TSTP Solution File: SET943+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:54:54 EDT 2023
% Result : Theorem 109.28s 20.11s
% Output : Refutation 109.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of formulae : 226 ( 58 unt; 18 typ; 0 def)
% Number of atoms : 542 ( 153 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 2142 ( 239 ~; 214 |; 32 &;1603 @)
% ( 6 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 512 ( 0 ^; 498 !; 14 ?; 512 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i > $o ).
thf(sk7_type,type,
sk7: $i > $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $o ).
thf(sk11_type,type,
sk11: $i > $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(48,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[49]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( union @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( union @ A ) @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( union @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( union @ A ) @ ( union @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i,B: $i] :
( ( union @ ( set_union2 @ A @ B ) )
= ( set_union2 @ ( union @ A ) @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( set_union2 @ ( union @ sk1 ) @ ( union @ sk2 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
( ( set_union2 @ ( union @ sk1 ) @ ( union @ sk2 ) )
!= ( union @ ( set_union2 @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(172,plain,
! [A: $i] :
( ( A
!= ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ ( union @ sk1 ) @ ( union @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,20]) ).
thf(178,plain,
( ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk1 ) )
| ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk2 ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(324,plain,
( ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk1 ) )
| ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( ( union @ sk2 )
!= ( union @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[178]) ).
thf(347,plain,
( ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk1 ) )
| ( ( union @ sk2 )
!= ( union @ sk1 ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( union @ A ) @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( union @ A ) @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_union2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_union2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
=> ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_union2 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ B )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[52]) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ B )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(3,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(21,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
~ ( empty @ sk3 ),
inference(cnf,[status(esa)],[22]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(35,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,plain,
empty @ sk4,
inference(cnf,[status(esa)],[35]) ).
thf(118,plain,
( ( empty @ sk4 )
!= ( empty @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[36,23]) ).
thf(119,plain,
sk4 != sk3,
inference(simp,[status(thm)],[118]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( in @ ( sk8 @ C @ B @ A ) @ B )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( in @ ( sk8 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( in @ ( sk8 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[61]) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( in @ ( sk8 @ C @ B @ A ) @ B )
| ( C
!= ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( union @ sk1 ) @ ( union @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,20]) ).
thf(655,plain,
! [A: $i] :
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ A )
| ( in @ ( sk8 @ A @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk8 @ A @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk2 ) )
| ( A
!= ( union @ ( set_union2 @ sk1 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( union @ sk1 )),bind(B,$thf( union @ sk2 )),bind(C,$thf( C ))]]) ).
thf(779,plain,
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk2 ) ) ),
inference(simp,[status(thm)],[655]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( B
= ( union @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(81,plain,
( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(miniscope,[status(thm)],[80]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( sk9 @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[81]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( sk9 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( union @ A ) )
| ( in @ ( sk9 @ B @ ( union @ A ) @ A ) @ A ) ),
inference(simp,[status(thm)],[90]) ).
thf(5841,plain,
! [B: $i,A: $i] :
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk9 @ B @ ( union @ A ) @ A ) @ A )
| ( ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk2 ) )
!= ( in @ B @ ( union @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[779,91]) ).
thf(5842,plain,
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk9 @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk2 ) @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5841:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(46,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( sk10 @ A @ B )
| ( in @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) )
| ( B
= ( union @ A ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( sk10 @ A @ B )
| ( in @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( sk10 @ A @ B )
| ( in @ ( sk12 @ B @ A ) @ ( sk13 @ B @ A ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(284,plain,
( ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk1 ) )
| ( ( set_union2 @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[178]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[52]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[37]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(121,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( B ))]]) ).
thf(122,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[121]) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[64,122]) ).
thf(1092,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ A ),
inference(pattern_uni,[status(thm)],[1091:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( set_union2 @ E @ F )),bind(D,$thf( set_union2 @ E @ F ))]]) ).
thf(1115,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ A ),
inference(simp,[status(thm)],[1092]) ).
