%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM814^5 : 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 : n026.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 64.07s 15.93s
% Output : Refutation 64.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 89 ( 31 unt; 0 typ; 7 def)
% Number of atoms : 272 ( 255 equ; 65 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1185 ( 225 ~; 219 |; 20 &; 700 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 257 ( 57 ^; 192 !; 5 ?; 257 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c0_decl,type,
c0: $i ).
thf(cS_decl,type,
cS: $i > $i ).
thf(cEVEN1_decl,type,
cEVEN1: $i > $o ).
thf(cIND_decl,type,
cIND: $o ).
thf(cODD1_decl,type,
cODD1: $i > $o ).
thf(cPEANO1_decl,type,
cPEANO1: $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(cEVEN1_def,definition,
( cEVEN1
= ( ^ [A: $i] :
! [B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(cIND_def,definition,
( cIND
= ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) ) ) ).
thf(cODD1_def,definition,
( cODD1
= ( ^ [A: $i] :
~ ( cEVEN1 @ A ) ) ) ).
thf(cPEANO1_def,definition,
( cPEANO1
= ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) )
& cIND ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( cS @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o,B: $i] :
@+[C: $i] :
~ ( ( A @ C )
=> ( A @ ( cS @ ( cS @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( cS @ B ) )
= B ) ) ) ).
thf(1,conjecture,
( cPEANO1
=> ? [A: $i] : ( cODD1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM404) ).
thf(2,negated_conjecture,
~ ( cPEANO1
=> ? [A: $i] : ( cODD1 @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) )
& ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) )
=> ? [A: $i] :
~ ! [B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: $i] :
( ( cS @ A )
= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) )
& ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) )
=> ~ ! [A: $i,B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [G: $i > $o,F: $i,E: $i,D: $i > $o,C: $i,B: $i,A: $i] :
( ( ( cS @ A )
!= c0 )
& ( ( ( cS @ B )
!= ( cS @ C ) )
| ( B = C ) )
& ( ~ ( D @ c0 )
| ( D @ ( sk1 @ D ) )
| ( D @ E ) )
& ( ~ ( D @ c0 )
| ~ ( D @ ( cS @ ( sk1 @ D ) ) )
| ( D @ E ) )
& ( ~ ( G @ c0 )
| ( G @ ( sk2 @ G @ F ) )
| ( G @ F ) )
& ( ~ ( G @ c0 )
| ~ ( G @ ( cS @ ( cS @ ( sk2 @ G @ F ) ) ) )
| ( G @ F ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ ( sk2 @ B @ A ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
= ( sk2 @ ( (=) @ $i @ c0 ) @ A ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[7:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ c0 ))]]) ).
thf(24,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk2 @ ( (=) @ $i @ c0 ) @ A )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(25,plain,
! [A: $i] :
( ( ( sk2 @ ( (=) @ $i @ c0 ) @ A )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[24]) ).
thf(11,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(29,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[11]) ).
thf(60,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29]) ).
thf(77,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(131,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: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(prim_subst,[status(thm)],[77:[bind(A,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(149,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 @ c0 ) ) ) ) )
& ( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) )
& ( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) )
& ( ~ ( C @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(153,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(cnfConj,[status(thm)],[149]) ).
thf(157,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(54,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)],[29,29]) ).
thf(55,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)],[54]) ).
thf(68,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( cS @ ( sk1 @ C ) )
!= ( cS @ ( sk1 @ ( (=) @ $i @ ( cS @ ( sk1 @ C ) ) ) ) ) )
| ( ( cS @ ( sk1 @ C ) )
= D )
| ( ( A @ B )
!= ( ( cS @ ( sk1 @ C ) )
= c0 ) ) ),
inference(replace_leibeq,[status(thm)],[55:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ $i @ ( cS @ ( sk1 @ C ) ) ))]]) ).
thf(74,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)],[68]) ).
thf(6,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
! [A: $i] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(26,plain,
! [A: $i] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(27,plain,
! [A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[26]) ).
thf(9,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(23,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(lifteq,[status(thm)],[9]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,23]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( A
!= ( cS @ B ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( cS @ C )),bind(B,$thf( C ))]]) ).
thf(22,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(270,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)],[22,22]) ).
thf(271,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)],[270]) ).
thf(326,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk1 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[271:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(360,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)],[326]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( c0
= ( sk1 @ ( (=) @ $i @ B ) ) )
| ( c0
= ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) ) )
| ( c0 = A ) ),
inference(pre_uni,[status(thm)],[360:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(451,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)],[367]) ).
thf(452,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)],[451]) ).
thf(3237,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)],[452]) ).
