TSTP Solution File: SET973+1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET973+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Tue May 7 08:08:35 EDT 2024
% Result : Theorem 172.35s 37.28s
% Output : Refutation 173.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 56
% Syntax : Number of formulae : 765 ( 221 unt; 30 typ; 0 def)
% Number of atoms : 2063 ( 941 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 9964 (1366 ~;1055 |; 66 &;7402 @)
% ( 9 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 8 con; 0-4 aty)
% Number of variables : 2052 ( 0 ^2026 !; 26 ?;2052 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $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(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
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 ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $o ).
thf(sk9_type,type,
sk9: $i > $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i > $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i > $o ).
thf(sk14_type,type,
sk14: $i > $i > $i > $i ).
thf(sk15_type,type,
sk15: $i > $i > $i > $i ).
thf(sk16_type,type,
sk16: $i > $i > $i > $i ).
thf(sk17_type,type,
sk17: $i > $i > $i > $i ).
thf(sk18_type,type,
sk18: $i > $i > $i > $o ).
thf(sk19_type,type,
sk19: $i > $i > $i > $i ).
thf(sk20_type,type,
sk20: $i > $i > $i > $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(37,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)],[5]) ).
thf(38,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)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[42]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(75,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(76,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[76]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( set_difference @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ A @ C ) @ B ) @ ( cartesian_product2 @ A @ ( set_difference @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( set_difference @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ A @ C ) @ B ) @ ( cartesian_product2 @ A @ ( set_difference @ B @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( set_difference @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ A @ C ) @ B ) @ ( cartesian_product2 @ A @ ( set_difference @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) @ ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
( ( set_union2 @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) @ ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(199,plain,
! [A: $i] :
( ( A
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) @ ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,30]) ).
thf(201,plain,
( ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(298,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
= ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
= ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(149,plain,
( ! [A: $i,B: $i,C: $i] :
( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
= ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
= ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
= ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
= ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(66201,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[298,153,154]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(78,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)],[16]) ).
thf(79,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)],[78]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( sk8 @ A @ B @ C )
| ~ ( in @ ( sk10 @ C @ B @ A ) @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk8 @ A @ B @ C )
| ~ ( in @ ( sk10 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk8 @ A @ B @ C )
| ~ ( in @ ( sk10 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[100]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(58,plain,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(59,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[58]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_intersection2 @ B @ A ) @ C )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,59]) ).
thf(213,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_intersection2 @ B @ A ) @ C )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[71,213]) ).
thf(223,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(10,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(62,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,plain,
empty @ sk7,
inference(cnf,[status(esa)],[62]) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(34,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[34]) ).
thf(36,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[35]) ).
thf(195,plain,
( ( empty @ sk7 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[63,36]) ).
thf(196,plain,
sk7 != sk5,
inference(simp,[status(thm)],[195]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk5 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[43,196]) ).
thf(230,plain,
! [A: $i] :
( ~ ( subset @ sk7 @ A )
| ~ ( subset @ A @ sk7 )
| ( A != sk5 ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( sk7 ))]]) ).
thf(549,plain,
( ~ ( subset @ sk7 @ sk5 )
| ~ ( subset @ sk5 @ sk7 ) ),
inference(simp,[status(thm)],[230]) ).
thf(649,plain,
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[549]) ).
thf(652,plain,
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ B )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[223,652]) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_intersection2 @ B @ A )
!= sk5 )
| ( B != sk7 ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1179,plain,
! [A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_intersection2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[1159]) ).
thf(648,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ A )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[213,549]) ).
thf(655,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_intersection2 @ B @ A )
!= sk5 )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[648]) ).
thf(666,plain,
! [A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_intersection2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[655]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(286,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(53060,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk1 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[286,153,154]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(116,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( cartesian_product2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(117,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
=> ( ! [D: $i] :
( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) )
& ! [D: $i] :
( ? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
=> ( in @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) )
& ! [D: $i] :
( ? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( cartesian_product2 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[116]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A @ B @ C )
| ( ( sk15 @ C @ B @ A )
= ( ordered_pair @ ( sk16 @ C @ B @ A ) @ ( sk17 @ C @ B @ A ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ C @ B @ A )
= ( ordered_pair @ ( sk16 @ C @ B @ A ) @ ( sk17 @ C @ B @ A ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ C @ B @ A )
= ( ordered_pair @ ( sk16 @ C @ B @ A ) @ ( sk17 @ C @ B @ A ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C ) ),
inference(simp,[status(thm)],[132]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(10166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ C @ B @ A )
= ( unordered_pair @ ( unordered_pair @ ( sk16 @ C @ B @ A ) @ ( sk17 @ C @ B @ A ) ) @ ( singleton @ ( sk16 @ C @ B @ A ) ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C ) ),
inference(rewrite,[status(thm)],[133,66]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(cnf,[status(esa)],[189]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[79]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[67]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[68]) ).
thf(218,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( B ))]]) ).
thf(219,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[218]) ).
thf(1497,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)],[89,219]) ).
thf(1498,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ A ),
inference(pattern_uni,[status(thm)],[1497:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( set_union2 @ E @ F )),bind(D,$thf( set_union2 @ E @ F ))]]) ).
thf(1529,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ A ),
inference(simp,[status(thm)],[1498]) ).
thf(1545,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)],[191,1529]) ).
thf(1546,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[1545:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1558,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)],[89,1546]) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ B ),
inference(pattern_uni,[status(thm)],[1558:[bind(A,$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(1576,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ B ),
inference(simp,[status(thm)],[1559]) ).
thf(6354,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)],[191,1576]) ).
thf(6355,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ B ),
inference(pattern_uni,[status(thm)],[6354:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(113,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(114,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ~ ? [B: $i] : ( empty @ ( set_union2 @ B @ A ) ) ),
inference(miniscope,[status(thm)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( ( set_union2 @ B @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) @ ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,30]) ).
thf(615,plain,
( ( set_union2 @ ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[614:[bind(A,$thf( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )),bind(B,$thf( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ))]]) ).
thf(20116,plain,
( ( set_union2 @ ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) @ ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[615,153]) ).
thf(21802,plain,
( ( set_union2 @ ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) @ ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[20116,154]) ).
thf(98871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) @ ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[106,21802]) ).
thf(98872,plain,
( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( set_intersection2 @ ( cartesian_product2 @ sk1 @ sk4 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[98871:[bind(A,$thf( cartesian_product2 @ sk1 @ sk2 )),bind(B,$thf( cartesian_product2 @ sk1 @ sk4 )),bind(C,$thf( cartesian_product2 @ sk3 @ sk2 ))]]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) )
= ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(99443,plain,
( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[98872,159]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A @ B @ C )
| ( in @ ( sk16 @ C @ B @ A ) @ A )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ( in @ ( sk16 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ( in @ ( sk16 @ C @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[144]) ).
thf(99444,plain,
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ sk1 @ sk2 ) )
| ( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) )
!= ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[99443]) ).
thf(99912,plain,
( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) )
!= ( cartesian_product2 @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[99444]) ).
thf(100099,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A @ B @ C )
| ( in @ ( sk16 @ C @ B @ A ) @ A )
| ( C
!= ( cartesian_product2 @ sk3 @ sk4 ) )
| ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[145,99912]) ).
thf(100100,plain,
! [A: $i] :
( ( sk13 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) @ A )
| ( in @ ( sk16 @ A @ ( set_intersection2 @ sk4 @ sk2 ) @ ( set_intersection2 @ sk1 @ sk3 ) ) @ ( set_intersection2 @ sk1 @ sk3 ) )
| ( A
!= ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[100099:[bind(A,$thf( set_intersection2 @ sk1 @ sk3 )),bind(B,$thf( set_intersection2 @ sk4 @ sk2 )),bind(C,$thf( C ))]]) ).
thf(100234,plain,
( ( sk13 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk4 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
| ( in @ ( sk16 @ ( cartesian_product2 @ sk3 @ sk4 ) @ ( set_intersection2 @ sk4 @ sk2 ) @ ( set_intersection2 @ sk1 @ sk3 ) ) @ ( set_intersection2 @ sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[100100]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ B )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[79]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ~ ( in @ D @ B )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(4039,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ E @ D ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[99,1546]) ).
thf(4040,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ C ),
inference(pattern_uni,[status(thm)],[4039:[bind(A,$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(4048,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ C ) ) @ C ),
inference(simp,[status(thm)],[4040]) ).
