%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n020.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 08:28:49 AM UTC 2026
% Result : Unsatisfiable 11.97s 5.09s
% Output : Refutation 13.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 126 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 104 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 999 ( 189 ~; 147 |; 0 &; 663 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 256 ( 0 ^; 256 !; 0 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(as_decl,type,
as: $i ).
thf(bs_decl,type,
bs: $i ).
thf(cs_decl,type,
cs: $i ).
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(complement_decl,type,
complement: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(member_of_1_not_of_2_decl,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ member ) )
| ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ member ) )
| ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( A @ member ) )
| ( B @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(4,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(27,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ complement @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ complement @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ complement )
!= empty_set )
| ( A != C )
| ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( A @ complement )
!= empty_set )
| ( A @ ( B @ member ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ complement @ ( C @ member ) )
| ~ $true
| ( ( A @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[87,34]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ complement @ ( C @ member ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( A @ complement @ ( B @ member ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ~ $true
| ( ( C @ complement )
!= empty_set )
| ( ( A @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[87,98]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ( ( C @ complement )
!= empty_set )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ complement )
!= empty_set )
| ( ( A @ complement @ complement )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( E @ complement )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ complement )
!= empty_set )
| ( ( A @ complement @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[116]) ).
thf(19,axiom,
cs @ ( bs @ subset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_subset_of_c) ).
thf(56,plain,
cs @ ( bs @ subset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ equal_sets ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_set_equal) ).
thf(24,plain,
! [A: $i] : ( A @ ( A @ equal_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equal_sets ) )
!= ( C @ ( B @ equal_sets ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,43]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equal_sets ) )
!= ( C @ ( B @ equal_sets ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1,negated_conjecture,
~ ( cs @ ( bs @ ( as @ union ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
thf(22,plain,
~ ( cs @ ( bs @ ( as @ union ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
~ ( cs @ ( bs @ ( as @ union ) @ subset ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77,23]) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: $i] :
( ( A != cs )
| ( A
!= ( bs @ ( as @ union ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
( ( bs @ ( as @ union ) )
!= cs ),
inference(simp,[status(thm)],[91]) ).
thf(11,axiom,
cs @ ( as @ subset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_subset_of_c) ).
thf(41,plain,
cs @ ( as @ subset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[55,28]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( empty_set )),bind(B,$thf( E )),bind(C,$thf( E @ ( empty_set @ member_of_1_not_of_2 ) ))]]) ).
thf(135,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[123]) ).
thf(137,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[135,23]) ).
thf(138,plain,
! [A: $i] :
( ( A @ ( empty_set @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
! [A: $i] :
( ( A != cs )
| ( ( bs @ ( as @ union ) )
!= empty_set ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
( ( bs @ ( as @ union ) )
!= empty_set ),
inference(simp,[status(thm)],[139]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ complement @ ( A @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ~ $true
| ( ( C @ complement )
!= empty_set )
| ( B @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[26,98]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ complement @ ( A @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ( ( C @ complement )
!= empty_set )
| ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= empty_set )
| ( B @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( D @ complement @ ( C @ member ) ) )
| ~ $true
| ~ ( D @ ( C @ member ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[87,34]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( D @ complement @ ( C @ member ) ) )
| ~ ( D @ ( C @ member ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ( ( B @ complement @ complement )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( E @ complement )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ( ( B @ complement @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[101]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equal_sets ) )
| ~ ( C @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_set_equal) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equal_sets ) )
| ~ ( C @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ~ $true
| ( ( C @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[55,98]) ).
thf(131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( C @ complement @ ( D @ member ) ) )
| ( ( C @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= empty_set )
| ( A @ ( B @ complement @ subset ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( G @ complement )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ complement @ member_of_1_not_of_2 ) ))]]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= empty_set )
| ( A @ ( B @ complement @ subset ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ $true
| ( ( D @ complement @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[55,111]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( D @ ( C @ member ) ) )
| ( ( D @ complement @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( A @ complement @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ member_of_1_not_of_2 ) )),bind(D,$thf( E ))]]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( ( A @ complement @ complement )
!= empty_set )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ~ $true
| ( ( A @ complement @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[203,23]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ( ( A @ complement @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
( ( bs @ ( as @ union ) @ complement @ complement )
!= empty_set ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( bs @ ( as @ union ) )),bind(B,$thf( cs ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(170,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( ( A @ complement @ complement )
!= ( A @ complement ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(eqfactor_ordered,[status(thm)],[120]) ).
