%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU668^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n016.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 08:28:58 AM UTC 2026
% Result : Theorem 14.36s 4.66s
% Output : Refutation 12.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 113 ( 58 unt; 0 typ; 13 def)
% Number of atoms : 381 ( 132 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1222 ( 137 ~; 80 |; 53 &; 905 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 363 ( 69 ^; 255 !; 30 ?; 363 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(setukpairinjL_decl,type,
setukpairinjL: $o ).
thf(setukpairinjR_decl,type,
setukpairinjR: $o ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(setukpairinjL_def,definition,
( setukpairinjL
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) ) ) ) ).
thf(setukpairinjR_def,definition,
( setukpairinjR
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) ) ) ) ).
thf(dpsetconstr_def,definition,
( dpsetconstr
= ( ^ [A: $i,B: $i,C: $i > $i > $o] :
( dsetconstr @ ( cartprod @ A @ B )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( C @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( C @ D @ E ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i > $i > $o,C: $i] :
( ( in @ C @ sk1 )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ ( kpair @ C @ D )
@ ( dsetconstr @ ( cartprod @ sk1 @ A )
@ ^ [E: $i] :
? [F: $i] :
( ( in @ F @ sk1 )
& ? [G: $i] :
( ( in @ G @ A )
& ( B @ F @ G )
& ( E
= ( kpair @ F @ G ) ) ) ) ) )
=> ( B @ C @ D ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $o] :
~ ! [B: $i] :
( ( in @ B @ sk1 )
=> ! [C: $i] :
( ( in @ C @ sk2 )
=> ( ( in @ ( kpair @ B @ C )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ? [F: $i] :
( ( in @ F @ sk2 )
& ( A @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ! [B: $i] :
( ( in @ B @ sk2 )
=> ( ( in @ ( kpair @ A @ B )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [C: $i] :
? [D: $i] :
( ( in @ D @ sk1 )
& ? [E: $i] :
( ( in @ E @ sk2 )
& ( sk3 @ D @ E )
& ( C
= ( kpair @ D @ E ) ) ) ) ) )
=> ( sk3 @ A @ B ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( in @ A @ sk2 )
=> ( ( in @ ( kpair @ sk4 @ A )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [B: $i] :
? [C: $i] :
( ( in @ C @ sk1 )
& ? [D: $i] :
( ( in @ D @ sk2 )
& ( sk3 @ C @ D )
& ( B
= ( kpair @ C @ D ) ) ) ) ) )
=> ( sk3 @ sk4 @ A ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( A @ B @ ( kpair @ B @ C ) )
= C ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( A @ C @ ( kpair @ B @ C ) )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3 @ A @ B )
& ( ( kpair @ sk4 @ sk5 )
= ( kpair @ A @ B ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( in @ A @ sk2 )
& ( sk3 @ sk8 @ A )
& ( ( kpair @ sk4 @ sk5 )
= ( kpair @ sk8 @ A ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ) ) ),
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,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) )
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) )
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( C @ D @ E ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) )
& ( ( ( kpair @ D @ E )
!= ( kpair @ F @ G ) )
| ( D = F ) )
& ( ( ( kpair @ H @ I )
!= ( kpair @ J @ K ) )
| ( I = K ) )
& ( in @ sk4 @ sk1 )
& ( in @ sk5 @ sk2 )
& ( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [L: $i] :
? [M: $i] :
( ( in @ M @ sk1 )
& ? [N: $i] :
( ( in @ N @ sk2 )
& ( sk3 @ M @ N )
& ( L
= ( kpair @ M @ N ) ) ) ) ) )
& ~ ( sk3 @ sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(6,plain,
~ ( sk3 @ sk4 @ sk5 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ~ $true
| ( ( B @ C )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(23,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(42,plain,
! [A: $i] :
~ ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[23:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(10,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(simp,[status(thm)],[13]) ).
thf(7,plain,
in @ sk5 @ sk2,
inference(cnfConj,[status(thm)],[5]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $false ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ),
inference(simp,[status(thm)],[34]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( in @ sk5 @ sk2 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,47]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( in @ sk5 @ sk2 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( sk5 != B )
| ( ( dsetconstr @ A
@ ^ [C: $i] : $false )
!= sk2 ) ),
inference(simp,[status(thm)],[176]) ).
thf(189,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk2 ),
inference(simp,[status(thm)],[181]) ).
thf(41,plain,
! [A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[23:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( sk3 @ D @ sk5 ) )),bind(C,$thf( sk4 ))]]) ).
thf(30,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( ~ ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(43,plain,
! [A: $i] :
~ ( in
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) )
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) ) ),
inference(pre_uni,[status(thm)],[30:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ D ) )),bind(C,$thf( dsetconstr @ A @ ^ [D: $i] : ~ ( in @ D @ D ) ))]]) ).
thf(382,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ~ $true
| ( ( B @ C )
!= ( in
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) )
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,43]) ).