thf(6571,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ ( set_union2 @ E @ F ) ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[89,4048]) ).
thf(6572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) ) @ C ),
inference(pattern_uni,[status(thm)],[6571:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ G @ ( set_union2 @ I @ ( set_union2 @ K @ L ) ) )),bind(D,$thf( G )),bind(E,$thf( I )),bind(F,$thf( set_union2 @ K @ L ))]]) ).
thf(6650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) ) @ C ),
inference(simp,[status(thm)],[6572]) ).
thf(18386,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ ( set_union2 @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,6650]) ).
thf(18387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) ) @ C ),
inference(pattern_uni,[status(thm)],[18386:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(18527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) ) @ C ),
inference(simp,[status(thm)],[18387]) ).
thf(45514,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,18527]) ).
thf(45515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) ) @ B ),
inference(pattern_uni,[status(thm)],[45514:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_difference @ 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_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(164,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ 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_difference @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[163]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( sk18 @ A @ B @ C )
| ( in @ ( sk20 @ C @ B @ A ) @ A )
| ( C
= ( set_difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ( in @ ( sk20 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[165]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ( in @ ( sk20 @ C @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[175]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ C )
| ( C
= ( set_difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[177]) ).
thf(27777,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ( F
= ( set_difference @ D @ E ) )
| ( sk18 @ D @ E @ F )
| ( ( in @ ( sk20 @ C @ B @ A ) @ A )
!= ( in @ ( sk20 @ F @ E @ D ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[176,178]) ).
thf(27778,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
= A )
| ( sk18 @ A @ B @ A )
| ( ( set_difference @ A @ B )
= A )
| ( sk18 @ A @ B @ A ) ),
inference(pattern_uni,[status(thm)],[27777:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(28300,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
= A )
| ( sk18 @ A @ B @ A ) ),
inference(simp,[status(thm)],[27778]) ).
thf(226,plain,
( ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[201]) ).
thf(228,plain,
( ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[226]) ).
thf(20112,plain,
( ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[228,153]) ).
thf(21315,plain,
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ sk1 @ sk2 ) )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[20112]) ).
thf(21598,plain,
( ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[21315]) ).
thf(21610,plain,
( ( sk3 != sk1 )
| ( sk4 != sk4 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[21598]) ).
thf(21781,plain,
( ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[21610]) ).
thf(30837,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,21781]) ).
thf(30838,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk1 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[30837:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(30993,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[30838]) ).
thf(31057,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( A != sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,30993]) ).
thf(31058,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk2 ) ),
inference(pattern_uni,[status(thm)],[31057:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(31131,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[31058]) ).
thf(34291,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( ( sk18 @ sk2 @ sk4 @ sk2 )
!= ( sk18 @ sk1 @ sk3 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31131]) ).
thf(34293,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[34291]) ).
thf(34296,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[34293]) ).
thf(38020,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( B != sk1 )
| ( sk4 != sk3 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,34296]) ).
thf(38021,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ A )
| ~ ( subset @ A @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[38020:[bind(A,$thf( sk2 ))]]) ).
thf(38062,plain,
( ~ ( subset @ sk2 @ sk1 )
| ~ ( subset @ sk1 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[38021]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_intersection2 @ A @ B ) @ C )
| ( ( set_intersection2 @ B @ A )
!= ( set_intersection2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,59]) ).
thf(215,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ B ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(625,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ B )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[223,549]) ).
thf(650,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_intersection2 @ B @ A )
!= sk7 )
| ( B != sk5 ) ),
inference(simp,[status(thm)],[625]) ).
thf(662,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_intersection2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[650]) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( subset @ ( set_intersection2 @ A @ B ) @ B )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[215,662]) ).
thf(3040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( set_intersection2 @ A @ B )
!= sk5 )
| ( B != sk7 ) ),
inference(simp,[status(thm)],[3038]) ).
thf(3044,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ B )
!= sk7 )
| ( ( set_intersection2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[3040]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ B )
| ( C
= ( set_difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ~ ( in @ ( sk20 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[185]) ).
thf(31705,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( sk18 @ A @ B @ C )
| ( F
= ( set_difference @ D @ E ) )
| ( sk18 @ D @ E @ F )
| ( ( in @ ( sk20 @ C @ B @ A ) @ A )
!= ( in @ ( sk20 @ F @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[176,186]) ).
thf(31706,plain,
! [B: $i,A: $i] :
( ( B
= ( set_difference @ A @ A ) )
| ( sk18 @ A @ A @ B )
| ( B
= ( set_difference @ A @ A ) )
| ( sk18 @ A @ A @ B ) ),
inference(pattern_uni,[status(thm)],[31705:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(32546,plain,
! [B: $i,A: $i] :
( ( B
= ( set_difference @ A @ A ) )
| ( sk18 @ A @ A @ B ) ),
inference(simp,[status(thm)],[31706]) ).
thf(30839,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( A != sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,21781]) ).
thf(30840,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(pattern_uni,[status(thm)],[30839:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(30994,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[30840]) ).
thf(33138,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ A @ B )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk3 != sk1 )
| ( B != sk1 )
| ( ( set_difference @ A @ A )
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[32546,30994]) ).
thf(33837,plain,
! [A: $i] :
( ( sk18 @ A @ A @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[33138]) ).
thf(33880,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[33837]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( empty @ A )
| ( B != sk7 ) ),
inference(paramod_ordered,[status(thm)],[43,63]) ).
thf(340,plain,
! [A: $i] :
( ~ ( subset @ A @ sk7 )
| ~ ( subset @ sk7 @ A )
| ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(1534,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)],[89,1529]) ).
thf(1535,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ B ),
inference(pattern_uni,[status(thm)],[1534:[bind(A,$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(1555,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ B ),
inference(simp,[status(thm)],[1535]) ).
thf(6271,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ ( set_union2 @ E @ F ) @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[99,1555]) ).
thf(6272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) @ A ) @ D ),
inference(pattern_uni,[status(thm)],[6271:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ ( set_union2 @ ( set_union2 @ K @ L ) @ J ) @ H )),bind(D,$thf( H )),bind(E,$thf( set_union2 @ K @ L )),bind(F,$thf( J ))]]) ).
thf(6279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) @ A ) @ D ),
inference(simp,[status(thm)],[6272]) ).
thf(14596,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ ( set_union2 @ E @ F ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[191,6279]) ).
thf(14597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) @ B ) @ D ),
inference(pattern_uni,[status(thm)],[14596:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(14673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) @ B ) @ D ),
inference(simp,[status(thm)],[14597]) ).
thf(26832,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ D ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,14673]) ).
thf(26833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ D ) @ B ),
inference(pattern_uni,[status(thm)],[26832:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(6383,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ ( set_union2 @ E @ F ) ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[99,1576]) ).
thf(6384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) ) @ D ),
inference(pattern_uni,[status(thm)],[6383:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ G @ ( set_union2 @ ( set_union2 @ K @ L ) @ J ) )),bind(D,$thf( G )),bind(E,$thf( set_union2 @ K @ L )),bind(F,$thf( J ))]]) ).
thf(6411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) ) @ D ),
inference(simp,[status(thm)],[6384]) ).
thf(15775,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6411]) ).
thf(15776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) ) @ B ),
inference(pattern_uni,[status(thm)],[15775:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(276,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(43160,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[276,153,154]) ).
thf(15777,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( set_union2 @ E @ F ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[191,6411]) ).
thf(15778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) ) @ D ),
inference(pattern_uni,[status(thm)],[15777:[bind(A,$thf( set_union2 @ G @ H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(15870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) ) @ D ),
inference(simp,[status(thm)],[15778]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(48,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)],[6]) ).
thf(49,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)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( in @ ( sk6 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( in @ ( sk6 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[50]) ).
thf(1507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( in @ E @ ( set_union2 @ C @ D ) )
| ( ( in @ ( sk6 @ B @ A ) @ A )
!= ( in @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,89]) ).
thf(1508,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk6 @ B @ C ) @ ( set_union2 @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[1507:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk6 @ F @ G ))]]) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk6 @ B @ C ) @ ( set_union2 @ C @ A ) ) ),
inference(simp,[status(thm)],[1508]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk6 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk6 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[51]) ).