thf(1142,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[64,1115]) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ B ),
inference(pattern_uni,[status(thm)],[1142:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( set_union2 @ ( set_union2 @ H @ I ) @ G )),bind(D,$thf( set_union2 @ H @ I )),bind(E,$thf( G ))]]) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ B ),
inference(simp,[status(thm)],[1143]) ).
thf(1529,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ D )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[117,1170]) ).
thf(1530,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[1529:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(2098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ E ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1530]) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[2098:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ B ),
inference(simp,[status(thm)],[2099]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[40]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[41]) ).
thf(1097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( in @ E @ ( set_union2 @ C @ D ) )
| ( ( in @ ( sk5 @ B @ A ) @ A )
!= ( in @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,64]) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk5 @ B @ C ) @ ( set_union2 @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk5 @ B @ C ) @ ( set_union2 @ C @ A ) ) ),
inference(simp,[status(thm)],[1098]) ).
thf(1360,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk5 @ D @ E ) @ ( set_union2 @ B @ A ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1118]) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk5 @ C @ A ) @ ( set_union2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1360:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk5 @ C @ A ) @ ( set_union2 @ B @ A ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ E )
| ( in @ ( sk5 @ E @ C ) @ ( set_union2 @ A @ B ) )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1412]) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk5 @ C @ A ) @ ( set_union2 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[1665:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk5 @ C @ A ) @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[1666]) ).
thf(1132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ A ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[117,1115]) ).
thf(1133,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ E @ D ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[64,1133]) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ B ),
inference(pattern_uni,[status(thm)],[1183:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( set_union2 @ F @ ( set_union2 @ H @ I ) )),bind(D,$thf( set_union2 @ H @ I )),bind(E,$thf( F ))]]) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ B ),
inference(simp,[status(thm)],[1184]) ).
thf(1597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ D )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[117,1203]) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[1597:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(2801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ A ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ ( set_union2 @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,1598]) ).
thf(2802,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ C ),
inference(pattern_uni,[status(thm)],[2801:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ F @ G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( A ))]]) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ C ),
inference(simp,[status(thm)],[2802]) ).
thf(25,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[25]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[29]) ).
thf(350,plain,
( ( ( set_union2 @ sk1 @ sk2 )
!= sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[324]) ).
thf(378,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != sk1 )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[50,350]) ).
thf(396,plain,
( ( sk2 != sk1 )
| ( sk1 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[378]) ).
thf(402,plain,
sk2 != sk1,
inference(simp,[status(thm)],[396]) ).
thf(421,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[30,402]) ).
thf(422,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ A )
| ~ ( subset @ A @ sk2 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[421:[bind(A,$thf( sk2 ))]]) ).
thf(425,plain,
( ~ ( subset @ sk2 @ sk1 )
| ~ ( subset @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[422]) ).
thf(481,plain,
( ~ ( subset @ sk1 @ sk2 )
| ( ( subset @ sk2 @ sk1 )
!= ( subset @ sk1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[425]) ).
thf(485,plain,
( ~ ( subset @ sk1 @ sk2 )
| ( ( subset @ sk2 @ sk1 )
!= ( subset @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(348,plain,
( ( ( set_union2 @ sk1 @ sk2 )
!= sk1 )
| ( ( union @ sk2 )
!= ( union @ sk1 ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk7 @ C @ B @ A ) @ B )
| ~ ( sk6 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk7 @ C @ B @ A ) @ B )
| ~ ( sk6 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk7 @ C @ B @ A ) @ B )
| ~ ( sk6 @ A @ B @ C ) ),
inference(simp,[status(thm)],[69]) ).
thf(1173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ A ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1133]) ).
thf(1174,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ D )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[117,1203]) ).
thf(1602,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ B ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(285,plain,
( ( ( set_union2 @ sk1 @ sk2 )
!= sk1 )
| ( ( set_union2 @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[178]) ).
thf(1533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ D )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[117,1170]) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[1533:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(4155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( in @ E @ ( set_union2 @ C @ D ) )
| ( ( in @ ( sk5 @ B @ A ) @ A )
!= ( in @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,74]) ).
thf(4156,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk5 @ B @ C ) @ ( set_union2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[4155:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk5 @ F @ G ))]]) ).
