TSTP Solution File: SEU265+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:57:55 EDT 2023
% Result : Theorem 23.14s 4.54s
% Output : Refutation 23.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 55
% Syntax : Number of formulae : 142 ( 46 unt; 27 typ; 0 def)
% Number of atoms : 257 ( 62 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 777 ( 84 ~; 39 |; 32 &; 567 @)
% ( 7 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 9 con; 0-3 aty)
% Number of variables : 228 ( 0 ^; 203 !; 25 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(relation_dom_as_subset_type,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(relation_type,type,
relation: $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_rng_type,type,
relation_rng: $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: $o ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(68,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(69,plain,
! [A: $i] : ( element @ ( sk10 @ A ) @ A ),
inference(cnf,[status(esa)],[68]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(41,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[41]) ).
thf(7,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(52,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(47,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,plain,
empty @ sk7,
inference(cnf,[status(esa)],[47]) ).
thf(8,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(53,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(691,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk7 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48,55]) ).
thf(692,plain,
sk7 = empty_set,
inference(pattern_uni,[status(thm)],[691:[bind(A,$thf( sk7 ))]]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(97,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_dom @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_dom @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(80,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)],[18]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
= ( ordered_pair @ A @ B ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
= ( ordered_pair @ C @ D ) )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[58,82]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
= ( ordered_pair @ A @ B ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ A @ B )
= ( unordered_pair @ D @ C ) )
| ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[203,58]) ).
thf(512,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
= ( ordered_pair @ B @ A ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( G )),bind(B,$thf( E )),bind(C,$thf( unordered_pair @ E @ G )),bind(D,$thf( singleton @ G ))]]) ).
thf(531,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
= ( ordered_pair @ B @ A ) ),
inference(simp,[status(thm)],[512]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(43,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(134,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(135,plain,
~ ? [A: $i,B: $i] : ( empty @ ( ordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(136,plain,
! [B: $i,A: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(73,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[74]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52,75]) ).
thf(153,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(44,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
<=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
<=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) )
& ( ( ( relation_dom_as_subset @ B @ A @ C )
= B )
=> ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ( ~ ? [D: $i] :
( ( in @ D @ B )
& ~ ? [E: $i] : ( in @ ( ordered_pair @ D @ E ) @ C ) )
=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) )
& ( ( ( relation_dom_as_subset @ B @ A @ C )
= B )
=> ~ ? [D: $i] :
( ( in @ D @ B )
& ~ ? [E: $i] : ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[30]) ).
thf(37,plain,
( sk4
| ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
= sk2 ) ),
inference(cnf,[status(esa)],[31]) ).
thf(38,plain,
( ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
= sk2 )
| sk4 ),
inference(lifteq,[status(thm)],[37]) ).
thf(35,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( in @ ( ordered_pair @ A @ ( sk5 @ A ) ) @ sk3 )
| ~ sk4 ),
inference(cnf,[status(esa)],[31]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ sk2 )
| ~ sk4
| ~ ( empty @ C )
| ( ( in @ ( ordered_pair @ A @ ( sk5 @ A ) ) @ sk3 )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,75]) ).
thf(155,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( F )),bind(B,$thf( ordered_pair @ F @ ( sk5 @ F ) )),bind(C,$thf( sk3 ))]]) ).
thf(160,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(simp,[status(thm)],[155]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(124,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(76,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(77,plain,
! [B: $i,A: $i] : ( relation_of2_as_subset @ ( sk11 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[76]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,82]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
= ( ordered_pair @ B @ A ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( singleton @ G )),bind(B,$thf( unordered_pair @ G @ F )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
= ( ordered_pair @ B @ A ) ),
inference(simp,[status(thm)],[209]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(34,plain,
relation_of2_as_subset @ sk3 @ sk2 @ sk1,
inference(cnf,[status(esa)],[31]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(49,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
( sk4
| ( in @ sk6 @ sk2 ) ),
inference(cnf,[status(esa)],[31]) ).
thf(158,plain,
! [B: $i,A: $i] :
( sk4
| ~ ( empty @ B )
| ( ( in @ sk6 @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36,75]) ).
thf(159,plain,
( sk4
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(33,plain,
! [A: $i] :
( sk4
| ~ ( in @ ( ordered_pair @ sk6 @ A ) @ sk3 ) ),
inference(cnf,[status(esa)],[31]) ).
thf(39,plain,
! [A: $i] :
( sk4
| ~ ( in @ ( ordered_pair @ sk6 @ A ) @ sk3 ) ),
inference(simp,[status(thm)],[33]) ).
thf(50,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[49]) ).
thf(51,plain,
~ ( empty @ sk8 ),
inference(cnf,[status(esa)],[50]) ).
thf(139,plain,
( ( empty @ sk8 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[52,51]) ).
thf(140,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[139]) ).
thf(12,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(66,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[52,136]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[148]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(67,plain,
! [B: $i,A: $i] : ( relation_of2 @ ( sk9 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[66]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,plain,
( ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
!= sk2 )
| ~ sk4 ),
inference(cnf,[status(esa)],[31]) ).
thf(40,plain,
( ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
!= sk2 )
| ~ sk4 ),
inference(lifteq,[status(thm)],[32]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(119,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(161,plain,
( sk4
| ( ( empty @ sk2 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[52,159]) ).
thf(163,plain,
( sk4
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[161]) ).
thf(167,plain,
( ( sk2 != empty_set )
| ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
!= sk2 )
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[163,40]) ).
thf(168,plain,
( ( sk2 != empty_set )
| ( ( relation_dom_as_subset @ sk2 @ sk1 @ sk3 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[167:[]]) ).
thf(60,plain,
( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[60]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(83,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6452,plain,
$false,
inference(e,[status(thm)],[69,42,52,692,117,97,53,59,531,43,203,136,56,153,46,93,78,38,160,70,124,77,212,129,41,134,73,34,64,49,159,76,39,140,66,80,35,150,95,67,127,40,55,75,82,119,58,36,168,30,51,47,163,68,62,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 13:25:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.98 % [INFO] Parsing done (128ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.56/1.18 % [INFO] eprover registered as external prover.
% 1.56/1.18 % [INFO] cvc4 registered as external prover.
% 1.76/1.19 % [INFO] Scanning for conjecture ...
% 1.93/1.25 % [INFO] Found a conjecture and 37 axioms. Running axiom selection ...
% 1.93/1.30 % [INFO] Axiom selection finished. Selected 27 axioms (removed 10 axioms).
% 1.93/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.33 % [INFO] Type checking passed.
% 2.24/1.33 % [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 ...
% 23.14/4.54 % External prover 'e' found a proof!
% 23.14/4.54 % [INFO] Killing All external provers ...
% 23.14/4.54 % Time passed: 4020ms (effective reasoning time: 3553ms)
% 23.14/4.54 % 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)>
% 23.14/4.54 % Axioms used in derivation (27): redefinition_m2_relset_1, fc1_zfmisc_1, dt_k4_relset_1, dt_m2_relset_1, t6_boole, t5_subset, t2_tarski, t4_subset, t7_boole, existence_m2_relset_1, reflexivity_r1_tarski, t20_relat_1, t2_subset, redefinition_k4_relset_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, t1_subset, d4_relat_1, existence_m1_relset_1, t3_subset, cc1_relset_1, existence_m1_subset_1, commutativity_k2_tarski, t8_boole, rc1_xboole_0
% 23.14/4.54 % No. of inferences in proof: 115
% 23.14/4.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4020 ms resp. 3553 ms w/o parsing
% 23.14/4.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.14/4.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------