thf(3657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( subset @ D @ E )
| ( ( in @ ( sk6 @ B @ C ) @ ( set_union2 @ C @ A ) )
!= ( in @ ( sk6 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1521,54]) ).
thf(3658,plain,
! [B: $i,A: $i] :
( ( subset @ A @ ( set_union2 @ A @ B ) )
| ( subset @ A @ ( set_union2 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[3657:[bind(A,$thf( G )),bind(B,$thf( set_union2 @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( set_union2 @ F @ G ))]]) ).
thf(3690,plain,
! [B: $i,A: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
inference(simp,[status(thm)],[3658]) ).
thf(4091,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)],[191,3690]) ).
thf(4092,plain,
! [B: $i,A: $i] : ( subset @ A @ ( set_union2 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[4091:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ ( set_difference @ A @ ( set_intersection2 @ B @ C ) ) )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[106,4092]) ).
thf(4139,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ B @ C ) @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[4138:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( set_difference @ H @ I )),bind(E,$thf( set_difference @ H @ G ))]]) ).
thf(4198,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ B @ C ) @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) ),
inference(simp,[status(thm)],[4139]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(388,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(83043,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[388,153]) ).
thf(39901,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15870]) ).
thf(39902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[39901:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ A @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(404,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ A @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[403:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(96638,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ A @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[404,153]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk19 @ C @ B @ A ) @ C )
| ~ ( sk18 @ A @ B @ C )
| ( C
= ( set_difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( in @ ( sk19 @ C @ B @ A ) @ C )
| ~ ( sk18 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ( in @ ( sk19 @ C @ B @ A ) @ C )
| ~ ( sk18 @ A @ B @ C ) ),
inference(simp,[status(thm)],[173]) ).
thf(34292,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( ( sk18 @ sk2 @ sk4 @ sk2 )
!= ( sk18 @ sk1 @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[34291]) ).
thf(36867,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( A != sk1 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,33880]) ).
thf(36868,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[36867:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(36888,plain,
( ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[36868]) ).
thf(3653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk6 @ D @ E ) @ ( set_union2 @ B @ A ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[191,1521]) ).
thf(3654,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk6 @ C @ A ) @ ( set_union2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[3653:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(3688,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk6 @ C @ A ) @ ( set_union2 @ B @ A ) ) ),
inference(simp,[status(thm)],[3654]) ).
thf(6616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ ( set_union2 @ E @ F ) ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[99,4048]) ).
thf(6617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) ) @ D ),
inference(pattern_uni,[status(thm)],[6616:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ G @ ( set_union2 @ I @ ( set_union2 @ K @ L ) ) )),bind(D,$thf( G )),bind(E,$thf( I )),bind(F,$thf( set_union2 @ K @ L ))]]) ).
thf(6637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) ) @ D ),
inference(simp,[status(thm)],[6617]) ).
thf(15921,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ ( set_union2 @ C @ A ) ) @ E )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[77,6637]) ).
thf(15922,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ C @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[15921:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[164]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( set_difference @ A @ B ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(390,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(87458,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[390,153]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,plain,
~ ? [A: $i,B: $i] : ( empty @ ( ordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[73]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[63,74]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= sk7 ),
inference(simp,[status(thm)],[197]) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= sk7 ),
inference(rewrite,[status(thm)],[198,66]) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= sk7 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,780]) ).
thf(818,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[817:[bind(A,$thf( unordered_pair @ G @ F )),bind(B,$thf( singleton @ G )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(838,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= sk7 ),
inference(simp,[status(thm)],[818]) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( set_difference @ A @ ( set_intersection2 @ B @ C ) )
= D )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[106,77]) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( set_difference @ B @ ( set_intersection2 @ A @ A ) )
= ( set_difference @ B @ A ) ),
inference(pattern_uni,[status(thm)],[882:[bind(A,$thf( E )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( set_difference @ E @ C ))]]) ).
thf(975,plain,
! [B: $i,A: $i] :
( ( set_difference @ B @ ( set_intersection2 @ A @ A ) )
= ( set_difference @ B @ A ) ),
inference(simp,[status(thm)],[883]) ).
thf(4074,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ ( set_difference @ A @ ( set_intersection2 @ B @ C ) ) )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[106,3690]) ).
thf(4075,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ B @ A ) @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[4074:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( set_difference @ H @ G )),bind(E,$thf( set_difference @ H @ I ))]]) ).
thf(4134,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ B @ A ) @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) ),
inference(simp,[status(thm)],[4075]) ).
thf(4229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_difference @ B @ A ) @ ( set_difference @ D @ ( set_intersection2 @ C @ E ) ) )
| ( ( set_difference @ B @ ( set_intersection2 @ A @ A ) )
!= ( set_difference @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[975,4134]) ).
thf(4230,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ A @ ( set_intersection2 @ ( set_intersection2 @ C @ C ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[4229:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( set_intersection2 @ G @ G )),bind(D,$thf( B )),bind(E,$thf( E ))]]) ).
thf(4275,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ A @ ( set_intersection2 @ ( set_intersection2 @ C @ C ) @ B ) ) ),
inference(simp,[status(thm)],[4230]) ).
thf(18384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6650]) ).
thf(18385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[18384:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(3981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[99,1529]) ).
thf(3982,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ C ),
inference(pattern_uni,[status(thm)],[3981:[bind(A,$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(4051,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ C ) @ A ) @ C ),
inference(simp,[status(thm)],[3982]) ).
thf(6683,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ ( set_union2 @ E @ F ) @ D ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[89,4051]) ).
thf(6684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) @ A ) @ C ),
inference(pattern_uni,[status(thm)],[6683:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ ( set_union2 @ I @ ( set_union2 @ K @ L ) ) @ H )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( set_union2 @ K @ L ))]]) ).
thf(6756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) @ A ) @ C ),
inference(simp,[status(thm)],[6684]) ).
thf(19694,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ ( set_union2 @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,6756]) ).
thf(19695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) @ B ) @ C ),
inference(pattern_uni,[status(thm)],[19694:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(19851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) @ B ) @ C ),
inference(simp,[status(thm)],[19695]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(294,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(60259,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[294,153,154]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(6338,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ D @ ( set_union2 @ E @ F ) ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[89,1576]) ).
thf(6339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) ) @ C ),
inference(pattern_uni,[status(thm)],[6338:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ G @ ( set_union2 @ ( set_union2 @ K @ L ) @ J ) )),bind(D,$thf( G )),bind(E,$thf( set_union2 @ K @ L )),bind(F,$thf( J ))]]) ).
thf(6392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) ) @ C ),
inference(simp,[status(thm)],[6339]) ).
thf(15140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( set_union2 @ E @ F ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[191,6392]) ).
thf(15141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) ) @ C ),
inference(pattern_uni,[status(thm)],[15140:[bind(A,$thf( set_union2 @ G @ H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(15232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) ) @ C ),
inference(simp,[status(thm)],[15141]) ).
thf(36590,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15232]) ).
thf(36591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[36590:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(19692,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) @ C ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6756]) ).
thf(19693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[19692:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ B )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[223,662]) ).
thf(3042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( set_intersection2 @ B @ A )
!= sk5 )
| ( B != sk7 ) ),
inference(simp,[status(thm)],[3021]) ).
thf(3046,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ B )
!= sk7 )
| ( ( set_intersection2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[3042]) ).
thf(3655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( in @ ( sk6 @ D @ E ) @ ( set_union2 @ A @ B ) )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[191,1521]) ).
thf(3656,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk6 @ C @ B ) @ ( set_union2 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[3655:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(3689,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk6 @ C @ B ) @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[3656]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( sk8 @ A @ B @ C )
| ( in @ ( sk10 @ C @ B @ A ) @ A )
| ( in @ ( sk10 @ C @ B @ A ) @ B )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk8 @ A @ B @ C )
| ( in @ ( sk10 @ C @ B @ A ) @ A )
| ( in @ ( sk10 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( sk8 @ A @ B @ C )
| ( in @ ( sk10 @ C @ B @ A ) @ A )
| ( in @ ( sk10 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[92]) ).
thf(15977,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ ( set_union2 @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,6637]) ).
