%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n017.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 08:18:14 AM UTC 2026
% Result : Theorem 58.88s 15.96s
% Output : Refutation 59.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 103 ( 26 unt; 0 typ; 3 def)
% Number of atoms : 407 ( 394 equ; 91 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1328 ( 297 ~; 263 |; 8 &; 752 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 306 ( 89 ^; 211 !; 4 ?; 306 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c0_decl,type,
c0: $i ).
thf(cS_decl,type,
cS: $i > $i ).
thf(cIND_decl,type,
cIND: $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(cIND_def,definition,
( cIND
= ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( cS @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ) ) ).
thf(1,conjecture,
( cIND
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM578) ).
thf(2,negated_conjecture,
~ ( cIND
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) )
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i,A: $i > $o] :
( ( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) )
& ( sk2 != c0 )
& ( sk2
!= ( cS @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(13,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[13]) ).
thf(29,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( sk1 @ ( (=) @ $i @ c0 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(30,plain,
( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 @ ( (=) @ $i @ c0 ) ))]]) ).
thf(6,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(35,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) )
| ( A @ B )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,6]) ).
thf(36,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
!= ( cS @ c0 ) )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( (=) @ $i @ c0 )),bind(B,$thf( B ))]]) ).
thf(51,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( cS @ c0 )
!= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(79,plain,
! [A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[51]) ).
thf(39,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(57,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(158,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( B @ c0 )
| ~ ( B @ c0 )
| ( ( B @ C )
!= ( ~ ( B @ c0 ) ) )
| ( A
!= ( cS @ ( sk1 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,57]) ).
thf(159,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( B @ c0 )
| ( ( B @ C )
!= ( ~ ( B @ c0 ) ) )
| ( A
!= ( cS @ ( sk1 @ B ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [B: $i > $o,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( B @ c0 )
| ( ( B @ A )
!= ( ~ ( B @ c0 ) ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( cS @ ( sk1 @ E ) )),bind(B,$thf( E )),bind(C,$thf( C ))]]) ).
thf(194,plain,
! [B: $i > $o,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( B @ c0 )
| ( ( B @ A )
!= ( ~ ( B @ c0 ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(400,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( ( cS @ c0 )
!= c0 )
| ~ ( C @ A )
| ( ( C @ B )
!= ( ~ ( C @ c0 ) ) )
| ( c0 != c0 ) ),
inference(paramod_ordered,[status(thm)],[79,194]) ).
thf(401,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( C @ A )
| ( ( C @ B )
!= ( ~ ( C @ c0 ) ) )
| ( c0 != c0 ) ),
inference(simp,[status(thm)],[400]) ).
thf(402,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( C @ A )
| ( ( C @ B )
!= ( ~ ( C @ c0 ) ) ) ),
inference(pattern_uni,[status(thm)],[401:[]]) ).
thf(501,plain,
! [D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( ( cS @ c0 )
!= c0 )
| ~ ( D @ B )
| ( ( ~ ( D @ A ) )
!= ( D @ C ) )
| ( c0 != c0 ) ),
inference(paramod_ordered,[status(thm)],[79,402]) ).
thf(502,plain,
! [D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( D @ B )
| ( ( ~ ( D @ A ) )
!= ( D @ C ) )
| ( c0 != c0 ) ),
inference(simp,[status(thm)],[501]) ).
thf(503,plain,
! [D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( D @ B )
| ( ( ~ ( D @ A ) )
!= ( D @ C ) ) ),
inference(pattern_uni,[status(thm)],[502:[]]) ).
thf(1585,plain,
! [D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ~ ( D @ B )
| ~ ( D @ A )
| ( D @ C ) ),
inference(bool_ext,[status(thm)],[503]) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( B != B )
| ( B != A )
| ( B = C ) ),
inference(replace_leibeq,[status(thm)],[1585:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( (=) @ $i @ B ))]]) ).
thf(1644,plain,
! [C: $i,B: $i,A: $i] :
( ( B != B )
| ( B = C )
| ( ( cS @ c0 )
!= c0 )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1632]) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ( B != B )
| ( B = C )
| ( ( cS @ c0 )
!= c0 )
| ( B != A ) ),
inference(cnf,[status(esa)],[1644]) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ( B != A )
| ( B != B )
| ( B = C )
| ( ( cS @ c0 )
!= c0 ) ),
inference(lifteq,[status(thm)],[1692]) ).
