%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET934+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : Sun Sep 27 08:31:23 AM UTC 2026
% Result : Theorem 14.28s 4.60s
% Output : Refutation 12.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 138 ( 62 unt; 0 typ; 6 def)
% Number of atoms : 362 ( 130 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 1149 ( 174 ~; 101 |; 17 &; 819 @)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 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 : 257 ( 4 ^; 243 !; 4 ?; 257 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( B @ powerset @ ( A @ powerset @ set_union2 ) @ subset ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( A @ ( sk1 @ set_union2 ) @ powerset @ ( A @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( B @ ( C @ subset ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ subset ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
=> ( ! [C: $i] :
( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ powerset ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ~ ( E @ ( E @ ( F @ sk3 ) @ subset ) ) )
& ( ( F
= ( E @ powerset ) )
| ( E @ ( E @ ( F @ sk4 ) @ subset ) )
| ~ ( E @ ( E @ ( F @ sk3 ) @ subset ) ) )
& ( ( F
= ( E @ powerset ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( F
= ( E @ powerset ) )
| ( E @ ( E @ ( F @ sk4 ) @ subset ) )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( D @ subset ) )
| ( B
!= ( A @ powerset ) ) )
& ( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk3 ) @ subset ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk3 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ~ ( A @ ( A @ ( B @ sk3 ) @ subset ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(15,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(97,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(cnf,[status(esa)],[97]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B
!= ( A @ powerset ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B
!= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( B @ in ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( D @ subset ) ) )
| ( C @ powerset @ ( D @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,33]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( D @ subset ) ) )
| ( C @ powerset @ ( D @ in ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ set_union2 ) )),bind(D,$thf( E ))]]) ).
thf(216,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( A @ in ) ),
inference(simp,[status(thm)],[206]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(85,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( B @ powerset @ ( A @ powerset @ set_union2 ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( B @ powerset @ ( A @ powerset @ set_union2 ) @ subset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ powerset @ ( B @ powerset @ ( A @ powerset @ set_union2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
~ ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ),
inference(cnf,[status(esa)],[16]) ).
thf(86,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[86]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(82,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(93,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(94,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[93]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( B @ ( C @ subset ) ) )
| ( B @ powerset @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,33]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( B @ ( C @ subset ) ) )
| ( B @ powerset @ ( C @ in ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
! [A: $i] : ( A @ powerset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(127,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( B ))]]) ).
thf(128,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[127]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ powerset @ ( A @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,128]) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ powerset @ ( A @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[607]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ powerset )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[608]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ set_union2 ) @ powerset )
!= B ),
inference(simp,[status(thm)],[621]) ).
thf(11,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(88,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(89,plain,
sk9 @ empty,
inference(cnf,[status(esa)],[88]) ).
thf(12,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(90,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[90]) ).
thf(92,plain,
~ ( sk10 @ empty ),
inference(cnf,[status(esa)],[91]) ).
thf(99,plain,
( ( ( sk10 @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,92]) ).
thf(100,plain,
( ( sk10 @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
sk10 != sk9,
inference(simp,[status(thm)],[100]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( C @ in ) ) )
| ~ $true
| ~ ( C @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[200,19]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( C @ in ) ) )
| ~ ( C @ ( B @ in ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ in ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( D )),bind(B,$thf( D @ powerset )),bind(C,$thf( D ))]]) ).
thf(226,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ in ) ),
inference(simp,[status(thm)],[224]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( B @ in ) )
!= ( C @ ( C @ powerset @ in ) ) )
| ~ $true
| ~ ( A @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,226]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( B @ in ) )
!= ( C @ ( C @ powerset @ in ) ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ powerset @ subset ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( E )),bind(B,$thf( E @ powerset @ powerset )),bind(C,$thf( E @ powerset ))]]) ).
thf(243,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ powerset @ subset ) ),
inference(simp,[status(thm)],[241]) ).
thf(108,plain,
! [A: $i] :
( ( ( A @ ( A @ set_union2 ) )
!= ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) ) )
| ~ ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[87,17]) ).
thf(112,plain,
! [A: $i] :
( ( A
!= ( sk2 @ powerset ) )
| ( A
!= ( sk1 @ powerset ) )
| ~ ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(113,plain,
( ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) )
| ~ ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk1 @ powerset @ subset ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(177,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk1 @ powerset @ subset ) ) )
| ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,113]) ).
thf(178,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk1 @ powerset @ subset ) ) )
| ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(185,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset ) )
| ( A
!= ( sk1 @ powerset ) )
| ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(192,plain,
( ( ( sk2 @ ( sk1 @ set_union2 ) @ powerset )
!= ( sk1 @ powerset ) )
| ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,17]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset ) )
| ( A
!= ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(137,plain,
! [A: $i] :
( ( A @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ set_union2 ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset ) ),
inference(simp,[status(thm)],[135]) ).
thf(102,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,17]) ).