thf(15978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) ) @ D ),
inference(pattern_uni,[status(thm)],[15977:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(16114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) ) @ D ),
inference(simp,[status(thm)],[15978]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(55,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( D
= ( ordered_pair @ ( sk11 @ D @ C @ B @ A ) @ ( sk12 @ D @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ( ordered_pair @ ( sk11 @ D @ C @ B @ A ) @ ( sk12 @ D @ C @ B @ A ) )
= D )
| ~ ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) @ ( sk12 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) )
= C )
| ~ ( in @ C @ ( cartesian_product2 @ A @ B ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(12022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) @ ( sk12 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) ) @ ( singleton @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) ) )
= C )
| ~ ( in @ C @ ( cartesian_product2 @ A @ B ) ) ),
inference(rewrite,[status(thm)],[137,66]) ).
thf(12172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartesian_product2 @ A @ B ) )
| ( C != sk7 )
| ( ( unordered_pair @ ( unordered_pair @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) @ ( sk12 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) ) @ ( singleton @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) ) )
!= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[12022,780]) ).
thf(12173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( cartesian_product2 @ C @ B ) )
| ( A != sk7 ) ),
inference(pattern_uni,[status(thm)],[12172:[bind(A,$thf( O )),bind(B,$thf( N )),bind(C,$thf( L )),bind(D,$thf( sk11 @ L @ ( cartesian_product2 @ O @ N ) @ N @ O )),bind(E,$thf( sk12 @ L @ ( cartesian_product2 @ O @ N ) @ N @ O ))]]) ).
thf(12420,plain,
! [B: $i,A: $i] :
~ ( in @ sk7 @ ( cartesian_product2 @ B @ A ) ),
inference(simp,[status(thm)],[12173]) ).
thf(20207,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) )
| ( ( cartesian_product2 @ C @ ( set_difference @ A @ B ) )
!= ( cartesian_product2 @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[153,12420]) ).
thf(20208,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[20207:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( set_difference @ F @ G )),bind(E,$thf( C ))]]) ).
thf(20259,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ A @ C ) ) ),
inference(simp,[status(thm)],[20208]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(292,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(57698,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[292,153,154]) ).
thf(647,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ A )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[213,549]) ).
thf(651,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_intersection2 @ B @ A )
!= sk7 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[647]) ).
thf(663,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_intersection2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[651]) ).
thf(4941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( subset @ ( set_intersection2 @ A @ B ) @ A )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[59,663]) ).
thf(4973,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( set_intersection2 @ A @ B )
!= sk5 )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[4941]) ).
thf(4988,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ sk5 )
!= sk7 )
| ( ( set_intersection2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[4973]) ).
thf(42832,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,16114]) ).
thf(42833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) ) @ B ),
inference(pattern_uni,[status(thm)],[42832:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(22246,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,21781]) ).
thf(22247,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( A != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[22246:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(22288,plain,
( ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[22247]) ).
thf(30879,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,22288]) ).
thf(30880,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( sk1 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[30879:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(30962,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[30880]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ C @ B ) @ ( set_difference @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(192,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ C @ B ) @ ( set_difference @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] : ( subset @ ( set_difference @ C @ B ) @ ( set_difference @ C @ A ) ) ),
inference(miniscope,[status(thm)],[192]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( set_difference @ C @ B ) @ ( set_difference @ C @ A ) ) ),
inference(cnf,[status(esa)],[193]) ).
thf(37220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_difference @ E @ D ) @ ( set_difference @ E @ C ) )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3690,194]) ).
thf(37221,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ ( set_union2 @ B @ C ) ) @ ( set_difference @ A @ B ) ),
inference(pattern_uni,[status(thm)],[37220:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( set_union2 @ F @ G ))]]) ).
thf(37309,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ ( set_union2 @ B @ C ) ) @ ( set_difference @ A @ B ) ),
inference(simp,[status(thm)],[37221]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ ( sk12 @ D @ C @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[117]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ ( sk12 @ D @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartesian_product2 @ A @ B ) )
| ( in @ ( sk12 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[146]) ).
thf(33058,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ A @ B )
| ( sk3 != sk1 )
| ( B != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( ( set_difference @ A @ A )
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[32546,21781]) ).
thf(33839,plain,
! [A: $i] :
( ( sk18 @ A @ A @ sk1 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( A != sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[33058]) ).
thf(33881,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[33839]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(400,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(95780,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[400,153]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ A @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(282,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ A @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(47964,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[282,153,154]) ).
thf(30939,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,21598]) ).
thf(30940,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( sk1 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[30939:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(30987,plain,
( ( sk18 @ sk1 @ sk3 @ sk1 )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[30940]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(384,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(81355,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[384,153]) ).
thf(26838,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ D ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,14673]) ).
thf(26839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ D ) @ A ),
inference(pattern_uni,[status(thm)],[26838:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(6699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[191,4051]) ).
thf(6700,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[6699:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ A @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(280,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk1 @ sk3 ) )
| ~ ( subset @ ( set_difference @ sk1 @ sk3 ) @ A )
| ( ( cartesian_product2 @ A @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( A )),bind(B,$thf( set_difference @ sk1 @ sk3 ))]]) ).
thf(46346,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk1 @ sk3 ) )
| ~ ( subset @ ( set_difference @ sk1 @ sk3 ) @ A )
| ( ( cartesian_product2 @ A @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[280,153]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(394,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(91771,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[394,153]) ).
thf(38018,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( B != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk3 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,34296]) ).
thf(38019,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( A != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[38018:[bind(A,$thf( sk3 ))]]) ).
thf(38061,plain,
( ~ ( subset @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[38019]) ).
thf(22240,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( B != sk2 )
| ( A
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,21781]) ).
thf(22241,plain,
! [A: $i] :
( ~ ( subset @ ( set_difference @ sk2 @ sk4 ) @ A )
| ~ ( subset @ A @ ( set_difference @ sk2 @ sk4 ) )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[22240:[bind(A,$thf( set_difference @ sk2 @ sk4 )),bind(B,$thf( B ))]]) ).
thf(22282,plain,
( ~ ( subset @ ( set_difference @ sk2 @ sk4 ) @ sk2 )
| ~ ( subset @ sk2 @ ( set_difference @ sk2 @ sk4 ) )
| ( sk3 != sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[22241]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(304,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(72950,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[304,153,154]) ).
thf(6587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[191,4048]) ).
thf(6588,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ A ),
inference(pattern_uni,[status(thm)],[6587:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(60,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ sk1 @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(380,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk2 @ sk4 ) )
| ~ ( subset @ ( set_difference @ sk2 @ sk4 ) @ A )
| ( ( cartesian_product2 @ sk1 @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[379:[bind(A,$thf( A )),bind(B,$thf( set_difference @ sk2 @ sk4 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(108,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[107]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) ),
inference(cnf,[status(esa)],[108]) ).
thf(6079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) ),
inference(rewrite,[status(thm)],[110,66]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(160,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
!= sk7 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[33,780]) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(22987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= E )
| ( ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) )
!= ( set_intersection2 @ E @ E ) ) ),
inference(paramod_ordered,[status(thm)],[159,57]) ).
thf(22988,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ ( set_intersection2 @ B @ B ) )
= ( cartesian_product2 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[22987:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D )),bind(D,$thf( D )),bind(E,$thf( cartesian_product2 @ B @ D ))]]) ).
thf(23141,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ ( set_intersection2 @ B @ B ) )
= ( cartesian_product2 @ A @ B ) ),
inference(simp,[status(thm)],[22988]) ).
thf(27169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ ( set_intersection2 @ C @ C ) )
= ( cartesian_product2 @ B @ C ) )
| ( ( set_intersection2 @ A @ A )
!= ( set_intersection2 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,23141]) ).
thf(27170,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ A @ ( set_intersection2 @ B @ B ) )
= ( cartesian_product2 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[27169:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(27347,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ A @ ( set_intersection2 @ B @ B ) )
= ( cartesian_product2 @ A @ B ) ),
inference(simp,[status(thm)],[27170]) ).
thf(27171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ A )
= ( cartesian_product2 @ B @ C ) )
| ( ( set_intersection2 @ A @ A )
!= ( set_intersection2 @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[57,23141]) ).
thf(27172,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ A )
= ( cartesian_product2 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[27171:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(28829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ D @ C ) )
| ( ( cartesian_product2 @ A @ ( set_intersection2 @ B @ B ) )
!= ( cartesian_product2 @ ( set_intersection2 @ D @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27347,27172]) ).