thf(1694,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( cS @ c0 )
!= c0 ) ),
inference(simp,[status(thm)],[1693]) ).
thf(8,plain,
! [A: $i] :
( sk2
!= ( cS @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
! [A: $i] :
( ( cS @ A )
!= sk2 ),
inference(lifteq,[status(thm)],[8]) ).
thf(17,plain,
! [A: $i] :
( ( cS @ A )
!= sk2 ),
inference(simp,[status(thm)],[16]) ).
thf(2193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( B != sk2 )
| ( A
!= ( cS @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1694,17]) ).
thf(2194,plain,
! [A: $i] :
( ( ( cS @ c0 )
!= c0 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[2193:[bind(A,$thf( cS @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2448,plain,
( ( cS @ c0 )
!= c0 ),
inference(simp,[status(thm)],[2194]) ).
thf(31,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ $true
| ~ ( C @ ( cS @ ( sk1 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[6,6]) ).
thf(32,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( C @ ( cS @ ( sk1 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(47,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( cS @ ( sk1 @ C ) )
!= ( cS @ ( sk1 @ ( (=) @ $i @ ( cS @ ( sk1 @ C ) ) ) ) ) )
| ( ( cS @ ( sk1 @ C ) )
= D )
| ( ( A @ B )
!= ( ( cS @ ( sk1 @ C ) )
= c0 ) ) ),
inference(replace_leibeq,[status(thm)],[32:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ $i @ ( cS @ ( sk1 @ C ) ) ))]]) ).
thf(52,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ( ( cS @ ( sk1 @ C ) )
!= ( cS @ ( sk1 @ ( (=) @ $i @ ( cS @ ( sk1 @ C ) ) ) ) ) )
| ( ( cS @ ( sk1 @ C ) )
= D )
| ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ( cS @ ( sk1 @ C ) )
= c0 ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(201,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ~ $true
| ( C @ ( sk1 @ C ) )
| ( C @ D )
| ( ( A @ ( sk1 @ A ) )
!= ( C @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[5,5]) ).
thf(202,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( C @ ( sk1 @ C ) )
| ( C @ D )
| ( ( A @ ( sk1 @ A ) )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(255,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk1 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[202:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(274,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk1 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( c0
= ( sk1 @ ( (=) @ $i @ B ) ) )
| ( c0
= ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) ) )
| ( c0 = A ) ),
inference(pre_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( (=) @ $i @ B ) )
= c0 )
| ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( (=) @ $i @ B ) )
= c0 )
| ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[364]) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( (=) @ $i @ B ) )
= c0 )
| ( c0 = A )
| ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
!= ( sk1 @ ( (=) @ $i @ B ) ) )
| ( c0 != c0 ) ),
inference(eqfactor_ordered,[status(thm)],[365]) ).
thf(1978,plain,
! [A: $i] :
( ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[1954:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ^ [C: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ C ) ) ) ))]]) ).
thf(2831,plain,
! [A: $i] :
( ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1978]) ).
thf(2854,plain,
( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [A: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ A ) ) ) ) ) )
= c0 ),
inference(pattern_uni,[status(thm)],[2831:[bind(A,$thf( sk1 @ ( (=) @ $i @ ( sk1 @ ^ [B: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ))]]) ).
thf(2910,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2854,57]) ).
thf(2911,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 )
| ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) ) ),
inference(pattern_uni,[status(thm)],[2910:[bind(A,$thf( (=) @ $i @ ( sk1 @ ^ [C: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ C ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2931,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 )
| ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) ) ),
inference(lifteq,[status(thm)],[2911]) ).
thf(2943,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 )
| ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) ) ),
inference(simp,[status(thm)],[2931]) ).
thf(3370,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
!= ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,2943]) ).
thf(3371,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
!= ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3370]) ).
thf(3428,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( (=) @ $i @ c0 )
!= ( ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3371]) ).
thf(3453,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( ^ [B: $i] : c0 )
!= ( ^ [B: $i] : c0 ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk1 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3428]) ).
thf(3568,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk1 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3453]) ).
