%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n010.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 07:45:46 AM UTC 2026
% Result : Theorem 135.19s 116.22s
% Output : Refutation 135.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 334 ( 62 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 728 ( 63 ~; 41 |; 23 &; 590 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 105 ( 0 ^; 101 !; 0 ?; 105 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/UNION_decl',type,
'const/sets/UNION':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('const/sets/SUBSET_decl',type,
'const/sets/SUBSET':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('const/sets/INTER_decl',type,
'const/sets/INTER':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/sets/DISJOINT_decl',type,
'const/sets/DISJOINT':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('const/realax/real_add_decl',type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(sk1_decl,type,
sk1: skt1 > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt1 > $o ).
thf(sk4_decl,type,
sk4: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: skt1 > $o,C: skt1 > $o,D: skt1 > $o] :
( ( ( 'const/sets/FINITE' @ skt1 @ D )
& ( ( 'const/sets/INTER' @ skt1 @ B @ C )
= ( 'const/sets/EMPTY' @ skt1 ) )
& ( ( 'const/sets/UNION' @ skt1 @ B @ C )
= D ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ B @ A ) @ ( 'const/iterate/sum' @ skt1 @ C @ A ) )
= ( 'const/iterate/sum' @ skt1 @ D @ A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o,C: skt1 > $o] :
( ( ( 'const/sets/FINITE' @ skt1 @ C )
& ( ( 'const/sets/INTER' @ skt1 @ A @ B )
= ( 'const/sets/EMPTY' @ skt1 ) )
& ( ( 'const/sets/UNION' @ skt1 @ A @ B )
= C ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ B @ sk1 ) )
= ( 'const/iterate/sum' @ skt1 @ C @ sk1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o] :
( ( ( 'const/sets/FINITE' @ skt1 @ B )
& ( ( 'const/sets/INTER' @ skt1 @ sk2 @ A )
= ( 'const/sets/EMPTY' @ skt1 ) )
& ( ( 'const/sets/UNION' @ skt1 @ sk2 @ A )
= B ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) )
= ( 'const/iterate/sum' @ skt1 @ B @ sk1 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: skt1 > $o] :
~ ( ( ( 'const/sets/FINITE' @ skt1 @ A )
& ( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
= ( 'const/sets/EMPTY' @ skt1 ) )
& ( ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 )
= A ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
= ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) ) ) ) ) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_0') ).
thf(19,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o,C: TA > $o,D: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ D )
& ( ( 'const/sets/INTER' @ TA @ B @ C )
= ( 'const/sets/EMPTY' @ TA ) )
& ( ( 'const/sets/UNION' @ TA @ B @ C )
= D ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) )
= ( 'const/iterate/sum' @ TA @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_EQ_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o,C: TA > $o,D: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ D )
& ( ( 'const/sets/INTER' @ TA @ B @ C )
= ( 'const/sets/EMPTY' @ TA ) )
& ( ( 'const/sets/UNION' @ TA @ B @ C )
= D ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) )
= ( 'const/iterate/sum' @ TA @ D @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o,C: TA > $o,D: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ D )
& ( ( 'const/sets/INTER' @ TA @ B @ C )
= ( 'const/sets/EMPTY' @ TA ) )
& ( ( 'const/sets/UNION' @ TA @ B @ C )
= D ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) )
= ( 'const/iterate/sum' @ TA @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk4 )
& ( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
= ( 'const/sets/EMPTY' @ skt1 ) )
& ( ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 )
= sk4 )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk4 @ sk1 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
'const/sets/FINITE' @ skt1 @ sk4,
inference(cnfConj,[status(thm)],[9]) ).
thf(12,plain,
( ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 )
= sk4 ),
inference(cnfConj,[status(thm)],[9]) ).
thf(15,plain,
( sk4
= ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(30,plain,
'const/sets/FINITE' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ),
inference(rewrite,[status(thm)],[10,15]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/SUBSET' @ TA @ A @ B ) )
=> ( 'const/sets/FINITE' @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(21,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/SUBSET' @ TA @ A @ B ) )
=> ( 'const/sets/FINITE' @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(157,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ $true
| ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,22]) ).
thf(158,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
| ( 'const/sets/FINITE' @ skt1 @ A ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( A )),bind(B,$thf( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1090,plain,
! [TA: $tType,C: skt1 > $o,B: TA > $o,A: TA > $o] :
( ~ $true
| ( 'const/sets/FINITE' @ skt1 @ C )
| ( ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ A @ B ) )
!= ( 'const/sets/SUBSET' @ skt1 @ C @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,159]) ).
thf(1091,plain,
! [TA: $tType,C: skt1 > $o,B: TA > $o,A: TA > $o] :
( ( 'const/sets/FINITE' @ skt1 @ C )
| ( ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ A @ B ) )
!= ( 'const/sets/SUBSET' @ skt1 @ C @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[1090]) ).
thf(1092,plain,
'const/sets/FINITE' @ skt1 @ sk2,
inference(pattern_uni,[status(thm)],[1091:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(7,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o,C: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/FINITE' @ TA @ C )
& ( 'const/sets/DISJOINT' @ TA @ B @ C ) )
=> ( ( 'const/iterate/sum' @ TA @ ( 'const/sets/UNION' @ TA @ B @ C ) @ A )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_') ).