thf(28830,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ B )
= ( cartesian_product2 @ A @ ( set_intersection2 @ B @ B ) ) ),
inference(pattern_uni,[status(thm)],[28829:[bind(A,$thf( set_intersection2 @ F @ F )),bind(B,$thf( H )),bind(C,$thf( set_intersection2 @ H @ H )),bind(D,$thf( F ))]]) ).
thf(28948,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ B )
= ( cartesian_product2 @ A @ ( set_intersection2 @ B @ B ) ) ),
inference(simp,[status(thm)],[28830]) ).
thf(6695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[191,4051]) ).
thf(6696,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[6695:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(1569,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)],[191,1546]) ).
thf(1570,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[1569:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk4 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(288,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(55585,plain,
! [A: $i] :
( ~ ( subset @ A @ sk4 )
| ~ ( subset @ sk4 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ A ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[288,153,154]) ).
thf(4083,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,549]) ).
thf(4114,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( A != sk7 )
| ( ( set_union2 @ A @ B )
!= sk5 ) ),
inference(simp,[status(thm)],[4083]) ).
thf(4128,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_union2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[4114]) ).
thf(4146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,662]) ).
thf(4178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( A != sk5 )
| ( ( set_union2 @ B @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4146]) ).
thf(4192,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ B )
!= sk7 )
| ( ( set_union2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[4178]) ).
thf(6728,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ ( set_union2 @ E @ F ) @ D ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[99,4051]) ).
thf(6729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) @ A ) @ D ),
inference(pattern_uni,[status(thm)],[6728:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ ( set_union2 @ I @ ( set_union2 @ K @ L ) ) @ H )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( set_union2 @ K @ L ))]]) ).
thf(6743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ ( set_union2 @ C @ D ) ) @ A ) @ D ),
inference(simp,[status(thm)],[6729]) ).
thf(18601,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ ( set_union2 @ E @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,6743]) ).
thf(18602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) @ B ) @ D ),
inference(pattern_uni,[status(thm)],[18601:[bind(A,$thf( A )),bind(B,$thf( set_union2 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(18718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ A ) @ B ) @ D ),
inference(simp,[status(thm)],[18602]) ).
thf(50374,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ D ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,18718]) ).
thf(50375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ D ) @ B ),
inference(pattern_uni,[status(thm)],[50374:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk9 @ C @ B @ A ) @ B )
| ~ ( sk8 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk9 @ C @ B @ A ) @ B )
| ~ ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk9 @ C @ B @ A ) @ B )
| ~ ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[96]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ A @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(378,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( cartesian_product2 @ A @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(76360,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[378,153]) ).
thf(6226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( set_union2 @ A @ B ) )
!= ( in @ ( set_union2 @ ( set_union2 @ E @ F ) @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[89,1555]) ).
thf(6227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) @ A ) @ C ),
inference(pattern_uni,[status(thm)],[6226:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( set_union2 @ ( set_union2 @ ( set_union2 @ K @ L ) @ J ) @ H )),bind(D,$thf( H )),bind(E,$thf( set_union2 @ K @ L )),bind(F,$thf( J ))]]) ).
thf(6292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ C @ D ) @ B ) @ A ) @ C ),
inference(simp,[status(thm)],[6227]) ).
thf(14937,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ ( set_union2 @ E @ F ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[191,6292]) ).
thf(14938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) @ B ) @ C ),
inference(pattern_uni,[status(thm)],[14937:[bind(A,$thf( set_union2 @ G @ H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(15067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ ( set_union2 @ C @ D ) ) @ B ) @ C ),
inference(simp,[status(thm)],[14938]) ).
thf(32646,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ D ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15067]) ).
thf(32647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) @ D ) @ B ),
inference(pattern_uni,[status(thm)],[32646:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(626,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ B )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[223,549]) ).
thf(654,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_intersection2 @ B @ A )
!= sk5 )
| ( B != sk7 ) ),
inference(simp,[status(thm)],[626]) ).
thf(665,plain,
! [A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_intersection2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[654]) ).
thf(16446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ E )
| ( in @ ( sk6 @ E @ C ) @ ( set_union2 @ A @ B ) )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[191,3688]) ).
thf(16447,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk6 @ C @ A ) @ ( set_union2 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[16446:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(16601,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( in @ ( sk6 @ C @ A ) @ ( set_union2 @ A @ B ) ) ),
inference(simp,[status(thm)],[16447]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B
!= ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(396,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
| ~ ( subset @ ( cartesian_product2 @ sk3 @ sk4 ) @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( A )),bind(B,$thf( cartesian_product2 @ sk3 @ sk4 ))]]) ).
thf(94144,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
| ~ ( subset @ ( cartesian_product2 @ sk3 @ sk4 ) @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[396,153]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ( in @ ( sk19 @ C @ B @ A ) @ B )
| ~ ( sk18 @ A @ B @ C )
| ( C
= ( set_difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ( in @ ( sk19 @ C @ B @ A ) @ B )
| ~ ( sk18 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_difference @ A @ B ) )
| ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ( in @ ( sk19 @ C @ B @ A ) @ B )
| ~ ( sk18 @ A @ B @ C ) ),
inference(simp,[status(thm)],[187]) ).
thf(36596,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15232]) ).
thf(36597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[36596:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(100013,plain,
! [A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ A )
!= ( cartesian_product2 @ sk3 @ sk4 ) )
| ( ( set_intersection2 @ A @ A )
!= ( set_intersection2 @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[57,99912]) ).
thf(100208,plain,
! [A: $i] :
( ( ( set_intersection2 @ sk1 @ sk3 )
!= sk3 )
| ( A != sk4 )
| ( A != sk4 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[100013]) ).
thf(100263,plain,
( ( ( set_intersection2 @ sk1 @ sk3 )
!= sk3 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[100208]) ).
thf(100596,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk4 != sk2 )
| ( ( set_intersection2 @ A @ A )
!= ( set_intersection2 @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[57,100263]) ).
thf(100677,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[100596]) ).
thf(100679,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[100677]) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( subset @ ( set_intersection2 @ A @ B ) @ B )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[215,652]) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_intersection2 @ A @ B )
!= sk5 )
| ( B != sk7 ) ),
inference(simp,[status(thm)],[1155]) ).
thf(1182,plain,
! [A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_intersection2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[1162]) ).
thf(6238,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)],[191,1555]) ).
thf(6239,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[6238:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(779,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(rewrite,[status(thm)],[74,66]) ).
thf(39907,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15870]) ).
thf(39908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ C @ ( set_union2 @ A @ B ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[39907:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(42838,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,16114]) ).
thf(42839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) ) @ A ),
inference(pattern_uni,[status(thm)],[42838:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(28819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ C @ ( set_intersection2 @ B @ A ) )
= ( cartesian_product2 @ C @ D ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,27347]) ).
thf(28820,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ B @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[28819:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(28943,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ B @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ B @ A ) ),
inference(simp,[status(thm)],[28820]) ).
thf(4173,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,652]) ).
thf(4181,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( A != sk5 )
| ( ( set_union2 @ B @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4173]) ).
thf(4195,plain,
! [A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_union2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[4181]) ).
thf(30941,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( A != sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,21598]) ).
thf(30942,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(pattern_uni,[status(thm)],[30941:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(30988,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ( ( cartesian_product2 @ sk3 @ sk4 )
!= ( cartesian_product2 @ sk1 @ sk4 ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[30942]) ).
thf(6048,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( subset @ ( set_intersection2 @ A @ B ) @ B )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[215,665]) ).
thf(6053,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( set_intersection2 @ A @ B )
!= sk7 )
| ( B != sk5 ) ),
inference(simp,[status(thm)],[6048]) ).
thf(6070,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ B )
!= sk5 )
| ( ( set_intersection2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[6053]) ).
thf(15975,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6637]) ).
thf(15976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[15975:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
!= sk7 )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[33,780]) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(19698,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) @ C ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6756]) ).
thf(19699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[19698:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(1547,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)],[191,1529]) ).
thf(1548,plain,
! [B: $i,A: $i] :
~ ( in @ ( set_union2 @ A @ B ) @ B ),
inference(pattern_uni,[status(thm)],[1547:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(45,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[44]) ).
thf(6242,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)],[191,1555]) ).