thf(172,plain,
! [A: $i] :
( ( ( A @ complement )
!= A )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[170]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ complement @ ( A @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[34]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= B )
| ( A != A )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= B )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_for_set_equal) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( ( A @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[87,28]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
( ( empty_set @ complement )
!= empty_set ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( empty_set )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ complement @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ~ $true
| ( ( B @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[134,23]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ complement @ subset ) )
!= ( cs @ ( bs @ ( as @ union ) @ subset ) ) )
| ( ( B @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( A != cs )
| ( ( B @ complement )
!= ( bs @ ( as @ union ) ) )
| ( ( B @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
! [A: $i] :
( ( ( A @ complement )
!= ( bs @ ( as @ union ) ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[262]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ union ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ union ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(61,plain,
( ( ( cs @ ( bs @ ( as @ union ) @ subset ) )
!= ( cs @ ( bs @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,23]) ).
thf(62,plain,
( ( cs @ ( bs @ ( as @ union ) @ subset ) )
!= ( cs @ ( bs @ subset ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(65,plain,
( ( cs != cs )
| ( ( bs @ ( as @ union ) )
!= bs ) ),
inference(simp,[status(thm)],[62]) ).
thf(67,plain,
( ( bs @ ( as @ union ) )
!= bs ),
inference(simp,[status(thm)],[65]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(252,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( E @ ( D @ intersection ) @ ( C @ member ) ) )
| ( D @ ( C @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[55,32]) ).
thf(253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
!= ( E @ ( D @ intersection ) @ ( C @ member ) ) )
| ( D @ ( C @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ intersection ) @ member_of_1_not_of_2 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( I @ ( H @ intersection ) )),bind(B,$thf( G )),bind(C,$thf( G @ ( I @ ( H @ intersection ) @ member_of_1_not_of_2 ) )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ intersection ) @ member_of_1_not_of_2 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ complement @ complement )
!= ( A @ complement ) )
| ( ( A @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[170]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equal_sets ) )
| ~ ( C @ ( B @ equal_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) )
| ~ ( C @ ( B @ union ) @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(63,plain,
( ( ( cs @ ( bs @ ( as @ union ) @ subset ) )
!= ( cs @ ( as @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,23]) ).
thf(64,plain,
( ( cs @ ( bs @ ( as @ union ) @ subset ) )
!= ( cs @ ( as @ subset ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(66,plain,
( ( cs != cs )
| ( ( bs @ ( as @ union ) )
!= as ) ),
inference(simp,[status(thm)],[64]) ).
thf(68,plain,
( ( bs @ ( as @ union ) )
!= as ),
inference(simp,[status(thm)],[66]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ complement @ ( C @ member ) )
| ~ $true
| ( ( B @ complement )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[119,34]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ complement @ ( C @ member ) )
| ( ( B @ complement )
!= empty_set ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( B @ complement @ ( A @ member ) )
| ( ( B @ complement )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(638,plain,
$false,
inference(e,[status(thm)],[120,56,52,60,92,77,41,54,140,43,119,111,42,24,37,25,46,57,29,28,33,134,266,32,34,22,44,59,27,172,113,39,98,135,35,48,95,263,50,67,31,87,203,40,26,258,55,171,23,30,51,68,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n020.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 06:50:49 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.44/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.63 % [INFO] Parsing done (285ms).
% 1.99/1.65 % [INFO] Running in sequential loop mode.
% 3.03/2.27 % [INFO] eprover registered as external prover.
% 3.03/2.29 % [INFO] Scanning for conjecture ...
% 3.45/2.42 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 3.64/2.51 % [INFO] Axiom selection finished. Selected 20 axioms (removed 3 axioms).
% 3.64/2.55 % [INFO] Problem is propositional (TPTP CNF).
% 3.64/2.55 % [INFO] Type checking passed.
% 3.64/2.56 % [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 ...
% 11.97/5.08 % External prover 'e' found a proof!
% 11.97/5.09 % [INFO] Killing All external provers ...
% 11.97/5.09 % Time passed: 4380ms (effective reasoning time: 3426ms)
% 11.97/5.09 % Axioms used in derivation (20): member_of_intersection_is_member_of_set2, reflexivity_for_set_equal, set_equal_sets_are_subsets2, subsets_are_set_equal_sets, member_of_intersection_is_member_of_set1, set_equal_sets_are_subsets1, transitivity_for_set_equal, a_subset_of_c, member_of_set_or_complement, symmetry_for_set_equal, member_of_set1_is_member_of_union, member_of_union_is_member_of_one_set, not_member_of_set_and_complement, subsets_axiom2, b_subset_of_c, empty_set, member_of_set2_is_member_of_union, member_of_both_is_member_of_intersection, membership_in_subsets, subsets_axiom1
% 11.97/5.09 % No. of inferences in proof: 126
% 11.97/5.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4380 ms resp. 3426 ms w/o parsing
% 13.49/5.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.49/5.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------