%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU675^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n012.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 08:28:59 AM UTC 2026
% Result : Theorem 10.73s 2.93s
% Output : Refutation 10.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 19 unt; 0 typ; 11 def)
% Number of atoms : 228 ( 48 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 910 ( 52 ~; 33 |; 35 &; 764 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 159 ( 80 ^; 59 !; 15 ?; 159 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(ex1_decl,type,
ex1: $i > ( $i > $o ) > $o ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(funcSet_decl,type,
funcSet: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(ex1_def,definition,
( ex1
= ( ^ [A: $i,B: $i > $o] : ( singleton @ ( dsetconstr @ A @ B ) ) ) ) ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(func_def,definition,
( func
= ( ^ [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
& ! [D: $i] :
( ( in @ D @ A )
=> ( ex1 @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).
thf(funcSet_def,definition,
( funcSet
= ( ^ [A: $i,B: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) ) @ ( func @ A @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
& ! [E: $i] :
( ( in @ E @ A )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
=> ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ A ) )
@ ^ [C: $i] :
( ( subset @ C @ ( cartprod @ sk1 @ A ) )
& ! [D: $i] :
( ( in @ D @ sk1 )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ A
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ A
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) )
=> ( ( subset @ B @ ( cartprod @ sk1 @ A ) )
& ! [C: $i] :
( ( in @ C @ sk1 )
=> ? [D: $i] :
( ( in @ D
@ ( dsetconstr @ A
@ ^ [E: $i] : ( in @ ( kpair @ C @ E ) @ B ) ) )
& ( ( dsetconstr @ A
@ ^ [E: $i] : ( in @ ( kpair @ C @ E ) @ B ) )
= ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [B: $i] :
( ( subset @ B @ ( cartprod @ sk1 @ sk2 ) )
& ! [C: $i] :
( ( in @ C @ sk1 )
=> ? [D: $i] :
( ( in @ D
@ ( dsetconstr @ sk2
@ ^ [E: $i] : ( in @ ( kpair @ C @ E ) @ B ) ) )
& ( ( dsetconstr @ sk2
@ ^ [E: $i] : ( in @ ( kpair @ C @ E ) @ B ) )
= ( setadjoin @ D @ emptyset ) ) ) ) ) ) )
=> ( ( subset @ A @ ( cartprod @ sk1 @ sk2 ) )
& ! [B: $i] :
( ( in @ B @ sk1 )
=> ? [C: $i] :
( ( in @ C
@ ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) ) )
& ( ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ? [B: $i] :
( ( in @ B
@ ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) ) )
& ( ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) )
= ( setadjoin @ B @ emptyset ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( in @ B
@ ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) ) )
& ( ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) )
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
& ! [E: $i] :
( ( in @ E @ A )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
=> ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) )
& ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [E: $i] :
( ( subset @ E @ ( cartprod @ sk1 @ sk2 ) )
& ! [F: $i] :
( ( in @ F @ sk1 )
=> ? [G: $i] :
( ( in @ G
@ ( dsetconstr @ sk2
@ ^ [H: $i] : ( in @ ( kpair @ F @ H ) @ E ) ) )
& ( ( dsetconstr @ sk2
@ ^ [H: $i] : ( in @ ( kpair @ F @ H ) @ E ) )
= ( setadjoin @ G @ emptyset ) ) ) ) ) ) )
& ( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ( in @ sk4 @ sk1 ) )
& ( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ D
@ ( dsetconstr @ sk2
@ ^ [E: $i] : ( in @ ( kpair @ sk4 @ E ) @ sk3 ) ) )
| ( ( dsetconstr @ sk2
@ ^ [E: $i] : ( in @ ( kpair @ sk4 @ E ) @ sk3 ) )
!= ( setadjoin @ D @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [A: $i] :
( ( subset @ A @ ( cartprod @ sk1 @ sk2 ) )
& ! [B: $i] :
( ( in @ B @ sk1 )
=> ? [C: $i] :
( ( in @ C
@ ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) ) )
& ( ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ ( kpair @ B @ D ) @ A ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ $true
| ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ sk1 @ sk2 ) )
& ! [E: $i] :
( ( in @ E @ sk1 )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,5]) ).