thf(6243,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[6242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ),
inference(cnf,[status(esa)],[164]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_difference @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(simp,[status(thm)],[179]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ A @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(274,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( cartesian_product2 @ ( set_difference @ A @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(41060,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( set_difference @ ( cartesian_product2 @ A @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[274,153,154]) ).
thf(14945,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) @ C ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6292]) ).
thf(14946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[14945:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(54893,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ D ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,19851]) ).
thf(54894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) @ D ) @ A ),
inference(pattern_uni,[status(thm)],[54893:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(36885,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk3 != sk1 )
| ( ( sk18 @ sk2 @ sk4 @ sk2 )
!= ( sk18 @ sk1 @ sk1 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[33880]) ).
thf(36887,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[36885]) ).
thf(36890,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[36887]) ).
thf(50380,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ D ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,18718]) ).
thf(50381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ D ) @ A ),
inference(pattern_uni,[status(thm)],[50380:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(4084,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,549]) ).
thf(4113,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( A != sk5 )
| ( ( set_union2 @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[4084]) ).
thf(4127,plain,
! [A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_union2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4113]) ).
thf(14594,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) @ C ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6279]) ).
thf(14595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[14594:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(16444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ E )
| ( in @ ( sk6 @ E @ C ) @ ( set_union2 @ B @ A ) )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[191,3688]) ).
thf(16445,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk6 @ C @ B ) @ ( set_union2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[16444:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(16600,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( in @ ( sk6 @ C @ B ) @ ( set_union2 @ B @ A ) ) ),
inference(simp,[status(thm)],[16445]) ).
thf(36886,plain,
( ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk3 != sk1 )
| ( ( sk18 @ sk2 @ sk4 @ sk2 )
!= ( sk18 @ sk1 @ sk1 @ sk1 ) ) ),
inference(simp,[status(thm)],[36885]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B
!= ( cartesian_product2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(296,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk1 @ sk2 ) )
| ~ ( subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( A )),bind(B,$thf( cartesian_product2 @ sk1 @ sk2 ))]]) ).
thf(64092,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk1 @ sk2 ) )
| ~ ( subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[296,153,154]) ).
thf(1556,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_difference @ A @ ( set_intersection2 @ B @ C ) ) @ D )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[106,1546]) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) @ ( set_difference @ B @ C ) ),
inference(pattern_uni,[status(thm)],[1556:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( set_difference @ H @ I )),bind(E,$thf( set_difference @ H @ G ))]]) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) @ ( set_difference @ B @ C ) ),
inference(simp,[status(thm)],[1557]) ).
thf(18550,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ C @ A ) @ B ) @ E )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[77,6743]) ).
thf(18551,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ C @ A ) @ B ) @ A ),
inference(pattern_uni,[status(thm)],[18550:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( unordered_pair @ B @ A ) )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,779]) ).
thf(788,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[787:[bind(A,$thf( unordered_pair @ G @ F )),bind(B,$thf( singleton @ G )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(811,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) ) ),
inference(simp,[status(thm)],[788]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(284,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk2 @ sk4 ) )
| ~ ( subset @ ( set_difference @ sk2 @ sk4 ) @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( A )),bind(B,$thf( set_difference @ sk2 @ sk4 ))]]) ).
thf(51214,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk2 @ sk4 ) )
| ~ ( subset @ ( set_difference @ sk2 @ sk4 ) @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( cartesian_product2 @ sk1 @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[284,154]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( sk9 @ C @ B @ A ) @ A )
| ~ ( sk8 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk9 @ C @ B @ A ) @ A )
| ~ ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ~ ( in @ ( sk9 @ C @ B @ A ) @ A )
| ~ ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[102]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C )
| ( C
= ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( in @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_union2 @ A @ B ) )
| ( in @ ( sk9 @ C @ B @ A ) @ C )
| ~ ( sk8 @ A @ B @ C ) ),
inference(simp,[status(thm)],[90]) ).
thf(18611,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) @ C ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6743]) ).
thf(18612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[18611:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(32640,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ D ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,15067]) ).
thf(32641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ D ) @ A ),
inference(pattern_uni,[status(thm)],[32640:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(4970,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,663]) ).
thf(4975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( A != sk5 )
| ( ( set_union2 @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[4970]) ).
thf(4990,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ sk5 )
!= sk7 )
| ( ( set_union2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4975]) ).
thf(4946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ A )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[213,663]) ).
thf(4977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( set_intersection2 @ B @ A )
!= sk5 )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[4946]) ).
thf(4993,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ sk5 )
!= sk7 )
| ( ( set_intersection2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[4977]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ A ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(272,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ A ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(38069,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ A @ sk2 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[272,153,154]) ).
thf(15781,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6411]) ).
thf(15782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) ) @ A ),
inference(pattern_uni,[status(thm)],[15781:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) ) )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[33,779]) ).
thf(790,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) ) ),
inference(pattern_uni,[status(thm)],[789:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( unordered_pair @ A @ B ) )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ ( unordered_pair @ D @ C ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,790]) ).
thf(850,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( singleton @ G )),bind(B,$thf( unordered_pair @ E @ G )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(868,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) ) ),
inference(simp,[status(thm)],[850]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk14 @ C @ B @ A ) @ C )
| ~ ( sk13 @ A @ B @ C )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( in @ ( sk14 @ C @ B @ A ) @ C )
| ~ ( sk13 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( in @ ( sk14 @ C @ B @ A ) @ C )
| ~ ( sk13 @ A @ B @ C ) ),
inference(simp,[status(thm)],[134]) ).
thf(14534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ A @ C ) @ B ) @ E )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[77,6279]) ).
thf(14535,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ A @ C ) @ B ) @ A ),
inference(pattern_uni,[status(thm)],[14534:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(161,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ~ ? [B: $i] : ( empty @ ( set_union2 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(6804,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk7 )
!= sk5 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,666]) ).
thf(6823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk7 )
!= sk5 )
| ( A != sk7 )
| ( ( set_union2 @ B @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[6804]) ).
thf(6843,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ sk7 )
!= sk5 )
| ( ( set_union2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[6823]) ).
thf(14939,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) @ C ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6292]) ).
thf(14940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) @ C ) @ A ),
inference(pattern_uni,[status(thm)],[14939:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(2396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ B @ A ) )
!= sk7 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33,838]) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ B @ A ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[2396:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(81,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)],[79]) ).
thf(94,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)],[81]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_union2 @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(simp,[status(thm)],[94]) ).
thf(40805,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( B != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk1 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,36890]) ).
thf(40806,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( A != sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[40805:[bind(A,$thf( sk3 ))]]) ).
thf(40850,plain,
( ~ ( subset @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( sk2 != sk1 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[40806]) ).
thf(34273,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( A != sk1 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,31131]) ).
thf(34274,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[34273:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(34294,plain,
( ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( sk18 @ sk2 @ sk4 @ sk2 )
| ( sk18 @ sk1 @ sk3 @ sk1 ) ),
inference(simp,[status(thm)],[34274]) ).
thf(6047,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,665]) ).
thf(6052,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( A != sk7 )
| ( ( set_union2 @ A @ B )
!= sk5 ) ),
inference(simp,[status(thm)],[6047]) ).
thf(6069,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ B )
!= sk5 )
| ( ( set_union2 @ sk7 @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[6052]) ).
thf(36996,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( B != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,33881]) ).
thf(36997,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[36996:[bind(A,$thf( sk3 ))]]) ).
thf(37062,plain,
( ~ ( subset @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ( sk18 @ sk1 @ sk1 @ sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[36997]) ).
thf(4148,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,549]) ).
thf(4176,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( A != sk5 )
| ( ( set_union2 @ B @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4148]) ).
thf(4190,plain,
! [A: $i] :
( ~ ( subset @ sk7 @ sk5 )
| ( ( set_union2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[4176]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ D @ A ) ),
inference(cnf,[status(esa)],[164]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ D @ A ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_difference @ A @ B ) )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[181]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(7243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) @ ( cartesian_product2 @ C @ D ) ) ),
inference(rewrite,[status(thm)],[112,66]) ).
thf(120,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) )
| ( in @ D @ C ) ),
inference(cnf,[status(esa)],[117]) ).
thf(128,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( D
!= ( ordered_pair @ E @ F ) )
| ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( in @ D @ C ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ B )
| ( in @ ( ordered_pair @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(8509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( cartesian_product2 @ A @ B ) ) ),
inference(rewrite,[status(thm)],[129,66]) ).