thf(3285,plain,
! [A: $i] :
( ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [B: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ B ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[3237:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ^ [C: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ C ) ) ) ))]]) ).
thf(3491,plain,
! [B: $i,A: $i] :
( ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3285,23]) ).
thf(3492,plain,
! [B: $i,A: $i] :
( ( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [C: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ C ) ) ) ) ) )
= c0 )
| ( A
!= ( cS @ B ) ) ),
inference(simp,[status(thm)],[3491]) ).
thf(3493,plain,
( ( sk1
@ ( (=) @ $i
@ ( sk1
@ ^ [A: $i] :
( c0
= ( sk1 @ ( (=) @ $i @ A ) ) ) ) ) )
= c0 ),
inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( cS @ C )),bind(B,$thf( C ))]]) ).
thf(3589,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)],[3493,77]) ).
thf(3590,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 @ ( (=) @ $i @ B ) ) ) )
!= c0 ) ) ),
inference(pattern_uni,[status(thm)],[3589:[bind(A,$thf( (=) @ $i @ ( sk1 @ ^ [C: $i] : ( c0 = ( sk1 @ ( (=) @ $i @ C ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(3612,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)],[3590]) ).
thf(3622,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)],[3612]) ).
thf(4097,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)],[40,3622]) ).
thf(4098,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)],[4097]) ).
thf(4140,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)],[4098]) ).
thf(152,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(cnfConj,[status(thm)],[149]) ).
thf(156,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(simp,[status(thm)],[16]) ).
thf(56,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)],[29,29]) ).
thf(57,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)],[56]) ).
thf(75,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)],[57:[]]) ).
thf(76,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)],[75:[]]) ).
thf(151,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(cnfConj,[status(thm)],[149]) ).
thf(155,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cS
@ ( sk1
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ c0 )
| ( C @ c0 ) ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(298,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(421,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[298]) ).
thf(422,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[421]) ).
thf(1834,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ~ ( B
@ ( sk1
@ ^ [C: $i] :
~ ~ ( B @ C ) ) )
| ~ ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(1900,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B
@ ( sk1
@ ^ [C: $i] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[1834]) ).
thf(1901,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ ( sk1 @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[1900]) ).
thf(61,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29]) ).
thf(87,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(238,plain,
! [A: $i] :
( ( c0 = A )
| ( ( sk2 @ ( (=) @ $i @ c0 ) @ A )
!= A )
| ( c0 != c0 ) ),
inference(eqfactor_ordered,[status(thm)],[25]) ).
thf(239,plain,
! [A: $i] :
( ( c0 = A )
| ( ( sk2 @ ( (=) @ $i @ c0 ) @ A )
!= A ) ),
inference(simp,[status(thm)],[238]) ).
thf(28,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ ( sk2 @ B @ A ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(18,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( cS @ B ) )
= B ),
inference(detectInverse,[status(thm)],[17]) ).
thf(19,plain,
! [A: $i] :
( ( sk3 @ ( cS @ A ) )
= A ),
inference(cnf,[status(esa)],[18]) ).
thf(33,plain,
! [A: $i] :
( ( sk3 @ ( cS @ A ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(150,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 @ c0 ) ) ) ) ),
inference(cnfConj,[status(thm)],[149]) ).
thf(154,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 @ c0 ) ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(124,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[77]) ).
thf(143,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[124:[]]) ).
thf(8,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk2 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(30,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk2 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(9503,plain,
$false,
inference(e,[status(thm)],[25,157,29,74,4140,156,17,22,76,155,3,1901,87,239,28,33,77,3622,3493,154,143,40,23,30,422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM814^5 : 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
% 0.12/0.29 % Computer : n026.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 13:04:12 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 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
% 1.15/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.24 % [INFO] Parsing done (271ms).
% 1.65/1.26 % [INFO] Running in sequential loop mode.
% 2.67/1.85 % [INFO] eprover registered as external prover.
% 2.67/1.86 % [INFO] Scanning for conjecture ...
% 2.86/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.10/2.06 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.10/2.07 % [INFO] Problem is higher-order (TPTP THF).
% 3.10/2.07 % [INFO] Type checking passed.
% 3.10/2.08 % [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 ...
% 64.07/15.93 % External prover 'e' found a proof!
% 64.07/15.93 % [INFO] Killing All external provers ...
% 64.07/15.93 % Time passed: 15427ms (effective reasoning time: 14655ms)
% 64.07/15.93 % 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)>
% 64.07/15.93 % Axioms used in derivation (0):
% 64.07/15.93 % No. of inferences in proof: 82
% 64.07/15.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15427 ms resp. 14655 ms w/o parsing
% 64.07/16.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 64.07/16.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------