%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV292^5 : 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 : n014.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 41.36s 11.63s
% Output : Refutation 34.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 238 ( 92 equ; 0 cnn)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 776 ( 185 ~; 72 |; 158 &; 348 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 242 ( 93 ^; 45 !; 102 ?; 242 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cP_decl,type,
cP: ( ( $i > $o ) > $o ) > $o ).
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(c_less__eq__decl,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(sk1_decl,type,
sk1: ( ( $i > $o ) > $o ) > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(sk3_decl,type,
sk3: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
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(c_less__eq__def,definition,
( c_less__eq_
= ( ^ [A: ( $i > $o ) > $o,B: ( $i > $o ) > $o] :
! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C @ A )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C @ ( cSUCC @ D ) ) ) )
=> ( C @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $o ) > $o] :
@+[B: ( ( $i > $o ) > $o ) > $o] :
~ ( ( ( B
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $o ) > $o] :
@+[B: ( ( $i > $o ) > $o ) > $o] :
~ ( ( ( B @ A )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ? [E: $i] :
( ( E != D )
& ( C @ E )
& ~ ? [F: $i] :
( ( F != E )
& ( F != D )
& ( C @ F ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( ( cP @ cONE )
=> ? [A: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ A )
& ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
& ( cP @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE7A) ).
thf(2,negated_conjecture,
~ ( ( cP @ cONE )
=> ? [A: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ A )
& ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
& ( cP @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
=> ? [A: ( $i > $o ) > $o] :
( ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ A )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ? [E: $i] :
( ( E != D )
& ( C @ E )
& ~ ? [F: $i] :
( ( F != E )
& ( F != D )
& ( C @ F ) ) ) ) ) )
& ( cP @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( cP
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ~ ? [F: $i] :
( ( F != E )
& ( D @ F ) ) ) )
& ( ( sk2 @ A
@ ^ [D: $i > $o] :
~ ? [E: $i] : ( D @ E ) )
| ~ ( sk1 @ A ) )
& ( ~ ( sk2 @ A @ B )
| ( sk2 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( B
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
| ~ ( sk1 @ A ) )
& ( ~ ( sk2 @ A @ A )
| ~ ( sk1 @ A ) )
& ( ( sk1 @ A )
| ( sk3 @ A @ A )
| ~ ( cP @ A ) )
& ( ( sk1 @ A )
| ~ ( sk3 @ A @ C )
| ( sk3 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
| ~ ( cP @ A ) )
& ( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ? [F: $i] :
( ( F != E )
& ( D @ F )
& ~ ? [G: $i] :
( ( G != F )
& ( G != E )
& ( D @ G ) ) ) ) )
| ~ ( cP @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ( sk3 @ A @ A )
| ~ ( cP @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A @ B )
| ( sk3 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A @ B )
| ( sk3 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(205,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk1 @ B )
| ~ $true
| ( sk3 @ B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
| ~ ( cP @ B )
| ( ( sk3 @ A @ A )
!= ( sk3 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,12]) ).
thf(206,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk1 @ B )
| ( sk3 @ B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
| ~ ( cP @ B )
| ( ( sk3 @ A @ A )
!= ( sk3 @ B @ C ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk1 @ A )
| ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
| ~ ( cP @ A ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(246,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(10,plain,
( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(73,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) )
| ~ $true
| ( ( cP
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(74,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) )
| ( ( cP
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
!= ( cP @ A ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
( ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).
thf(9,plain,
! [A: ( $i > $o ) > $o] :
( ( sk2 @ A
@ ^ [B: $i > $o] :
~ ? [C: $i] : ( B @ C ) )
| ~ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ B )
| ( sk2 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ A )
| ~ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(22,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ A )
| ~ $true
| ~ ( sk1 @ C )
| ( ( sk2 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( B
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
!= ( sk2 @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7,11]) ).
thf(23,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ A )
| ~ ( sk1 @ C )
| ( ( sk2 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( B
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
!= ( sk2 @ C @ C ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(25,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
@ A )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[23:[bind(A,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) ))]]) ).
thf(28,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
@ A )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(29,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk1 @ A )
| ~ $true
| ~ ( sk1
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ( ( sk2 @ A
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
!= ( sk2
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,28]) ).
thf(30,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk1 @ A )
| ~ ( sk1
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ( ( sk2 @ A
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
!= ( sk2
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) )
@ B ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(33,plain,
( ~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[30:[bind(A,$thf( ^ [C: $i > $o] : ? [D: $i] : ( ( C @ D ) & ~ ( ? [E: $i] : ( ( E != D ) & ( C @ E ) ) ) ) )),bind(B,$thf( ^ [C: $i > $o] : ~ ( ? [D: $i] : ( C @ D ) ) ))]]) ).
thf(35,plain,
~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(255,plain,
( $false
| ~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ) ),
inference(rewrite,[status(thm)],[75,35]) ).
thf(256,plain,
~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(306,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ~ $true
| ( ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
!= ( sk3
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) )
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[246,256]) ).
thf(307,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
!= ( sk3
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) )
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(312,plain,
( ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[307:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).
thf(319,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[312,35,10]) ).
thf(320,plain,
$false,
inference(simp,[status(thm)],[319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV292^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.11 % 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
% 0.10/0.29 % Computer : n014.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8046.5625MB
% 0.10/0.29 % OS : Linux 6.8.0-71-generic
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Sep 29 15:31:14 UTC 2026
% 0.10/0.30 % CPUTime :
% 0.10/0.30 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
% 1.38/1.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.40 % [INFO] Parsing done (279ms).
% 2.04/1.42 % [INFO] Running in sequential loop mode.
% 2.85/1.99 % [INFO] eprover registered as external prover.
% 2.85/2.00 % [INFO] Scanning for conjecture ...
% 3.37/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.44/2.21 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.44/2.21 % [INFO] Problem is higher-order (TPTP THF).
% 3.44/2.22 % [INFO] Type checking passed.
% 3.44/2.22 % [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 ...
% 41.36/11.62 % [INFO] Killing All external provers ...
% 41.36/11.63 % Time passed: 11124ms (effective reasoning time: 10197ms)
% 41.36/11.63 % 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)>
% 41.36/11.63 % Axioms used in derivation (0):
% 41.36/11.63 % No. of inferences in proof: 34
% 41.36/11.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11124 ms resp. 10197 ms w/o parsing
% 34.15/11.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.15/11.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------