thf(4109,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,652]) ).
thf(4118,plain,
! [B: $i,A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( A != sk5 )
| ( ( set_union2 @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[4109]) ).
thf(4132,plain,
! [A: $i] :
( ( ( subset @ sk7 @ sk5 )
!= ( subset @ sk5 @ sk7 ) )
| ( ( set_union2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4118]) ).
thf(14588,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) @ C ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6279]) ).
thf(14589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[14588:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(15084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ C ) ) @ D )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[77,6392]) ).
thf(15085,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ B @ ( set_union2 @ A @ C ) ) @ A ),
inference(pattern_uni,[status(thm)],[15084:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).
thf(2322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= sk7 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ D @ C ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,820]) ).
thf(2323,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[2322:[bind(A,$thf( unordered_pair @ E @ G )),bind(B,$thf( singleton @ G )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(2354,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= sk7 ),
inference(simp,[status(thm)],[2323]) ).
thf(15981,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) ) @ F )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6637]) ).
thf(15982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) ) @ A ),
inference(pattern_uni,[status(thm)],[15981:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(4953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,663]) ).
thf(4976,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ C @ sk5 )
!= sk7 )
| ( A != sk5 )
| ( ( set_union2 @ B @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4953]) ).
thf(4991,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ sk5 )
!= sk7 )
| ( ( set_union2 @ A @ sk5 )
!= sk7 ) ),
inference(simp,[status(thm)],[4976]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(382,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ A @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(78956,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ sk2 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ A ) @ ( cartesian_product2 @ sk1 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[382,153]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ ( sk11 @ D @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[117]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ ( sk11 @ D @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartesian_product2 @ A @ B ) )
| ( in @ ( sk11 @ C @ ( cartesian_product2 @ A @ B ) @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[142]) ).
thf(27201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ C @ C ) @ ( set_intersection2 @ B @ A ) )
= ( cartesian_product2 @ C @ D ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,23141]) ).
thf(27202,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[27201:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(27375,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ B @ A ) ),
inference(simp,[status(thm)],[27202]) ).
thf(38022,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( B != sk3 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[43,34296]) ).
thf(38023,plain,
! [A: $i] :
( ~ ( subset @ sk4 @ A )
| ~ ( subset @ A @ sk4 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[38022:[bind(A,$thf( sk4 ))]]) ).
thf(38063,plain,
( ~ ( subset @ sk4 @ sk3 )
| ~ ( subset @ sk3 @ sk4 )
| ( sk18 @ sk1 @ sk3 @ sk1 )
| ( sk3 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[38023]) ).
thf(1532,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_difference @ A @ ( set_intersection2 @ B @ C ) ) @ D )
| ( ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ A @ C ) )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[106,1529]) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) @ ( set_difference @ B @ A ) ),
inference(pattern_uni,[status(thm)],[1532:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( set_difference @ H @ G )),bind(E,$thf( set_difference @ H @ I ))]]) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_difference @ B @ ( set_intersection2 @ A @ C ) ) @ ( set_difference @ B @ A ) ),
inference(simp,[status(thm)],[1533]) ).
thf(6013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( subset @ ( set_intersection2 @ A @ B ) @ A )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[59,665]) ).
thf(6050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( set_intersection2 @ A @ B )
!= sk7 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[6013]) ).
thf(6068,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ B )
!= sk5 )
| ( ( set_intersection2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[6050]) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( set_difference @ B @ ( set_intersection2 @ C @ D ) ) )
| ( ( set_union2 @ A @ A )
!= ( set_union2 @ ( set_difference @ B @ C ) @ ( set_difference @ B @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,106]) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ B ) )
= ( set_difference @ A @ B ) ),
inference(pattern_uni,[status(thm)],[884:[bind(A,$thf( set_difference @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F ))]]) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( set_difference @ A @ ( set_intersection2 @ B @ B ) )
= ( set_difference @ A @ B ) ),
inference(simp,[status(thm)],[885]) ).
thf(2324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
!= sk7 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33,820]) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ B ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[2324:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ A @ B ) )
!= sk7 )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[33,2354]) ).
thf(3593,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
!= sk7 ),
inference(pattern_uni,[status(thm)],[3592:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( B
!= ( cartesian_product2 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,201]) ).
thf(300,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
| ~ ( subset @ ( cartesian_product2 @ sk3 @ sk4 ) @ A )
| ( ( cartesian_product2 @ ( set_difference @ sk1 @ sk3 ) @ sk2 )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( A )),bind(B,$thf( cartesian_product2 @ sk3 @ sk4 ))]]) ).
thf(70545,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
| ~ ( subset @ ( cartesian_product2 @ sk3 @ sk4 ) @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk2 ) ) )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[300,153,154]) ).
thf(37176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_difference @ E @ D ) @ ( set_difference @ E @ C ) )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4092,194]) ).
thf(37177,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ ( set_union2 @ B @ C ) ) @ ( set_difference @ A @ C ) ),
inference(pattern_uni,[status(thm)],[37176:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( set_union2 @ F @ G ))]]) ).
thf(37286,plain,
! [C: $i,B: $i,A: $i] : ( subset @ ( set_difference @ A @ ( set_union2 @ B @ C ) ) @ ( set_difference @ A @ C ) ),
inference(simp,[status(thm)],[37177]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A @ B @ C )
| ( in @ ( sk17 @ C @ B @ A ) @ B )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ( in @ ( sk17 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ( in @ ( sk17 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[138]) ).
thf(6583,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[191,4048]) ).
thf(6584,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ B ),
inference(pattern_uni,[status(thm)],[6583:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(15138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6392]) ).
thf(15139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ B @ A ) @ D ) ) @ A ),
inference(pattern_uni,[status(thm)],[15138:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(68499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ C @ ( set_intersection2 @ B @ A ) )
= ( cartesian_product2 @ ( set_intersection2 @ C @ C ) @ D ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,28948]) ).
thf(68500,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ B @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[68499:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(69689,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ B @ ( set_intersection2 @ A @ A ) )
= ( cartesian_product2 @ ( set_intersection2 @ B @ B ) @ A ) ),
inference(simp,[status(thm)],[68500]) ).
thf(4082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( ( subset @ A @ ( set_union2 @ A @ B ) )
!= ( subset @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3690,662]) ).
thf(4111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ C )
!= sk7 )
| ( A != sk5 )
| ( ( set_union2 @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[4082]) ).
thf(4125,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk5 @ B )
!= sk7 )
| ( ( set_union2 @ sk5 @ A )
!= sk7 ) ),
inference(simp,[status(thm)],[4111]) ).
thf(100050,plain,
! [B: $i,A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ B @ A ) )
!= ( cartesian_product2 @ sk3 @ sk4 ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[71,99912]) ).
thf(100051,plain,
( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk2 @ sk4 ) )
!= ( cartesian_product2 @ sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[100050:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ A )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(406,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ A )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(97948,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ A )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[406,153]) ).
thf(21894,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
| ( ( cartesian_product2 @ ( set_difference @ A @ B ) @ C )
!= ( cartesian_product2 @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[154,12420]) ).
thf(21895,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[21894:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( set_difference @ F @ G ))]]) ).
thf(21917,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ sk7 @ ( set_difference @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ C @ A ) ) ),
inference(simp,[status(thm)],[21895]) ).
thf(4174,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,652]) ).
thf(4179,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( A != sk7 )
| ( ( set_union2 @ B @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[4174]) ).
thf(4193,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ sk7 )
| ( ( set_union2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[4179]) ).
thf(18390,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6650]) ).
thf(18391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ D @ ( set_union2 @ A @ B ) ) ) @ B ),
inference(pattern_uni,[status(thm)],[18390:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B
!= ( cartesian_product2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[43,228]) ).
thf(392,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk1 @ sk2 ) )
| ~ ( subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( cartesian_product2 @ sk1 @ ( set_difference @ sk2 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( cartesian_product2 @ sk1 @ sk2 ))]]) ).
thf(88984,plain,
! [A: $i] :
( ~ ( subset @ A @ ( cartesian_product2 @ sk1 @ sk2 ) )
| ~ ( subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ A )
| ( ( set_difference @ A @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( set_difference @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk1 @ sk4 ) ) )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[392,153]) ).
