TSTP Solution File: SET772+4 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET772+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:54:17 EDT 2023
% Result : Theorem 9.34s 2.80s
% Output : Refutation 9.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 40
% Syntax : Number of formulae : 152 ( 42 unt; 23 typ; 0 def)
% Number of atoms : 484 ( 94 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 1583 ( 149 ~; 94 |; 104 &;1123 @)
% ( 17 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 423 ( 0 ^; 402 !; 21 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(partition_type,type,
partition: $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i > $o ).
thf(equivalence_type,type,
equivalence: $i > $i > $o ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(product_type,type,
product: $i > $i ).
thf(pre_order_type,type,
pre_order: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(equivalence_class_type,type,
equivalence_class: $i > $i > $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 > $i > $i ).
thf(sk19_type,type,
sk19: $i > $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( pre_order @ A @ B )
<=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pre_order) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( pre_order @ A @ B )
=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) )
=> ( pre_order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( singleton @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( member @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(124,plain,
( ! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( member @ A @ ( singleton @ B ) ) ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( singleton @ B ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( singleton @ B ) ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(128,plain,
! [A: $i] : ( member @ A @ ( singleton @ A ) ),
inference(simp,[status(thm)],[127]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( partition @ A @ B )
=> ( ! [D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( apply @ C @ D @ E )
<=> ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) ) ) )
=> ( equivalence @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII08) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( partition @ A @ B )
=> ( ! [D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( apply @ C @ D @ E )
<=> ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) ) ) )
=> ( equivalence @ C @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( partition @ A @ B )
=> ( ! [D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ C @ D @ E )
=> ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) ) )
& ( ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) )
=> ( apply @ C @ D @ E ) ) ) )
=> ( equivalence @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ! [A: $i,B: $i] :
( ( partition @ A @ B )
=> ! [C: $i] :
( ! [D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ C @ D @ E )
=> ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) ) )
& ( ? [F: $i] :
( ( member @ F @ A )
& ( member @ D @ F )
& ( member @ E @ F ) )
=> ( apply @ C @ D @ E ) ) ) )
=> ( equivalence @ C @ B ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ B @ sk2 )
| ~ ( member @ C @ sk1 )
| ~ ( member @ A @ C )
| ~ ( member @ B @ C )
| ( apply @ sk3 @ A @ B ) ),
inference(cnf,[status(esa)],[20]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ B @ sk2 )
| ~ ( member @ C @ sk1 )
| ~ ( member @ B @ C )
| ( apply @ sk3 @ A @ B )
| ( ( member @ A @ C )
!= ( member @ B @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(294,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ A @ sk2 )
| ~ ( member @ sk2 @ sk1 )
| ~ ( member @ A @ sk2 )
| ( apply @ sk3 @ A @ A ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(311,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ sk2 @ sk1 )
| ( apply @ sk3 @ A @ A ) ),
inference(simp,[status(thm)],[294]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( member @ sk2 @ sk1 )
| ( apply @ sk3 @ B @ B )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[128,311]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( apply @ sk3 @ B @ B )
| ~ ( member @ sk2 @ sk1 )
| ( A != B )
| ( ( singleton @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[432]) ).
thf(448,plain,
! [A: $i] :
( ( apply @ sk3 @ A @ A )
| ~ ( member @ sk2 @ sk1 )
| ( ( singleton @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[440]) ).
thf(14,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(196,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(197,plain,
~ ? [A: $i] : ( member @ A @ empty_set ),
inference(miniscope,[status(thm)],[196]) ).
thf(198,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(cnf,[status(esa)],[197]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[128,198]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( singleton @ A )
!= empty_set ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[228]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
<=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( difference @ C @ B ) )
=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) )
& ( ( ( member @ A @ C )
& ~ ( member @ A @ B ) )
=> ( member @ A @ ( difference @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(200,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ C )
& ~ ( member @ A @ B ) )
=> ( member @ A @ ( difference @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[199]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( difference @ C @ B ) )
| ~ ( member @ A @ B ) ),
inference(cnf,[status(esa)],[200]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ B @ ( difference @ D @ C ) )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[128,203]) ).