thf(4248,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk5 @ B @ C ) @ ( set_union2 @ A @ C ) ) ),
inference(simp,[status(thm)],[4156]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(108,plain,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,plain,
! [B: $i,A: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
inference(cnf,[status(esa)],[108]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(77,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk5 @ D @ E ) @ ( set_union2 @ A @ B ) )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1118]) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk5 @ C @ B ) @ ( set_union2 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk5 @ C @ B ) @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[1363]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk3 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[30,119]) ).
thf(152,plain,
! [A: $i] :
( ~ ( subset @ sk4 @ A )
| ~ ( subset @ A @ sk4 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( sk4 ))]]) ).
thf(167,plain,
( ~ ( subset @ sk4 @ sk3 )
| ~ ( subset @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[152]) ).
thf(243,plain,
( ~ ( subset @ sk3 @ sk4 )
| ( ( subset @ sk4 @ sk3 )
!= ( subset @ sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[167]) ).
thf(244,plain,
( ~ ( subset @ sk3 @ sk4 )
| ( ( subset @ sk4 @ sk3 )
!= ( subset @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ A @ B ) @ C )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[117,1115]) ).
thf(1135,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ B ),
inference(pattern_uni,[status(thm)],[1134:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[25]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(32,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[31]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk5 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[40]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk5 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[42]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk7 @ C @ B @ A ) @ C )
| ~ ( sk6 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( in @ ( sk7 @ C @ B @ A ) @ C )
| ~ ( sk6 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( in @ ( sk7 @ C @ B @ A ) @ C )
| ~ ( sk6 @ A @ B @ C ) ),
inference(simp,[status(thm)],[75]) ).
thf(2803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ E @ ( set_union2 @ B @ A ) ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1598]) ).
thf(2804,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ B ),
inference(pattern_uni,[status(thm)],[2803:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(2896,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ B ),
inference(simp,[status(thm)],[2804]) ).
thf(2102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ E ) @ C )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1530]) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[2102:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2180,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ A ),
inference(simp,[status(thm)],[2103]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ ( set_union2 @ B @ A ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[117,109]) ).
thf(199,plain,
! [B: $i,A: $i] : ( subset @ A @ ( set_union2 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[199,425]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( A != sk2 )
| ( ( set_union2 @ B @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[463]) ).
thf(494,plain,
! [A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( ( set_union2 @ A @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[487]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( sk10 @ A @ B )
| ( in @ ( sk13 @ B @ A ) @ A )
| ( B
= ( union @ A ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( sk10 @ A @ B )
| ( in @ ( sk13 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( sk10 @ A @ B )
| ( in @ ( sk13 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[102]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_union2 @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(simp,[status(thm)],[65]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[109,425]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( A != sk1 )
| ( ( set_union2 @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[460]) ).
thf(490,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( ( set_union2 @ sk1 @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[482]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(112,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ E @ ( set_union2 @ A @ B ) ) @ C )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1598]) ).
thf(2808,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ A ),
inference(pattern_uni,[status(thm)],[2807:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2899,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ A ),
inference(simp,[status(thm)],[2808]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( in @ ( sk11 @ B @ A ) @ B )
| ~ ( sk10 @ A @ B )
| ( B
= ( union @ A ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( in @ ( sk11 @ B @ A ) @ B )
| ~ ( sk10 @ A @ B ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( B
= ( union @ A ) )
| ( in @ ( sk11 @ B @ A ) @ B )
| ~ ( sk10 @ A @ B ) ),
inference(simp,[status(thm)],[94]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk7 @ C @ B @ A ) @ A )
| ~ ( sk6 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk7 @ C @ B @ A ) @ A )
| ~ ( sk6 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk7 @ C @ B @ A ) @ A )
| ~ ( sk6 @ A @ B @ C ) ),
inference(simp,[status(thm)],[71]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[40]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[199,425]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( A != sk1 )
| ( ( set_union2 @ B @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[464]) ).
thf(495,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ sk1 )
| ( ( set_union2 @ A @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[488]) ).