thf(26,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o,C: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/FINITE' @ TA @ C )
& ( 'const/sets/DISJOINT' @ TA @ B @ C ) )
=> ( ( 'const/iterate/sum' @ TA @ ( 'const/sets/UNION' @ TA @ B @ C ) @ A )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [TA: $tType,C: TA > $o,B: TA > $o,A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/sets/FINITE' @ TA @ C )
| ~ ( 'const/sets/DISJOINT' @ TA @ B @ C )
| ( ( 'const/iterate/sum' @ TA @ ( 'const/sets/UNION' @ TA @ B @ C ) @ A )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [TA: $tType,C: TA > $o,B: TA > $o,A: TA > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ ( 'const/sets/UNION' @ TA @ B @ C ) @ A )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/sets/FINITE' @ TA @ C )
| ~ ( 'const/sets/DISJOINT' @ TA @ B @ C ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(13,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk4 @ sk1 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(16,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk4 @ sk1 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(32,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
!= ( 'const/iterate/sum' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[16,15]) ).
thf(39,plain,
! [TA: $tType,C: TA > $o,B: TA > $o,A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/sets/FINITE' @ TA @ C )
| ~ ( 'const/sets/DISJOINT' @ TA @ B @ C )
| ( ( 'const/iterate/sum' @ TA @ ( 'const/sets/UNION' @ TA @ B @ C ) @ A )
!= ( 'const/iterate/sum' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) @ sk1 ) )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ B @ A ) @ ( 'const/iterate/sum' @ TA @ C @ A ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ skt1 @ sk2 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,32]) ).
thf(40,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk3 )
| ~ ( 'const/sets/DISJOINT' @ skt1 @ sk2 @ sk3 )
| ( ( 'const/iterate/sum' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) @ sk1 )
!= ( 'const/iterate/sum' @ skt1 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(49,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk3 )
| ~ ( 'const/sets/DISJOINT' @ skt1 @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[40]) ).
thf(11,plain,
( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
= ( 'const/sets/EMPTY' @ skt1 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(14,plain,
( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
= ( 'const/sets/EMPTY' @ skt1 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/DISJOINT' @ TA @ A @ B )
= ( ( 'const/sets/INTER' @ TA @ A @ B )
= ( 'const/sets/EMPTY' @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/DISJOINT_') ).
thf(23,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/DISJOINT' @ TA @ A @ B )
= ( ( 'const/sets/INTER' @ TA @ A @ B )
= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( 'const/sets/DISJOINT' @ TA @ A @ B )
= ( ( 'const/sets/INTER' @ TA @ A @ B )
= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( 'const/sets/DISJOINT' @ TA @ A @ B )
= ( ( 'const/sets/INTER' @ TA @ A @ B )
= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(65,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ( ( 'const/sets/DISJOINT' @ skt1 @ A @ B )
= ( ( 'const/sets/EMPTY' @ skt1 )
= ( 'const/sets/EMPTY' @ skt1 ) ) )
| ( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
!= ( 'const/sets/INTER' @ skt1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,25]) ).
thf(66,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ( 'const/sets/DISJOINT' @ skt1 @ A @ B )
| ( ( 'const/sets/INTER' @ skt1 @ sk2 @ sk3 )
!= ( 'const/sets/INTER' @ skt1 @ A @ B ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
'const/sets/DISJOINT' @ skt1 @ sk2 @ sk3,
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(79,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[49,67]) ).
thf(80,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk3 ) ),
inference(simp,[status(thm)],[79]) ).
thf(117,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/FINITE' @ skt1 @ sk3 )
!= ( 'const/sets/FINITE' @ skt1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[80]) ).
thf(120,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/FINITE' @ skt1 @ sk3 )
!= ( 'const/sets/FINITE' @ skt1 @ sk2 ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(1070,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[159,120]) ).
thf(1071,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 )
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1 @ sk3 ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
( ~ ( 'const/sets/SUBSET' @ skt1 @ sk3 @ ( 'const/sets/UNION' @ skt1 @ sk2 @ sk3 ) )
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( sk3 ))]]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_1') ).
thf(17,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNION' @ TA @ B @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(1165,plain,
( ~ $true
| ~ ( 'const/sets/FINITE' @ skt1 @ sk2 ) ),
inference(rewrite,[status(thm)],[1072,18]) ).
thf(1166,plain,
~ ( 'const/sets/FINITE' @ skt1 @ sk2 ),
inference(simp,[status(thm)],[1165]) ).
thf(1180,plain,
$false,
inference(rewrite,[status(thm)],[1092,1166]) ).
thf(1181,plain,
$false,
inference(simp,[status(thm)],[1180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n010.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 17:41:48 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.84/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (207ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.84/1.38 % [INFO] eprover registered as external prover.
% 1.84/1.39 % [INFO] Scanning for conjecture ...
% 2.03/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.16/1.53 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.16/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.56 % [INFO] Type checking passed.
% 2.16/1.56 % [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 ...
% 135.19/116.21 % [INFO] Killing All external provers ...
% 135.19/116.22 % Time passed: 115875ms (effective reasoning time: 115215ms)
% 135.19/116.22 % 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)>
% 135.19/116.22 % Axioms used in derivation (5): thm/sets/SUBSET_UNION_0, thm/sets/SUBSET_UNION_1, thm/iterate/SUM_UNION_, thm/sets/DISJOINT_, thm/sets/FINITE_SUBSET_
% 135.19/116.22 % No. of inferences in proof: 53
% 135.19/116.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 115875 ms resp. 115215 ms w/o parsing
% 135.19/116.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 135.19/116.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------