(thm)],[143]) ).
thf(160,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk10 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[145]) ).
thf(164,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk10 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(134,plain,
( ~ ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[125]) ).
thf(140,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(147,plain,
( ( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( sk11 != sk3 ) )
& ( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk11 ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(149,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk11 ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(221,plain,
( ( ( sk2 @ sk13 )
!= ( sk3 = sk13 ) )
| ( sk2 @ sk11 ) ),
inference(func_ext,[status(esa)],[149]) ).
thf(21,plain,
( ~ ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(23,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ sk3 )
| ( sk7 != sk3 ) )
& ( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ sk3 )
| ( sk2 @ sk7 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(26,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ sk3 )
| ( sk7 != sk3 ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(28,plain,
( ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ sk3 ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(148,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( sk11 != sk3 ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(150,plain,
( ( sk11 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(167,plain,
( ( sk2 @ sk3 )
| ( sk11 != sk3 )
| ( ( (=) @ $i @ sk3 )
!= ( (=) @ $i @ sk3 ) )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[30,150]) ).
thf(168,plain,
( ( sk2 @ sk3 )
| ( sk11 != sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[167]) ).
thf(169,plain,
( ( sk2 @ sk3 )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[168:[]]) ).
thf(433,plain,
( ( sk2 @ sk11 )
| ( sk2 @ sk13 )
| ( sk3 = sk13 ) ),
inference(bool_ext,[status(thm)],[221]) ).
thf(450,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk2 @ sk13 ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(484,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[450]) ).
thf(489,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk13 != sk11 ) ),
inference(simp,[status(thm)],[484]) ).
thf(27,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ sk3 )
| ( sk2 @ sk7 ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(144,plain,
( ( sk2 @ sk3 )
| ( sk10 != sk3 ) ),
inference(cnfConj,[status(thm)],[143]) ).
thf(146,plain,
( ( sk10 != sk3 )
| ( sk2 @ sk3 ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(180,plain,
( ( sk10 != sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ $true
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[146,28]) ).
thf(181,plain,
( ( sk10 != sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
( ( sk10 != sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[181:[]]) ).
thf(9,plain,
( ~ ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) )
| ~ ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( ~ ( sk1 @ A )
| ( ( sk4 @ A )
!= A )
| ( sk1
!= ( (=) @ $i @ B ) ) )
& ( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ A ) )
| ( sk1
!= ( (=) @ $i @ B ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ A ) )
| ( sk1
!= ( (=) @ $i @ B ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( sk1
!= ( (=) @ $i @ B ) )
| ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A )
| ( ( sk4 @ A )
!= A )
| ( sk1
!= ( (=) @ $i @ B ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ A )
!= A )
| ( sk1
!= ( (=) @ $i @ B ) )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(166,plain,
( ( ( sk2 @ sk12 )
!= ( sk3 = sk12 ) )
| ( sk11 != sk3 ) ),
inference(func_ext,[status(esa)],[150]) ).
thf(171,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 )
| ( sk3 = sk12 ) ),
inference(bool_ext,[status(thm)],[166]) ).
thf(179,plain,
( ( sk12 = sk3 )
| ( sk11 != sk3 )
| ( sk2 @ sk12 ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(170,plain,
( ( sk11 != sk3 )
| ~ ( sk2 @ sk12 )
| ( sk3 != sk12 ) ),
inference(bool_ext,[status(thm)],[166]) ).
thf(175,plain,
( ( sk12 != sk3 )
| ( sk11 != sk3 )
| ~ ( sk2 @ sk12 ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(265,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 )
| ( sk11 != sk3 )
| ~ $true
| ( ( sk2 @ sk12 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[169,175]) ).
thf(266,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 )
| ( ( sk2 @ sk12 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(281,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 )
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[266]) ).
thf(287,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[281]) ).
thf(305,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 )
| ( sk11 != sk3 )
| ( sk3 != sk3 )
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[179,287]) ).
thf(306,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 )
| ( sk12 != sk12 ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[306:[]]) ).
thf(432,plain,
( ( sk2 @ sk11 )
| ~ ( sk2 @ sk13 )
| ( sk3 != sk13 ) ),
inference(bool_ext,[status(thm)],[221]) ).
thf(451,plain,
( ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ~ ( sk2 @ sk13 ) ),
inference(lifteq,[status(thm)],[432]) ).
thf(517,plain,
( ( sk10 != sk3 )
| ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ~ $true
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[146,451]) ).
thf(518,plain,
( ( sk10 != sk3 )
| ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(521,plain,
( ( sk2 @ sk11 )
| ( sk10 != sk3 )
| ( sk13 != sk3 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[518]) ).
thf(529,plain,
( ( sk2 @ sk11 )
| ( sk10 != sk3 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[521]) ).
thf(31,plain,
! [A: $i] :
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( A = sk3 )
| ~ ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(32,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(229,plain,
( ( sk2 @ sk3 )
| ( ( (=) @ $i @ sk3 )
!= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk11 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[30,149]) ).
thf(230,plain,
( ( sk2 @ sk3 )
| ( sk2 @ sk11 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
( ( sk2 @ sk3 )
| ( sk2 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[230:[]]) ).
thf(243,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk11 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[231]) ).
thf(245,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk11 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(8,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) )
!= ( ^ [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(17,plain,
! [A: $i] :
( ( sk1 @ sk5 )
| ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(19,plain,
! [A: $i] :
( ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ( sk1 @ sk5 ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(942,plain,
$false,
inference(e,[status(thm)],[5,20,164,221,28,169,489,27,3,145,150,182,4,15,14,125,307,6,529,166,32,149,451,7,245,231,450,8,287,146,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n007.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 15:29:41 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
% 1.04/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.02 % [INFO] Parsing done (190ms).
% 1.43/1.04 % [INFO] Running in sequential loop mode.
% 1.94/1.43 % [INFO] eprover registered as external prover.
% 1.94/1.44 % [INFO] Scanning for conjecture ...
% 2.11/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.11/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.11/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.57 % [INFO] Type checking passed.
% 2.11/1.58 % [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 ...
% 11.66/3.81 % External prover 'e' found a proof!
% 11.66/3.81 % [INFO] Killing All external provers ...
% 11.66/3.81 % Time passed: 3453ms (effective reasoning time: 2771ms)
% 11.66/3.81 % 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)>
% 11.66/3.82 % Axioms used in derivation (0):
% 11.66/3.82 % No. of inferences in proof: 89
% 11.66/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3453 ms resp. 2771 ms w/o parsing
% 11.66/3.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.66/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------