%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n004.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 08:37:08 AM UTC 2026
% Result : Theorem 14.76s 4.41s
% Output : Refutation 14.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 98 ( 18 unt; 0 typ; 10 def)
% Number of atoms : 507 ( 297 equ; 67 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 758 ( 215 ~; 135 |; 62 &; 340 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 122 ( 26 ^; 40 !; 49 ?; 122 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% 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 > $i ) > ( $i > $i ) > $i ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $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(sk1_def,definition,
( sk1
= ( ^ [A: $i > $i,B: $i > $i] :
@+[C: $i] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( B != A )
& ( sk2 @ B ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( sk2 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk2 @ B ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
( sk2
= ( (=) @ $i @ B ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ( cONE
= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6101_EXT_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ( cONE
= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ( ( ^ [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,
! [B: $i > $i,A: $i > $i] :
( ( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) )
& ( ( ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( C @ E ) ) ) )
!= ( ^ [C: $i > $o] :
? [D: $i] :
( C
= ( (=) @ $i @ D ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,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)],[6]) ).
thf(9,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)],[8]) ).
thf(11,plain,
( ( ( sk3 @ sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(26,plain,
( ( ( sk3 @ sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
| ( sk3
= ( (=) @ $i @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(28,plain,
( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(33,plain,
! [A: $i] :
( ( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( sk3 @ sk4 ) )
& ( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( A = sk4 )
| ~ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(34,plain,
( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(37,plain,
( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( ( $true
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[34,11]) ).
thf(38,plain,
( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
( ( sk3
= ( (=) @ $i @ sk4 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[38:[]]) ).
thf(64,plain,
! [A: $i] :
( ( ( sk3 @ A )
= ( sk4 = A ) )
| ( ( ~ ? [B: $i] :
( ( B != sk4 )
& ( sk3 @ B ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[39]) ).
thf(94,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] :
( ( B != sk4 )
& ( sk3 @ B ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) )
| ( ( ( sk4 = A )
& ~ ? [B: $i] :
( ( B != sk4 )
& ( sk3 @ B ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) )
| ( ( sk3 @ A )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[64,11]) ).
thf(95,plain,
( ( ( ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) )
| ( ( ( sk4 = sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( sk4 ))]]) ).
thf(126,plain,
( ( ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( sk3
= ( (=) @ $i @ sk4 ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(130,plain,
( ~ ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) )
| ( sk3
!= ( (=) @ $i @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[126]) ).
thf(136,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(143,plain,
( ( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ( sk12 != sk4 ) )
& ( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ( sk3 @ sk12 ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(144,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ( sk12 != sk4 ) ),
inference(cnfConj,[status(thm)],[143]) ).
thf(146,plain,
( ( sk12 != sk4 )
| ( sk3
!= ( (=) @ $i @ sk4 ) ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(162,plain,
( ( ( sk3 @ sk13 )
!= ( sk4 = sk13 ) )
| ( sk12 != sk4 ) ),
inference(func_ext,[status(esa)],[146]) ).
thf(167,plain,
( ( sk12 != sk4 )
| ( sk3 @ sk13 )
| ( sk4 = sk13 ) ),
inference(bool_ext,[status(thm)],[162]) ).
thf(174,plain,
( ( sk13 = sk4 )
| ( sk12 != sk4 )
| ( sk3 @ sk13 ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(163,plain,
( ( sk3 @ sk4 )
| ( sk12 != sk4 )
| ( ( (=) @ $i @ sk4 )
!= ( (=) @ $i @ sk4 ) )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[34,146]) ).
thf(164,plain,
( ( sk3 @ sk4 )
| ( sk12 != sk4 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
( ( sk3 @ sk4 )
| ( sk12 != sk4 ) ),
inference(pattern_uni,[status(thm)],[164:[]]) ).
thf(166,plain,
( ( sk12 != sk4 )
| ~ ( sk3 @ sk13 )
| ( sk4 != sk13 ) ),
inference(bool_ext,[status(thm)],[162]) ).
thf(173,plain,
( ( sk13 != sk4 )
| ( sk12 != sk4 )
| ~ ( sk3 @ sk13 ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(259,plain,
( ( sk12 != sk4 )
| ( sk13 != sk4 )
| ( sk12 != sk4 )
| ~ $true
| ( ( sk3 @ sk13 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[165,173]) ).
