%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 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 : n003.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 : Sun Sep 27 08:30:54 AM UTC 2026
% Result : Unsatisfiable 11.07s 3.44s
% Output : Refutation 9.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 133 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 330 ( 104 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 1370 ( 181 ~; 101 |; 0 &;1088 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 180 ( 0 ^; 180 !; 0 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(union_decl,type,
union: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(eptset_decl,type,
eptset: $i ).
thf(un_decl,type,
un: $i > $i > $i ).
thf(unionE_sk1_decl,type,
unionE_sk1: $i > $i > $i ).
thf(subsetI_sk1_decl,type,
subsetI_sk1: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(converseE_sk2_decl,type,
converseE_sk2: $i > $i ).
thf(converseE_sk1_decl,type,
converseE_sk1: $i > $i ).
thf(converse_sk1_decl,type,
converse_sk1: $i > $i ).
thf(converse_sk2_decl,type,
converse_sk2: $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(10,axiom,
! [A: $i] :
~ ( eptset @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(33,plain,
! [A: $i] :
~ ( eptset @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,plain,
! [A: $i] :
~ ( eptset @ ( A @ member ) ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ union @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,34]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ ( C @ member ) ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(221,plain,
! [A: $i] :
~ ( eptset @ union @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( D )),bind(B,$thf( eptset )),bind(C,$thf( eptset @ ( D @ unionE_sk1 ) ))]]) ).
thf(255,plain,
! [A: $i] :
~ ( eptset @ union @ ( A @ member ) ),
inference(simp,[status(thm)],[221]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ union @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,255]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ ( C @ member ) ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
! [A: $i] :
~ ( eptset @ union @ union @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( D )),bind(B,$thf( eptset @ union )),bind(C,$thf( eptset @ union @ ( D @ unionE_sk1 ) ))]]) ).
thf(276,plain,
! [A: $i] :
~ ( eptset @ union @ union @ ( A @ member ) ),
inference(simp,[status(thm)],[258]) ).
thf(1,negated_conjecture,
eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
thf(15,plain,
eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ union @ ( A @ member ) ) )
| ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,21]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ union @ ( A @ member ) ) )
| ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
eptset @ ( b @ cons ) @ ( a @ cons ) @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ member ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( sk2 )),bind(B,$thf( eptset @ ( b @ cons ) @ ( a @ cons ) ))]]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ union @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,276]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ ( C @ member ) ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
! [A: $i] :
~ ( eptset @ union @ union @ union @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( D )),bind(B,$thf( eptset @ union @ union )),bind(C,$thf( eptset @ union @ union @ ( D @ unionE_sk1 ) ))]]) ).
thf(303,plain,
! [A: $i] :
~ ( eptset @ union @ union @ union @ ( A @ member ) ),
inference(simp,[status(thm)],[282]) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ union @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ union @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,303]) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ union @ ( C @ member ) ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1252]) ).
thf(1254,plain,
! [A: $i] :
~ ( eptset @ union @ union @ union @ union @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[1253:[bind(A,$thf( D )),bind(B,$thf( eptset @ union @ union @ union )),bind(C,$thf( eptset @ union @ union @ union @ ( D @ unionE_sk1 ) ))]]) ).
thf(1271,plain,
! [A: $i] :
~ ( eptset @ union @ union @ union @ union @ ( A @ member ) ),
inference(simp,[status(thm)],[1254]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unI1) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(2,negated_conjecture,
~ ( b @ ( a @ un ) @ ( sk2 @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
thf(16,plain,
~ ( b @ ( a @ un ) @ ( sk2 @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
~ ( b @ ( a @ un ) @ ( sk2 @ member ) ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ un ) @ ( A @ member ) )
!= ( b @ ( a @ un ) @ ( sk2 @ member ) ) )
| ~ $true
| ~ ( B @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ un ) @ ( A @ member ) )
!= ( b @ ( a @ un ) @ ( sk2 @ member ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
~ ( a @ ( sk2 @ member ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk2 )),bind(B,$thf( a )),bind(C,$thf( b ))]]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(102,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,66]) ).
thf(103,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( a @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(108,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= a )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[103]) ).
thf(111,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= a ),
inference(simp,[status(thm)],[108]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ converse_sk2 @ ( A @ converse_sk1 @ pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converseE_2) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ converse_sk2 @ ( A @ converse_sk1 @ pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(285,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,276]) ).
thf(286,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(296,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union @ union ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[286]) ).
thf(301,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union @ union ) ),
inference(simp,[status(thm)],[296]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ converse @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converseD) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ converse @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ union @ ( A @ member ) ) )
| ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,19]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ union @ ( A @ member ) ) )
| ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk2 )),bind(B,$thf( eptset @ ( b @ cons ) @ ( a @ cons ) ))]]) ).
thf(120,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( b @ ( a @ un ) @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,17]) ).
thf(121,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( b @ ( a @ un ) @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(128,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( b @ ( a @ un ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[121]) ).
thf(132,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( b @ ( a @ un ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(116,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,66]) ).
thf(117,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( a @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(129,plain,
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= a )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[117]) ).
thf(133,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= a ),
inference(simp,[status(thm)],[129]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( C @ ( B @ un ) @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,30]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( C @ ( B @ un ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [A: $i] : ( A @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ un ) @ ( sk2 @ member ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( sk2 )),bind(B,$thf( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )),bind(C,$thf( C ))]]) ).