thf(232,plain,
! [B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( singleton @ B ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( singleton @ E ))]]) ).
thf(237,plain,
! [B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( singleton @ B ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ C @ ( difference @ B @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,237]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( singleton @ A )
!= ( difference @ B @ ( singleton @ C ) ) ) ),
inference(simp,[status(thm)],[366]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( difference @ A @ ( singleton @ B ) )
!= ( singleton @ B ) ),
inference(simp,[status(thm)],[369]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( A = B )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( A = B )
| ( A = C ) ) )
& ( ( ( A = B )
| ( A = C ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(212,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( A = B )
| ( A = C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( A = C ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[211]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(217,plain,
! [B: $i,A: $i] : ( member @ A @ ( unordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[216]) ).
thf(242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ E @ D ) )
| ( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[217,203]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( unordered_pair @ F @ G ))]]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( member @ A @ ( difference @ C @ B ) )
!= ( member @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[203]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( A != A )
| ( ( difference @ C @ B )
!= B ) ),
inference(simp,[status(thm)],[233]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( difference @ C @ B )
!= B ) ),
inference(simp,[status(thm)],[236]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[217,198]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( unordered_pair @ A @ B )
!= empty_set ) ),
inference(simp,[status(thm)],[240]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ B @ A )
!= empty_set ),
inference(simp,[status(thm)],[244]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(219,plain,
! [B: $i,A: $i] : ( member @ B @ ( unordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[218]) ).
thf(373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[219,246]) ).
thf(376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( unordered_pair @ A @ C )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(24,plain,
~ ( equivalence @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[20]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ B @ sk2 )
| ~ ( apply @ sk3 @ A @ B )
| ( member @ ( sk4 @ B @ A ) @ sk1 ) ),
inference(cnf,[status(esa)],[20]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ B @ sk2 )
| ~ ( apply @ sk3 @ B @ C )
| ( member @ ( sk4 @ C @ B ) @ sk1 )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[128,25]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( sk4 @ C @ B ) @ sk1 )
| ~ ( member @ B @ sk2 )
| ~ ( apply @ sk3 @ B @ C )
| ( A != C )
| ( ( singleton @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ sk1 )
| ~ ( member @ A @ sk2 )
| ~ ( apply @ sk3 @ A @ B )
| ( ( singleton @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[256]) ).
thf(364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[219,237]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( singleton @ D ) ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ A @ C )
!= ( difference @ B @ ( singleton @ C ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ E @ D ) )
| ( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[219,203]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ C @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( unordered_pair @ F @ G ))]]) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ C @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ D @ ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,355]) ).
thf(488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( singleton @ A )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( unordered_pair @ B @ C ) )
!= ( singleton @ C ) ),
inference(simp,[status(thm)],[488]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ B @ C )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ ( difference @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,203]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ B @ C )
| ( A != B )
| ( ( singleton @ A )
!= ( difference @ D @ C ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( ( singleton @ A )
!= ( difference @ C @ B ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[219,198]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( unordered_pair @ A @ B )
!= empty_set ) ),
inference(simp,[status(thm)],[338]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[352]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ D @ ( equivalence_class @ C @ B @ A ) )
<=> ( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
thf(221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ D @ ( equivalence_class @ C @ B @ A ) )
=> ( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) )
& ( ( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( member @ D @ ( equivalence_class @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(112,plain,
( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(miniscope,[status(thm)],[111]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( member @ ( sk19 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[112]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( member @ ( sk19 @ B @ A ) @ A )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[113]) ).
thf(375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ C @ ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,246]) ).
thf(378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( singleton @ A )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( unordered_pair @ B @ C ) )
!= ( singleton @ B ) ),
inference(simp,[status(thm)],[378]) ).
thf(374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[217,246]) ).
thf(377,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( unordered_pair @ C @ A )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( member @ ( sk19 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[112]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( member @ ( sk19 @ B @ A ) @ B )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[114]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( product @ B ) )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( product @ B ) )
=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) )
& ( ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) )
=> ( member @ A @ ( product @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( equivalence @ B @ A )
<=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( equivalence @ B @ A )
=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) )
=> ( equivalence @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum @ B ) )
<=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(105,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( sum @ B ) )
=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) )
& ( ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( sum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
<=> ( ( member @ A @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(205,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( intersection @ B @ C ) )
=> ( ( member @ A @ B )
& ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( intersection @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk19 @ B @ A ) @ A )
!= ( member @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[116,198]) ).