thf(260,plain,
( ( sk12 != sk4 )
| ( sk13 != sk4 )
| ( ( sk3 @ sk13 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(267,plain,
( ( sk12 != sk4 )
| ( sk13 != sk4 )
| ( sk13 != sk4 ) ),
inference(simp,[status(thm)],[260]) ).
thf(274,plain,
( ( sk12 != sk4 )
| ( sk13 != sk4 ) ),
inference(simp,[status(thm)],[267]) ).
thf(287,plain,
( ( sk12 != sk4 )
| ( sk3 @ sk13 )
| ( sk12 != sk4 )
| ( sk4 != sk4 )
| ( sk13 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[174,274]) ).
thf(288,plain,
( ( sk12 != sk4 )
| ( sk3 @ sk13 )
| ( sk13 != sk13 ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( sk12 != sk4 )
| ( sk3 @ sk13 ) ),
inference(pattern_uni,[status(thm)],[288:[]]) ).
thf(10,plain,
( ( ? [A: $i] :
( ( sk2 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk2 @ B ) ) ) )
!= ( ? [A: $i] :
( sk2
= ( (=) @ $i @ A ) ) ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(12,plain,
( ( ^ [A: $i] :
( ( sk2 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk2 @ B ) ) ) )
!= ( ^ [A: $i] :
( sk2
= ( (=) @ $i @ A ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(25,plain,
( ~ ( ( sk3 @ sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
| ( sk3
!= ( (=) @ $i @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(27,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( ( sk3 @ sk4 )
& ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(29,plain,
( ( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( sk3 @ sk4 )
| ( sk8 != sk4 ) )
& ( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk8 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(31,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk8 ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(145,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ( sk3 @ sk12 ) ),
inference(cnfConj,[status(thm)],[143]) ).
thf(216,plain,
( ( sk3 @ sk4 )
| ( ( (=) @ $i @ sk4 )
!= ( (=) @ $i @ sk4 ) )
| ( sk3 @ sk12 )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[34,145]) ).
thf(217,plain,
( ( sk3 @ sk4 )
| ( sk3 @ sk12 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
( ( sk3 @ sk4 )
| ( sk3 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[217:[]]) ).
thf(209,plain,
( ( ( sk3 @ sk14 )
!= ( sk4 = sk14 ) )
| ( sk3 @ sk12 ) ),
inference(func_ext,[status(esa)],[145]) ).
thf(350,plain,
( ( sk3 @ sk12 )
| ( sk3 @ sk14 )
| ( sk4 = sk14 ) ),
inference(bool_ext,[status(thm)],[209]) ).
thf(364,plain,
( ( sk14 = sk4 )
| ( sk3 @ sk12 )
| ( sk3 @ sk14 ) ),
inference(lifteq,[status(thm)],[350]) ).
thf(133,plain,
( ( sk3 @ sk4 )
| ( ( ~ ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) )
!= ( ( (=) @ $i @ sk4 )
= ( (=) @ $i @ sk4 ) ) )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[34,126]) ).
thf(134,plain,
( ( sk3 @ sk4 )
| ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
( ( sk3 @ sk4 )
| ? [A: $i] :
( ( A != sk4 )
& ( sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[134:[]]) ).
thf(139,plain,
( ( ( sk3 @ sk4 )
| ( sk11 != sk4 ) )
& ( ( sk3 @ sk4 )
| ( sk3 @ sk11 ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(140,plain,
( ( sk3 @ sk4 )
| ( sk11 != sk4 ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(142,plain,
( ( sk11 != sk4 )
| ( sk3 @ sk4 ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(30,plain,
( ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( sk3 @ sk4 )
| ( sk8 != sk4 ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(32,plain,
( ( sk8 != sk4 )
| ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ ( sk3 @ sk4 ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(183,plain,
( ( sk11 != sk4 )
| ( sk8 != sk4 )
| ( sk3
!= ( (=) @ $i @ sk4 ) )
| ~ $true
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[142,32]) ).
thf(184,plain,
( ( sk11 != sk4 )
| ( sk8 != sk4 )
| ( sk3
!= ( (=) @ $i @ sk4 ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
( ( sk11 != sk4 )
| ( sk8 != sk4 )
| ( sk3
!= ( (=) @ $i @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[184:[]]) ).