thf(383,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) )
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) ) ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(393,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(pre_uni,[status(thm)],[383:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ E ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ E ) )),bind(D,$thf( D ))]]) ).
thf(402,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(8,plain,
( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [A: $i] :
? [B: $i] :
( ( in @ B @ sk1 )
& ? [C: $i] :
( ( in @ C @ sk2 )
& ( sk3 @ B @ C )
& ( A
= ( kpair @ B @ C ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(74,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ $true
| ( B @ C )
| ( ( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ? [F: $i] :
( ( in @ F @ sk2 )
& ( sk3 @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,11]) ).
thf(75,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ? [F: $i] :
( ( in @ F @ sk2 )
& ( sk3 @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
? [A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3 @ A @ B )
& ( ( kpair @ sk4 @ sk5 )
= ( kpair @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( cartprod @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ? [E: $i] : ( ( in @ E @ sk1 ) & ? [F: $i] : ( ( in @ F @ sk2 ) & ( sk3 @ E @ F ) & ( D = ( kpair @ E @ F ) ) ) ) )),bind(C,$thf( kpair @ sk4 @ sk5 ))]]) ).
thf(78,plain,
( ( in @ sk8 @ sk1 )
& ( in @ sk9 @ sk2 )
& ( sk3 @ sk8 @ sk9 )
& ( ( kpair @ sk4 @ sk5 )
= ( kpair @ sk8 @ sk9 ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(82,plain,
( ( kpair @ sk4 @ sk5 )
= ( kpair @ sk8 @ sk9 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(83,plain,
( ( kpair @ sk8 @ sk9 )
= ( kpair @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(15,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( A @ B @ ( kpair @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( kpair @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[15]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( kpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ A @ ( kpair @ sk4 @ sk5 ) )
= B )
| ( ( kpair @ sk8 @ sk9 )
!= ( kpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[83,21]) ).
thf(108,plain,
( ( sk6 @ sk8 @ ( kpair @ sk4 @ sk5 ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(130,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) )
!= ( in @ sk5 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,42]) ).
thf(131,plain,
! [A: $i] :
( ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) )
!= ( in @ sk5 @ sk2 ) ),
inference(simp,[status(thm)],[130]) ).
thf(140,plain,
! [A: $i] :
( ( sk5 != sk5 )
| ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[131]) ).
thf(145,plain,
! [A: $i] :
( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk2 ),
inference(simp,[status(thm)],[140]) ).
thf(9,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( A @ C @ ( kpair @ B @ C ) )
= B ),
inference(detectInverse,[status(thm)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( sk7 @ B @ ( kpair @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[19]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( sk7 @ B @ ( kpair @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(81,plain,
sk3 @ sk8 @ sk9,
inference(cnfConj,[status(thm)],[78]) ).
thf(100,plain,
( ~ $true
| ( ( sk3 @ sk8 @ sk9 )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[81,6]) ).
thf(101,plain,
( ( sk3 @ sk8 @ sk9 )
!= ( sk3 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
( ( sk8 != sk4 )
| ( sk9 != sk5 ) ),
inference(simp,[status(thm)],[101]) ).
thf(12,plain,
in @ sk4 @ sk1,
inference(cnfConj,[status(thm)],[5]) ).
thf(55,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) )
!= ( in @ sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,41]) ).
thf(56,plain,
! [A: $i] :
( ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) )
!= ( in @ sk4 @ sk1 ) ),
inference(simp,[status(thm)],[55]) ).
thf(61,plain,
! [A: $i] :
( ( sk4 != sk4 )
| ( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[56]) ).
thf(70,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk1 ),
inference(simp,[status(thm)],[61]) ).
thf(79,plain,
in @ sk8 @ sk1,
inference(cnfConj,[status(thm)],[78]) ).
thf(128,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk8 @ sk1 )
!= ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,42]) ).
thf(129,plain,
! [A: $i] :
( ( in @ sk8 @ sk1 )
!= ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(137,plain,
! [A: $i] :
( ( sk8 != sk5 )
| ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[129]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ B @ ( kpair @ sk4 @ sk5 ) )
= A )
| ( ( kpair @ sk8 @ sk9 )
!= ( kpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[83,146]) ).
thf(148,plain,
( ( sk7 @ sk9 @ ( kpair @ sk4 @ sk5 ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(32,plain,
! [C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [D: $i] :
~ ( C @ D ) ) )
| ~ ( C @ B ) ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ~ ( D @ E ) ))]]) ).
thf(44,plain,
! [C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [D: $i] :
~ ( C @ D ) ) )
| ~ ( C @ B ) ),
inference(cnf,[status(esa)],[32]) ).
thf(45,plain,
! [C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [D: $i] :
~ ( C @ D ) ) )
| ~ ( C @ B ) ),
inference(simp,[status(thm)],[44]) ).
thf(31,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( C @ B )
| ( D @ B ) ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).