thf(393,plain,
! [A: $i] : ( disjoint @ empty_set @ A ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( sk19 @ D @ empty_set ))]]) ).
thf(412,plain,
! [A: $i] : ( disjoint @ empty_set @ A ),
inference(simp,[status(thm)],[393]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ~ ( member @ B @ sk2 )
| ( apply @ sk3 @ B @ B )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,311]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( apply @ sk3 @ B @ B )
| ~ ( member @ B @ sk2 )
| ( A != sk2 )
| ( ( singleton @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[433]) ).
thf(444,plain,
! [A: $i] :
( ( apply @ sk3 @ A @ A )
| ~ ( member @ A @ sk2 )
| ( ( singleton @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[437]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ B @ sk2 )
| ~ ( apply @ sk3 @ A @ B )
| ( member @ A @ ( sk4 @ B @ A ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(118,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( power_set @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( member @ A @ ( power_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( ( member @ ( sk19 @ B @ A ) @ B )
!= ( member @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[117,198]) ).
thf(508,plain,
! [A: $i] : ( disjoint @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( E )),bind(B,$thf( empty_set )),bind(C,$thf( sk19 @ empty_set @ E ))]]) ).
thf(545,plain,
! [A: $i] : ( disjoint @ A @ empty_set ),
inference(simp,[status(thm)],[508]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( equal_set @ A @ B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( equal_set @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( union @ B @ C ) )
<=> ( ( member @ A @ B )
| ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( union @ B @ C ) )
=> ( ( member @ A @ B )
| ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
| ( member @ A @ C ) )
=> ( member @ A @ ( union @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(482,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ E @ ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[219,355]) ).
thf(486,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != E )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( unordered_pair @ D @ E ) ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( unordered_pair @ A @ D )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ),
inference(simp,[status(thm)],[486]) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[217,237]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( singleton @ D ) ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ C @ A )
!= ( difference @ B @ ( singleton @ C ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( partition @ A @ B )
<=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( partition @ A @ B )
=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) )
=> ( partition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ ( member @ B @ sk2 )
| ~ ( apply @ sk3 @ A @ B )
| ( member @ B @ ( sk4 @ B @ A ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(23,plain,
partition @ sk1 @ sk2,
inference(cnf,[status(esa)],[20]) ).
thf(1150,plain,
$false,
inference(cvc4,[status(thm)],[69,448,229,371,198,130,203,246,19,239,111,217,247,379,24,25,257,372,196,492,211,238,353,221,116,381,380,117,33,21,137,105,205,311,128,237,412,444,22,118,545,27,219,98,490,123,355,199,370,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET772+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:00:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.82/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/0.96 % [INFO] Parsing done (123ms).
% 1.27/0.97 % [INFO] Running in sequential loop mode.
% 1.77/1.17 % [INFO] eprover registered as external prover.
% 1.77/1.17 % [INFO] cvc4 registered as external prover.
% 1.77/1.17 % [INFO] Scanning for conjecture ...
% 1.94/1.23 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.94/1.27 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.94/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.31 % [INFO] Type checking passed.
% 1.94/1.32 % [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 ...
% 9.27/2.80 % External prover 'cvc4' found a proof!
% 9.27/2.80 % [INFO] Killing All external provers ...
% 9.34/2.80 % Time passed: 2285ms (effective reasoning time: 1826ms)
% 9.34/2.80 % 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)>
% 9.34/2.80 % Axioms used in derivation (16): power_set, unordered_pair, pre_order, intersection, empty_set, subset, equal_set, singleton, disjoint, difference, sum, product, equivalence, union, partition, equivalence_class
% 9.34/2.80 % No. of inferences in proof: 129
% 9.34/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2285 ms resp. 1826 ms w/o parsing
% 9.34/2.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.34/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------