thf(14,plain,
( ? [A: $i] :
( ( sk2 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk2 @ B ) ) )
| ? [A: $i] :
( sk2
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(20,plain,
! [A: $i] :
( ( ( sk2 @ sk6 )
| ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) ) )
& ( ( A = sk6 )
| ~ ( sk2 @ A )
| ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(22,plain,
! [A: $i] :
( ( A = sk6 )
| ~ ( sk2 @ A )
| ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(24,plain,
! [A: $i] :
( ( A = sk6 )
| ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(141,plain,
( ( sk3 @ sk4 )
| ( sk3 @ sk11 ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(156,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk11 )
!= ( sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[141]) ).
thf(160,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk11 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(349,plain,
( ( sk3 @ sk12 )
| ~ ( sk3 @ sk14 )
| ( sk4 != sk14 ) ),
inference(bool_ext,[status(thm)],[209]) ).
thf(362,plain,
( ( sk14 != sk4 )
| ( sk3 @ sk12 )
| ~ ( sk3 @ sk14 ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(5,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(63,plain,
! [C: $i,B: $i > $i,A: $i > $i] :
( ( ( A @ C )
= ( B @ C ) )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(13,plain,
( ~ ? [A: $i] :
( ( sk2 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk2 @ B ) ) )
| ~ ? [A: $i] :
( sk2
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ~ ( sk2 @ A )
| ( ( sk5 @ A )
!= A )
| ( sk2
!= ( (=) @ $i @ B ) ) )
& ( ~ ( sk2 @ A )
| ( sk2 @ ( sk5 @ A ) )
| ( sk2
!= ( (=) @ $i @ B ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( sk2 @ A )
| ( ( sk5 @ A )
!= A )
| ( sk2
!= ( (=) @ $i @ B ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ A )
!= A )
| ( sk2
!= ( (=) @ $i @ B ) )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(391,plain,
! [C: $i,B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( sk3
= ( (=) @ $i @ ( A @ C ) ) )
!= ( ~ ? [D: $i] :
( ( D != sk4 )
& ( sk3 @ D ) ) ) )
| ( ( B @ C )
!= sk4 ) ),
inference(paramod_ordered,[status(thm)],[63,126]) ).
thf(517,plain,
! [A: $i > $i] :
( ( ( A
@ ( sk1
@ ^ [B: $i] : B
@ A ) )
!= ( sk1
@ ^ [B: $i] : B
@ A ) )
| ( ( sk3
= ( (=) @ $i @ ( A @ sk4 ) ) )
!= ( ~ ? [B: $i] :
( ( B != sk4 )
& ( sk3 @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : D )),bind(C,$thf( sk4 ))]]) ).
thf(21,plain,
! [A: $i] :
( ( sk2 @ sk6 )
| ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(23,plain,
! [A: $i] :
( ( sk2
= ( (=) @ $i @ ( sk7 @ A ) ) )
| ( sk2 @ sk6 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(231,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk12 )
!= ( sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[218]) ).
thf(235,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk12 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk5 @ A ) )
| ( sk2
!= ( (=) @ $i @ B ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( sk2
!= ( (=) @ $i @ B ) )
| ~ ( sk2 @ A )
| ( sk2 @ ( sk5 @ A ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(1198,plain,
$false,
inference(e,[status(thm)],[289,12,3,31,11,218,126,364,10,142,185,24,160,165,9,141,32,34,274,362,7,162,209,145,63,18,517,23,8,235,146,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 15:32:07 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.99 % [INFO] Parsing done (188ms).
% 1.23/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.23/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.57 % [INFO] Type checking passed.
% 2.23/1.57 % [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 ...
% 14.76/4.40 % External prover 'e' found a proof!
% 14.76/4.40 % [INFO] Killing All external provers ...
% 14.76/4.41 % Time passed: 4040ms (effective reasoning time: 3398ms)
% 14.76/4.41 % 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)>
% 14.76/4.41 % Axioms used in derivation (0):
% 14.76/4.41 % No. of inferences in proof: 88
% 14.76/4.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4040 ms resp. 3398 ms w/o parsing
% 14.76/4.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.76/4.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------