thf(15144,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6392]) ).
thf(15145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ ( set_union2 @ A @ B ) @ D ) ) @ B ),
inference(pattern_uni,[status(thm)],[15144:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(4015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( in @ E @ ( set_union2 @ C @ D ) )
| ( ( in @ ( sk6 @ B @ A ) @ A )
!= ( in @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[53,99]) ).
thf(4016,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk6 @ B @ C ) @ ( set_union2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[4015:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk6 @ F @ G ))]]) ).
thf(4066,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( in @ ( sk6 @ B @ C ) @ ( set_union2 @ A @ C ) ) ),
inference(simp,[status(thm)],[4016]) ).
thf(18605,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) @ C ) @ F )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,6743]) ).
thf(18606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ D @ ( set_union2 @ B @ A ) ) @ C ) @ B ),
inference(pattern_uni,[status(thm)],[18605:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(54899,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ D ) @ E )
| ( ( set_union2 @ B @ A )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,19851]) ).
thf(54900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ ( set_union2 @ ( set_union2 @ A @ B ) @ C ) @ D ) @ B ),
inference(pattern_uni,[status(thm)],[54899:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ),
inference(cnf,[status(esa)],[108]) ).
thf(6424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ),
inference(rewrite,[status(thm)],[111,66]) ).
thf(28600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ ( set_intersection2 @ B @ A ) @ C )
= ( cartesian_product2 @ D @ C ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,27172]) ).
thf(28601,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ B )
= ( cartesian_product2 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[28600:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(28746,plain,
! [B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ A ) @ B )
= ( cartesian_product2 @ A @ B ) ),
inference(simp,[status(thm)],[28601]) ).
thf(6350,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)],[191,1576]) ).
thf(6351,plain,
! [C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ C @ ( set_union2 @ B @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[6350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(22248,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 )
| ( B
!= ( set_difference @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[43,21781]) ).
thf(22249,plain,
! [A: $i] :
( ~ ( subset @ A @ ( set_difference @ sk1 @ sk3 ) )
| ~ ( subset @ ( set_difference @ sk1 @ sk3 ) @ A )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[22248:[bind(A,$thf( A )),bind(B,$thf( set_difference @ sk1 @ sk3 ))]]) ).
thf(22291,plain,
( ~ ( subset @ sk1 @ ( set_difference @ sk1 @ sk3 ) )
| ~ ( subset @ ( set_difference @ sk1 @ sk3 ) @ sk1 )
| ( sk3 != sk1 )
| ( ( set_difference @ sk2 @ sk4 )
!= sk2 ) ),
inference(simp,[status(thm)],[22249]) ).
thf(30881,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ B @ A )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( A != sk2 )
| ( ( set_difference @ A @ B )
!= ( set_difference @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28300,22288]) ).
thf(30882,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(pattern_uni,[status(thm)],[30881:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(30963,plain,
( ( sk18 @ sk2 @ sk4 @ sk2 )
| ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk3 @ sk1 )
| ( ( set_difference @ sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[30882]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A @ B @ C )
| ~ ( in @ ( sk15 @ C @ B @ A ) @ C )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ~ ( in @ ( sk15 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
| ( sk13 @ A @ B @ C )
| ~ ( in @ ( sk15 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[130]) ).
thf(45508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) ) @ E )
| ( ( set_union2 @ A @ B )
!= ( set_union2 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[191,18527]) ).
thf(45509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( in @ ( set_union2 @ D @ ( set_union2 @ ( set_union2 @ B @ A ) @ C ) ) @ A ),
inference(pattern_uni,[status(thm)],[45508:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ E @ B )
| ( ( sk14 @ C @ B @ A )
!= ( ordered_pair @ D @ E ) )
| ~ ( sk13 @ A @ B @ C )
| ( C
= ( cartesian_product2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk14 @ C @ B @ A )
!= ( ordered_pair @ D @ E ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ B )
| ~ ( sk13 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk14 @ C @ B @ A )
!= ( ordered_pair @ D @ E ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ B )
| ~ ( sk13 @ A @ B @ C ) ),
inference(simp,[status(thm)],[140]) ).
thf(14310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk14 @ C @ B @ A )
!= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ B )
| ~ ( sk13 @ A @ B @ C ) ),
inference(rewrite,[status(thm)],[141,66]) ).
thf(6030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( ( subset @ A @ ( set_union2 @ B @ A ) )
!= ( subset @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4092,665]) ).
thf(6055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ C )
!= sk5 )
| ( A != sk7 )
| ( ( set_union2 @ B @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[6030]) ).
thf(6072,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ sk7 @ B )
!= sk5 )
| ( ( set_union2 @ A @ sk7 )
!= sk5 ) ),
inference(simp,[status(thm)],[6055]) ).
thf(125740,plain,
$false,
inference(e,[status(thm)],[66201,101,1179,666,53060,69,10166,6355,115,99443,100234,45515,38062,34296,3044,33880,340,153,21781,26833,1576,15776,43160,15870,4198,83043,39902,96638,174,99912,1529,37,34292,36888,3688,15922,184,87458,838,4275,18385,19851,60259,196,157,52,36591,19693,3046,3689,189,93,16114,57,20259,78,57698,4988,42833,30962,30994,37309,106,4134,147,33881,95780,89,116,47964,1521,30987,81355,26839,6700,46346,91771,38061,22282,72950,6588,60,380,6079,160,820,28948,192,6696,33,1570,28,55585,4128,4192,50375,1555,97,76360,6392,32647,6292,665,16601,156,18718,4048,94144,188,36597,53,100679,22288,77,1182,6239,15232,779,39908,42839,28943,4195,30988,6756,6070,6279,662,30993,6637,15976,824,19699,34,148,1548,45,6243,64,180,41060,14946,54894,975,176,191,36890,59,50381,21802,159,71,31131,54,4127,27172,113,219,14595,100263,16600,36886,64092,1574,18551,811,51214,20112,103,213,91,18612,66,32641,4990,4993,155,38069,28300,15782,868,780,223,135,14535,162,663,6843,194,14940,145,63,2397,95,40850,34294,48,6069,37062,67,4092,4190,182,7243,32546,8509,4132,14589,15085,2354,31,6650,15982,154,4991,72,78956,143,43,27375,99,38063,1553,6068,976,2325,14673,6743,3593,27347,104,70545,37286,15067,652,23141,186,55,139,6584,75,58,15139,549,69689,4125,100051,36,790,3690,97948,1546,21917,6411,107,4051,18527,4193,18391,88984,12022,12420,15145,4066,18606,54900,163,68,62,178,6424,28746,6351,22291,30963,131,21598,45509,14310,215,6072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET973+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n024.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 13:18:09 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.01 % [INFO] Parsing done (136ms).
% 1.36/1.02 % [INFO] Running in sequential loop mode.
% 1.85/1.24 % [INFO] eprover registered as external prover.
% 1.85/1.24 % [INFO] cvc4 registered as external prover.
% 1.85/1.24 % [INFO] Scanning for conjecture ...
% 1.85/1.30 % [INFO] Found a conjecture and 25 axioms. Running axiom selection ...
% 2.07/1.35 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.07/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/1.39 % [INFO] Type checking passed.
% 2.32/1.39 % [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 ...
% 172.35/37.27 % External prover 'e' found a proof!
% 172.35/37.27 % [INFO] Killing All external provers ...
% 172.35/37.27 % Time passed: 36736ms (effective reasoning time: 36246ms)
% 172.35/37.27 % 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)>
% 172.35/37.27 % Axioms used in derivation (25): idempotence_k3_xboole_0, commutativity_k3_xboole_0, fc2_xboole_0, commutativity_k2_xboole_0, t123_zfmisc_1, t54_xboole_1, t125_zfmisc_1, l55_zfmisc_1, d4_xboole_0, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, t17_xboole_1, fc1_zfmisc_1, t34_xboole_1, d5_tarski, fc3_xboole_0, d2_xboole_0, d2_zfmisc_1, commutativity_k2_tarski, d3_tarski, t119_zfmisc_1, reflexivity_r1_tarski, idempotence_k2_xboole_0, d10_xboole_0
% 172.35/37.27 % No. of inferences in proof: 735
% 172.35/37.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36736 ms resp. 36246 ms w/o parsing
% 173.10/37.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 173.10/37.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------