thf(53,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( C @ B )
| ( D @ B ) ),
inference(cnf,[status(esa)],[31]) ).
thf(54,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( C @ B )
| ( D @ B ) ),
inference(simp,[status(thm)],[53]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( in @ sk8 @ sk1 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,47]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( in @ sk8 @ sk1 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( sk8 != B )
| ( ( dsetconstr @ A
@ ^ [C: $i] : $false )
!= sk1 ) ),
inference(simp,[status(thm)],[174]) ).
thf(187,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk1 ),
inference(simp,[status(thm)],[179]) ).
thf(80,plain,
in @ sk9 @ sk2,
inference(cnfConj,[status(thm)],[78]) ).
thf(24,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ $true
| ( B @ C )
| ( ( in @ sk4 @ sk1 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,11]) ).
thf(25,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk4 @ sk1 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(36,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( sk4 != C )
| ( ( dsetconstr @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[25]) ).
thf(48,plain,
! [B: $i > $o,A: $i] :
( ( B @ sk4 )
| ( ( dsetconstr @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[36]) ).
thf(91,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk9 @ sk2 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,41]) ).
thf(92,plain,
! [A: $i] :
( ( in @ sk9 @ sk2 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(95,plain,
! [A: $i] :
( ( sk9 != sk4 )
| ( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[92]) ).
thf(120,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) )
!= ( in @ sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,42]) ).
thf(121,plain,
! [A: $i] :
( ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) )
!= ( in @ sk4 @ sk1 ) ),
inference(simp,[status(thm)],[120]) ).
thf(136,plain,
! [A: $i] :
( ( sk5 != sk4 )
| ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[121]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ~ $true
| ( ( B @ C )
!= ( in @ sk4
@ ( dsetconstr @ D
@ ^ [E: $i] : ( sk3 @ E @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,41]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ sk4
@ ( dsetconstr @ D
@ ^ [E: $i] : ( sk3 @ E @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(65,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ F @ ( dsetconstr @ ( G @ F ) @ ^ [G: $i] : ( sk3 @ G @ sk5 ) ) ) )),bind(C,$thf( sk4 )),bind(D,$thf( G @ sk4 ))]]) ).
thf(68,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(444,plain,
! [B: $i > $i,A: $i] :
( ~ $true
| ( ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) )
!= ( in @ sk4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,68]) ).
thf(445,plain,
! [B: $i > $i,A: $i] :
( ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) )
!= ( in @ sk4 @ sk1 ) ),
inference(simp,[status(thm)],[444]) ).
thf(458,plain,
! [B: $i > $i,A: $i] :
( ( sk4 != sk4 )
| ( ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[445]) ).
thf(464,plain,
! [B: $i > $i,A: $i] :
( ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[458]) ).
thf(57,plain,
! [A: $i] :
( ~ $true
| ( ( in @ sk5 @ sk2 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,41]) ).
thf(58,plain,
! [A: $i] :
( ( in @ sk5 @ sk2 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(62,plain,
! [A: $i] :
( ( sk5 != sk4 )
| ( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[58]) ).
thf(252,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( C @ F )
| ( D @ F )
| ( E @ F ) ) ) )
| ( C @ B )
| ( D @ B )
| ( E @ B ) ),
inference(prim_subst,[status(thm)],[54:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [G: $i] : ( ( E @ G ) | ( F @ G ) ) ))]]) ).
thf(363,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( C @ F )
| ( D @ F )
| ( E @ F ) ) ) )
| ( C @ B )
| ( D @ B )
| ( E @ B ) ),
inference(cnf,[status(esa)],[252]) ).
thf(364,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( C @ F )
| ( D @ F )
| ( E @ F ) ) ) )
| ( C @ B )
| ( D @ B )
| ( E @ B ) ),
inference(simp,[status(thm)],[363]) ).
thf(1192,plain,
$false,
inference(e,[status(thm)],[42,14,189,41,402,108,145,8,146,6,102,70,21,137,148,45,12,54,187,81,7,3,80,48,18,95,11,43,136,79,464,47,68,62,83,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU668^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:11:34 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (199ms).
% 1.17/1.00 % [INFO] Running in sequential loop mode.
% 1.77/1.40 % [INFO] eprover registered as external prover.
% 1.94/1.40 % [INFO] Scanning for conjecture ...
% 2.12/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.12/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.12/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.58 % [INFO] Type checking passed.
% 2.12/1.59 % [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 ...
% 14.36/4.65 % External prover 'e' found a proof!
% 14.36/4.65 % [INFO] Killing All external provers ...
% 14.36/4.65 % Time passed: 4312ms (effective reasoning time: 3649ms)
% 14.36/4.65 % 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)>
% 14.36/4.66 % Axioms used in derivation (0):
% 14.36/4.66 % No. of inferences in proof: 100
% 14.36/4.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4312 ms resp. 3649 ms w/o parsing
% 12.76/4.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.76/4.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------