thf(33,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( C @ c0 )
| ~ $true
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cS @ ( sk1 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,6]) ).
thf(34,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( C @ c0 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cS @ ( sk1 @ C ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(65,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( C @ c0 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cS @ ( sk1 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[34:[]]) ).
thf(66,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ( C @ D )
| ~ ( C @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( C @ ( cS @ ( sk1 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[65:[]]) ).
thf(37,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(54,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[37:[]]) ).
thf(55,plain,
! [B: $i,A: $i > $o] :
( ( A @ B )
| ~ ( A @ c0 )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[54:[]]) ).
thf(44,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( ( B @ c0 )
| ( C @ c0 ) )
| ~ ( ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(69,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( ~ ( B @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( C @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(71,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(75,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[71]) ).
thf(3480,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( c0 = A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( (=) @ $i @ c0 )
!= ( ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
!= ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,3428]) ).
thf(3540,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( c0 = A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( (=) @ $i @ c0 )
!= ( ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) )
| ( ( (=) @ $i @ c0 )
!= ( ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3480]) ).
thf(3559,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( c0 = A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( (=) @ $i @ c0 )
!= ( ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3540]) ).
thf(4098,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( c0 = A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( ^ [B: $i] : c0 )
!= ( ^ [B: $i] : c0 ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk1 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3559]) ).
thf(4189,plain,
! [A: $i] :
( ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= ( cS @ c0 ) )
| ( ( c0 = A )
!= ( ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk1 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[4098]) ).
thf(41,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ c0 )
| ~ ~ ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(67,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[41]) ).
thf(68,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[67]) ).
thf(4298,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B @ A )
| ( ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
!= ( B @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[68]) ).
thf(4316,plain,
! [A: $i] :
( ( A = c0 )
| ( A != A )
| ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = c0 ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[4298:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(4365,plain,
! [A: $i] :
( ( A = c0 )
| ( A != A )
| ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = c0 ) )
| ~ $true ),
inference(lifteq,[status(thm)],[4316]) ).
thf(4481,plain,
! [A: $i] :
( ( A = c0 )
| ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = c0 ) ) ),
inference(simp,[status(thm)],[4365]) ).
thf(7,plain,
sk2 != c0,
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
sk2 != c0,
inference(lifteq,[status(thm)],[7]) ).
thf(6700,plain,
! [A: $i] :
( ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = c0 ) )
| ( c0 != c0 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[4481,15]) ).
thf(6701,plain,
! [A: $i] :
( ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = c0 ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[6700]) ).
thf(6702,plain,
( ( sk2
= ( cS
@ ( sk1
@ ^ [A: $i] : ( sk2 != A ) ) ) )
!= ( sk2 = c0 ) ),
inference(pattern_uni,[status(thm)],[6701:[bind(A,$thf( sk2 ))]]) ).
thf(70,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(74,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[70]) ).
thf(63,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( C @ ( cS @ ( sk1 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[32:[]]) ).
thf(64,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ( C @ D )
| ~ ( C @ ( cS @ ( sk1 @ C ) ) )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[63:[]]) ).
thf(72,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(76,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[72]) ).
thf(40,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(62,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(7049,plain,
$false,
inference(e,[status(thm)],[2448,52,57,6,3428,3568,66,55,75,30,4189,5,2854,6702,3559,74,64,17,76,2943,3,4481,15,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:56:52 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.06 % [INFO] Parsing done (250ms).
% 1.50/1.08 % [INFO] Running in sequential loop mode.
% 2.43/1.61 % [INFO] eprover registered as external prover.
% 2.43/1.62 % [INFO] Scanning for conjecture ...
% 2.63/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.63/1.76 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.63/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 2.63/1.76 % [INFO] Type checking passed.
% 2.63/1.77 % [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 ...
% 58.88/15.95 % External prover 'e' found a proof!
% 58.88/15.96 % [INFO] Killing All external provers ...
% 58.88/15.96 % Time passed: 15610ms (effective reasoning time: 14869ms)
% 58.88/15.96 % 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)>
% 58.88/15.96 % Axioms used in derivation (0):
% 58.88/15.96 % No. of inferences in proof: 100
% 58.88/15.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 15610 ms resp. 14869 ms w/o parsing
% 59.67/16.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 59.67/16.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------