thf(78,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ~ ? [B: $i] : ( empty @ ( set_union2 @ B @ A ) ) ),
inference(miniscope,[status(thm)],[77]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(5437,plain,
( ( ( union @ sk2 )
!= ( union @ sk1 ) )
| ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk2 ) )
| ( ( union @ sk1 )
!= ( union @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[347]) ).
thf(5441,plain,
( ( ( union @ sk2 )
!= ( union @ sk1 ) )
| ( ( set_union2 @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[5437]) ).
thf(283,plain,
( ( ( set_union2 @ sk1 @ sk2 )
!= sk1 )
| ( ( union @ ( set_union2 @ sk1 @ sk2 ) )
!= ( union @ sk2 ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ C @ ( set_union2 @ A @ B ) )
| ( ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk2 ) )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[779,64]) ).
thf(1082,plain,
! [A: $i] :
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( set_union2 @ ( union @ sk2 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[1081:[bind(A,$thf( union @ sk2 )),bind(B,$thf( B )),bind(C,$thf( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ))]]) ).
thf(1129,plain,
! [A: $i] :
( ( sk6 @ ( union @ sk1 ) @ ( union @ sk2 ) @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( union @ sk1 ) )
| ( in @ ( sk8 @ ( union @ ( set_union2 @ sk1 @ sk2 ) ) @ ( union @ sk2 ) @ ( union @ sk1 ) ) @ ( set_union2 @ ( union @ sk2 ) @ A ) ) ),
inference(simp,[status(thm)],[1082]) ).
thf(1663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ E )
| ( in @ ( sk5 @ E @ C ) @ ( set_union2 @ B @ A ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,1412]) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk5 @ C @ B ) @ ( set_union2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk5 @ C @ B ) @ ( set_union2 @ B @ A ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ~ ( in @ ( sk8 @ C @ B @ A ) @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ~ ( in @ ( sk8 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ~ ( in @ ( sk8 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[67]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[109,425]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( A != sk2 )
| ( ( set_union2 @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[459]) ).
thf(496,plain,
! [A: $i] :
( ~ ( subset @ sk1 @ sk2 )
| ( ( set_union2 @ sk2 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[489]) ).
thf(2096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ A ) @ C )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( set_union2 @ D @ C ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[117,1530]) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ C ),
inference(pattern_uni,[status(thm)],[2096:[bind(A,$thf( set_union2 @ F @ G )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( B ))]]) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ C ),
inference(simp,[status(thm)],[2097]) ).
thf(68259,plain,
$false,
inference(cvc4,[status(thm)],[347,110,74,117,23,119,115,5842,24,37,20,46,93,284,1115,2178,1714,2893,485,106,348,70,21,1174,38,1602,285,1534,4248,1118,109,77,1414,1530,779,244,1170,1135,425,32,45,64,402,44,76,39,2896,2180,494,103,91,66,108,80,167,35,490,1203,112,2899,48,1598,18,95,50,199,72,43,495,1412,1133,36,30,51,79,5441,283,1129,62,178,1713,68,122,496,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:25:06 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.91/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (120ms).
% 1.23/0.95 % [INFO] Running in sequential loop mode.
% 1.58/1.15 % [INFO] eprover registered as external prover.
% 1.58/1.15 % [INFO] cvc4 registered as external prover.
% 1.68/1.15 % [INFO] Scanning for conjecture ...
% 1.68/1.21 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.87/1.24 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.87/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.27 % [INFO] Type checking passed.
% 1.87/1.27 % [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 ...
% 109.25/20.10 % External prover 'cvc4' found a proof!
% 109.28/20.10 % [INFO] Killing All external provers ...
% 109.28/20.10 % Time passed: 19592ms (effective reasoning time: 19141ms)
% 109.28/20.10 % 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)>
% 109.28/20.11 % Axioms used in derivation (15): t95_zfmisc_1, fc2_xboole_0, commutativity_k2_xboole_0, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc3_xboole_0, d2_xboole_0, d4_tarski, t8_xboole_1, d3_tarski, reflexivity_r1_tarski, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1
% 109.28/20.11 % No. of inferences in proof: 208
% 109.28/20.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19592 ms resp. 19141 ms w/o parsing
% 109.28/20.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 109.28/20.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------