thf(103,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset ) )
| ( A
!= ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
( ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) )
!= ( sk2 @ ( sk1 @ set_union2 ) @ powerset ) ),
inference(simp,[status(thm)],[104]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,226]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ powerset @ in ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= B )
| ( A
!= ( B @ powerset ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(244,plain,
! [A: $i] :
( ( A @ powerset @ powerset )
!= A ),
inference(simp,[status(thm)],[242]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( B @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true
| ~ ( A @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,128]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( B @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(203,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ subset ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( D )),bind(B,$thf( D @ powerset )),bind(C,$thf( D @ powerset ))]]) ).
thf(215,plain,
! [A: $i] :
~ ( A @ ( A @ powerset @ subset ) ),
inference(simp,[status(thm)],[203]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( C @ powerset @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,215]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( C @ powerset @ subset ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= C )
| ( A
!= ( C @ powerset ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ powerset @ set_union2 ) )
!= B ),
inference(simp,[status(thm)],[234]) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( C @ ( D @ set_union2 ) ) )
| ( ( A @ ( B @ set_union2 ) @ powerset )
!= D ) ),
inference(paramod_ordered,[status(thm)],[22,629]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ set_union2 ) @ powerset )
!= A ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ powerset ) )
| ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk4 ) @ subset ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ powerset ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(271,plain,
( ( ( sk2 @ ( sk1 @ set_union2 ) )
!= sk1 )
| ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( D @ ( C @ set_union2 ) ) )
| ( A @ ( B @ set_union2 ) @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[22,98]) ).
thf(158,plain,
! [B: $i,A: $i] : ( A @ ( B @ set_union2 ) @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( C @ powerset @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,215]) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ set_union2 ) @ ( A @ subset ) )
!= ( C @ ( C @ powerset @ subset ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_union2 ) )
!= C )
| ( A
!= ( C @ powerset ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ set_union2 ) )
!= B ),
inference(simp,[status(thm)],[263]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ subset ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ powerset ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( A @ powerset @ ( B @ in ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(95,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ ( A @ set_union2 ) )
!= ( sk2 @ ( sk1 @ set_union2 ) ) )
| ~ ( A @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[87,17]) ).
thf(111,plain,
! [A: $i] :
( ( A != sk2 )
| ( A != sk1 )
| ~ ( A @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(114,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk1 @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,114]) ).
thf(117,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk1 @ powerset @ ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) @ subset ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[116]) ).
thf(119,plain,
! [A: $i] :
( ( A
!= ( sk1 @ powerset ) )
| ( A
!= ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(121,plain,
( ( ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) )
!= ( sk1 @ powerset ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[119]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ ( A @ set_union2 ) )
!= ( sk2 @ powerset @ ( sk1 @ powerset @ set_union2 ) ) )
| ( A
!= ( sk1 @ powerset ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[87,121]) ).
thf(124,plain,
( ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) )
| ( ( sk1 @ powerset )
!= ( sk1 @ powerset ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[122]) ).
thf(125,plain,
( ( ( sk2 @ powerset )
!= ( sk1 @ powerset ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[124]) ).
thf(145,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[125]) ).
thf(146,plain,
sk2 != sk1,
inference(simp,[status(thm)],[145]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(79,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,128]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[218]) ).
thf(227,plain,
! [A: $i] :
( ( A @ powerset )
!= A ),
inference(simp,[status(thm)],[225]) ).
thf(2152,plain,
$false,
inference(e,[status(thm)],[37,216,85,17,16,87,82,200,629,101,88,20,93,89,243,192,137,33,92,97,128,105,244,22,44,71,236,919,113,39,98,271,226,267,35,18,95,158,23,146,19,79,94,90,227,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET934+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.14/0.38 % Computer : n016.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 08:31:15 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.89/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.16 % [INFO] Parsing done (193ms).
% 1.33/1.18 % [INFO] Running in sequential loop mode.
% 1.94/1.58 % [INFO] eprover registered as external prover.
% 1.94/1.59 % [INFO] Scanning for conjecture ...
% 2.14/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.32/1.72 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.32/1.75 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/1.76 % [INFO] Type checking passed.
% 2.32/1.76 % [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 ...
% 14.28/4.59 % External prover 'e' found a proof!
% 14.28/4.59 % [INFO] Killing All external provers ...
% 14.28/4.59 % Time passed: 4054ms (effective reasoning time: 3410ms)
% 14.28/4.59 % 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)>
% 14.28/4.60 % Axioms used in derivation (13): fc2_xboole_0, d1_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, t1_xboole_1, commutativity_k2_xboole_0, fc3_xboole_0, d2_xboole_0, d3_tarski, reflexivity_r1_tarski, idempotence_k2_xboole_0, t7_xboole_1
% 14.28/4.60 % No. of inferences in proof: 132
% 14.28/4.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4054 ms resp. 3410 ms w/o parsing
% 12.78/4.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.78/4.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------