thf(14,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( cartprod @ sk1 @ sk2 ) )
@ ^ [D: $i] :
( ( subset @ D @ ( cartprod @ sk1 @ sk2 ) )
& ! [E: $i] :
( ( in @ E @ sk1 )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ sk2
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
( ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
& ! [A: $i] :
( ( in @ A @ sk1 )
=> ? [B: $i] :
( ( in @ B
@ ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) ) )
& ( ( dsetconstr @ sk2
@ ^ [C: $i] : ( in @ ( kpair @ A @ C ) @ sk3 ) )
= ( setadjoin @ B @ emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( powerset @ ( cartprod @ sk1 @ sk2 ) )),bind(B,$thf( ^ [D: $i] : ( ( subset @ D @ ( cartprod @ sk1 @ sk2 ) ) & ! [E: $i] : ( ( in @ E @ sk1 ) => ? [F: $i] : ( ( in @ F @ ( dsetconstr @ sk2 @ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) ) & ( ( dsetconstr @ sk2 @ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) = ( setadjoin @ F @ emptyset ) ) ) ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(32,plain,
! [A: $i] :
( ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
& ( ~ ( in @ A @ sk1 )
| ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) ) )
& ( ~ ( in @ A @ sk1 )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
= ( setadjoin @ ( sk5 @ A ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(35,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
= ( setadjoin @ ( sk5 @ A ) @ emptyset ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
= ( setadjoin @ ( sk5 @ A ) @ emptyset ) )
| ~ ( in @ A @ sk1 ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(7,plain,
( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ( in @ sk4 @ sk1 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(33,plain,
subset @ sk3 @ ( cartprod @ sk1 @ sk2 ),
inference(cnfConj,[status(thm)],[32]) ).
thf(47,plain,
( ~ $true
| ( in @ sk4 @ sk1 ) ),
inference(rewrite,[status(thm)],[7,33]) ).
thf(48,plain,
in @ sk4 @ sk1,
inference(simp,[status(thm)],[47]) ).
thf(34,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(511,plain,
! [A: $i] :
( ~ $true
| ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) )
| ( ( in @ sk4 @ sk1 )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[48,34]) ).
thf(512,plain,
! [A: $i] :
( ( in @ ( sk5 @ A )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) ) )
| ( ( in @ sk4 @ sk1 )
!= ( in @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(513,plain,
( in @ ( sk5 @ sk4 )
@ ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ ( kpair @ sk4 @ A ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[512:[bind(A,$thf( sk4 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset @ sk3 @ ( cartprod @ sk1 @ sk2 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(115,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(rewrite,[status(thm)],[10,33]) ).
thf(116,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(570,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ sk4 )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) )
!= ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[513,116]) ).
thf(571,plain,
! [A: $i] :
( ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ sk4 )
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) )
!= ( in @ A
@ ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ) ),
inference(simp,[status(thm)],[570]) ).
thf(572,plain,
( ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ ( kpair @ sk4 @ A ) @ sk3 ) )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( sk5 @ sk4 ))]]) ).
thf(995,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ( setadjoin @ ( sk5 @ A ) @ emptyset )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) )
| ( ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ A @ B ) @ sk3 ) )
!= ( dsetconstr @ sk2
@ ^ [B: $i] : ( in @ ( kpair @ sk4 @ B ) @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,572]) ).
thf(996,plain,
( ~ ( in @ sk4 @ sk1 )
| ( ( setadjoin @ ( sk5 @ sk4 ) @ emptyset )
!= ( setadjoin @ ( sk5 @ sk4 ) @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[995:[bind(A,$thf( sk4 ))]]) ).
thf(1083,plain,
~ ( in @ sk4 @ sk1 ),
inference(simp,[status(thm)],[996]) ).
thf(1098,plain,
~ $true,
inference(rewrite,[status(thm)],[1083,48]) ).
thf(1099,plain,
$false,
inference(simp,[status(thm)],[1098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU675^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % 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
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 14:07:03 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 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
% 0.40/0.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.51 % [INFO] Parsing done (102ms).
% 0.56/0.52 % [INFO] Running in sequential loop mode.
% 1.03/0.71 % [INFO] eprover registered as external prover.
% 1.03/0.71 % [INFO] Scanning for conjecture ...
% 1.03/0.78 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.03/0.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.03/0.79 % [INFO] Problem is higher-order (TPTP THF).
% 1.03/0.80 % [INFO] Type checking passed.
% 1.23/0.80 % [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 ...
% 10.73/2.93 % [INFO] Killing All external provers ...
% 10.73/2.93 % Time passed: 2736ms (effective reasoning time: 2407ms)
% 10.73/2.93 % 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)>
% 10.73/2.93 % Axioms used in derivation (0):
% 10.73/2.93 % No. of inferences in proof: 33
% 10.73/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2736 ms resp. 2407 ms w/o parsing
% 10.73/2.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.73/2.98 % [INFO] Killing All external provers ...
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