thf(74,plain,
! [A: $i] : ( A @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ un ) @ ( sk2 @ member ) ),
inference(simp,[status(thm)],[61]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ cons ) @ ( A @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(118,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,34]) ).
thf(119,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ ( A @ member ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(130,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= eptset )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[119]) ).
thf(134,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= eptset ),
inference(simp,[status(thm)],[130]) ).
thf(306,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,276]) ).
thf(307,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(330,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= ( eptset @ union @ union ) )
| ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[307]) ).
thf(343,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= ( eptset @ union @ union ) ),
inference(simp,[status(thm)],[330]) ).
thf(1232,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,303]) ).
thf(1233,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ member ) )
!= ( eptset @ union @ union @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1264,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= ( eptset @ union @ union @ union ) )
| ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1273,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= ( eptset @ union @ union @ union ) ),
inference(simp,[status(thm)],[1264]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ $true
| ~ ( B @ union @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[19,66]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unionE_sk1 ) @ ( A @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unionE_sk1 ) )
!= a )
| ( A != sk2 )
| ~ ( B @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(113,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ unionE_sk1 ) )
!= a )
| ~ ( A @ union @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(261,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,255]) ).
thf(262,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(272,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[262]) ).
thf(274,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union ) ),
inference(simp,[status(thm)],[272]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A
= ( A @ converseE_sk1 @ ( A @ converseE_sk2 @ pair ) ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converseE_1) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ converseE_sk1 @ ( A @ converseE_sk2 @ pair ) ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(283,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,276]) ).
thf(284,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(294,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( eptset @ union @ union ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[284]) ).
thf(299,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( eptset @ union @ union ) ),
inference(simp,[status(thm)],[294]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ converse @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ converse @ ( A @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ un ) @ ( A @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ $true
| ~ ( B @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[30,66]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ un ) @ ( A @ member ) )
!= ( a @ ( sk2 @ member ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ un ) )
!= a )
| ( A != sk2 )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ un ) )
!= a )
| ~ ( A @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(44,plain,
( ( ( b @ ( a @ un ) @ ( sk2 @ member ) )
!= ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,17]) ).
thf(45,plain,
( ( b @ ( a @ un ) @ ( sk2 @ member ) )
!= ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(48,plain,
( ( ( b @ ( a @ un ) )
!= ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[45]) ).
thf(50,plain,
( ( b @ ( a @ un ) )
!= ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union ) ),
inference(simp,[status(thm)],[48]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unI2) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ un ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1261,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,303]) ).
thf(1262,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ union @ union @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1261]) ).
thf(1267,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union @ union @ union ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1276,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= ( eptset @ union @ union @ union ) ),
inference(simp,[status(thm)],[1267]) ).
thf(304,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= eptset ),
inference(simp,[status(thm)],[274]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) )
| ( B @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,25]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( B @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= B )
| ( ( B @ ( A @ subsetI_sk1 ) )
!= sk2 )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( A @ subsetI_sk1 ) )
!= sk2 )
| ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( B @ ( A @ subsetI_sk1 ) @ member ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(46,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,34]) ).
thf(47,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union @ ( sk2 @ member ) )
!= ( eptset @ ( A @ member ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(49,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= eptset )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[47]) ).
thf(51,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ union )
!= eptset ),
inference(simp,[status(thm)],[49]) ).
thf(305,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) )
!= ( eptset @ union ) ),
inference(simp,[status(thm)],[301]) ).
thf(259,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ union @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,255]) ).
thf(260,plain,
! [A: $i] :
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) @ ( sk2 @ member ) )
!= ( eptset @ union @ ( A @ member ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(269,plain,
! [A: $i] :
( ( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( eptset @ union ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[260]) ).
thf(277,plain,
( ( eptset @ ( b @ cons ) @ ( a @ cons ) @ ( sk2 @ unionE_sk1 ) )
!= ( eptset @ union ) ),
inference(simp,[status(thm)],[269]) ).
thf(1561,plain,
$false,
inference(e,[status(thm)],[276,216,22,1271,66,18,111,42,24,301,37,25,20,29,132,133,74,28,21,33,134,343,34,1273,17,113,274,39,303,299,35,255,112,50,16,31,1276,304,26,55,23,30,51,19,305,79,15,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 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
% 0.14/0.41 % Computer : n003.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 08:17:24 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.69/0.71 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/0.80 % [INFO] Parsing done (93ms).
% 0.93/0.81 % [INFO] Running in sequential loop mode.
% 1.14/1.00 % [INFO] eprover registered as external prover.
% 1.14/1.01 % [INFO] Scanning for conjecture ...
% 1.44/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 1.44/1.07 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.44/1.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.44/1.09 % [INFO] Type checking passed.
% 1.44/1.09 % [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 ...
% 11.07/3.44 % External prover 'e' found a proof!
% 11.07/3.44 % [INFO] Killing All external provers ...
% 11.07/3.44 % Time passed: 2935ms (effective reasoning time: 2624ms)
% 11.07/3.44 % Axioms used in derivation (12): converseD, unI2, converseE_2, unI1, clause131, converseE_1, clause112, clause158, clause132, clause120, clause10, clause119
% 11.07/3.44 % No. of inferences in proof: 133
% 11.07/3.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2935 ms resp. 2624 ms w/o parsing
% 9.71/3.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.71/3.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------