TSTP Solution File: SEU182+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:57:26 EDT 2023
% Result : Theorem 123.63s 20.92s
% Output : Refutation 124.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 49
% Syntax : Number of formulae : 228 ( 95 unt; 21 typ; 0 def)
% Number of atoms : 459 ( 112 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 1278 ( 184 ~; 97 |; 40 &; 898 @)
% ( 6 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 331 ( 0 ^; 296 !; 35 ?; 331 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(ordered_pair_type,type,
ordered_pair: $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 ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(51,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
~ ( empty @ sk4 ),
inference(cnf,[status(esa)],[52]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(41,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[58]) ).
thf(28,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(144,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(145,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[144]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(60,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(61,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk5 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(87,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)],[23]) ).
thf(88,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)],[87]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk5 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,90]) ).
thf(1819,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk5 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1818:[bind(A,$thf( D )),bind(B,$thf( sk5 @ D )),bind(C,$thf( D ))]]) ).
thf(1840,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk5 @ A ) @ A ) ),
inference(simp,[status(thm)],[1819]) ).
thf(11,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(57,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(37,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
~ ( subset @ ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) @ ( relation_dom @ sk1 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(346,plain,
! [A: $i] :
( ( subset @ A @ A )
!= ( subset @ ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) @ ( relation_dom @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,31]) ).
thf(347,plain,
! [A: $i] :
( ( A
!= ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) )
| ( A
!= ( relation_dom @ sk1 ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(348,plain,
( ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) )
!= ( relation_dom @ sk1 ) ),
inference(simp,[status(thm)],[347]) ).
thf(359,plain,
( ( relation_composition @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[348]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( A != sk1 )
| ( B
!= ( relation_composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[40,359]) ).
thf(388,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( relation_composition @ sk1 @ sk2 ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( relation_composition @ sk1 @ sk2 ))]]) ).
thf(395,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( relation_composition @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(497,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ ( relation_composition @ sk1 @ sk2 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[57,395]) ).
thf(518,plain,
( ~ ( empty @ sk1 )
| ( ( relation_composition @ sk1 @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[497]) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(79,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(80,plain,
! [A: $i] : ( empty @ ( sk6 @ A ) ),
inference(cnf,[status(esa)],[79]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(76,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,plain,
~ ? [A: $i,B: $i] : ( empty @ ( unordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[77]) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( sk6 @ A ) )
!= ( empty @ ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[80,78]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A )
!= ( unordered_pair @ B @ C ) ),
inference(simp,[status(thm)],[416]) ).
thf(14,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(63,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(64,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk6 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[80,65]) ).
thf(1116,plain,
! [A: $i] :
( ( sk6 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C ))]]) ).
thf(1394,plain,
! [A: $i] :
( ( sk6 @ A )
= empty_set ),
inference(simp,[status(thm)],[1116]) ).
thf(1686,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(rewrite,[status(thm)],[428,1394]) ).
thf(10,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(54,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(82,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,plain,
! [A: $i] : ( element @ ( sk7 @ A ) @ A ),
inference(cnf,[status(esa)],[82]) ).
thf(793,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( sk7 @ A ) @ A )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[83,59]) ).
thf(794,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(797,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[794]) ).
thf(1353,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ~ ( empty @ ( relation_composition @ empty_set @ sk2 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65,395]) ).
thf(1354,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk1 )
| ~ ( empty @ ( relation_composition @ empty_set @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1353:[bind(A,$thf( sk1 ))]]) ).
thf(1386,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ ( relation_composition @ empty_set @ sk2 ) ) ),
inference(simp,[status(thm)],[1354]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(46,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[71]) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[72]) ).
thf(1777,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[1776:[bind(A,$thf( B ))]]) ).
thf(1778,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[1777]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(95,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)],[25]) ).
thf(96,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)],[95]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[96]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[97]) ).
thf(47,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[47]) ).
thf(536,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,48]) ).
thf(537,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( in @ ( sk9 @ B @ A ) @ A )
!= ( in @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[100,537]) ).
thf(734,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( sk9 @ D @ empty_set ))]]) ).
thf(756,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(simp,[status(thm)],[734]) ).
thf(24,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(92,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(93,plain,
relation @ sk8,
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
empty @ sk8,
inference(cnf,[status(esa)],[92]) ).
thf(1121,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk8 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[94,65]) ).
thf(1122,plain,
sk8 = empty_set,
inference(pattern_uni,[status(thm)],[1121:[bind(A,$thf( sk8 ))]]) ).
thf(1450,plain,
relation @ empty_set,
inference(rewrite,[status(thm)],[93,1122]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ ( powerset @ C ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[145,91]) ).
thf(2118,plain,
! [A: $i] : ( element @ A @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[2117:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2141,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ A @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2118,59]) ).
thf(2142,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[2141:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( powerset @ D ))]]) ).
thf(2158,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[2142]) ).
thf(18,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(73,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(74,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[73]) ).
thf(75,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[74]) ).
thf(2232,plain,
! [A: $i] :
( $false
| ( in @ A @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[2158,75]) ).
thf(2233,plain,
! [A: $i] : ( in @ A @ ( powerset @ A ) ),
inference(simp,[status(thm)],[2232]) ).
thf(2246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2233,72]) ).
thf(2247,plain,
! [A: $i] :
~ ( in @ ( powerset @ A ) @ A ),
inference(pattern_uni,[status(thm)],[2246:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( powerset @ D ))]]) ).
thf(2259,plain,
! [A: $i] :
~ ( in @ ( powerset @ A ) @ A ),
inference(simp,[status(thm)],[2247]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(84,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,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(102,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)],[26]) ).
thf(16,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(68,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)],[16]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( empty @ ( unordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,78]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[418]) ).
thf(162,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,75]) ).
thf(165,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[162]) ).
thf(33,plain,
relation @ sk1,
inference(cnf,[status(esa)],[30]) ).
thf(909,plain,
! [A: $i] :
( ( subset @ empty_set @ A )
!= ( subset @ ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) @ ( relation_dom @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[756,31]) ).
thf(914,plain,
! [A: $i] :
( ( ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) )
!= empty_set )
| ( A
!= ( relation_dom @ sk1 ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(916,plain,
( ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) )
!= empty_set ),
inference(simp,[status(thm)],[914]) ).
thf(42,plain,
empty @ sk3,
inference(cnf,[status(esa)],[41]) ).
thf(1105,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk3 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,65]) ).
thf(1106,plain,
sk3 = empty_set,
inference(pattern_uni,[status(thm)],[1105:[bind(A,$thf( sk3 ))]]) ).
thf(85,plain,
~ ? [A: $i,B: $i] : ( empty @ ( ordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
! [B: $i,A: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[85]) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( sk6 @ A ) )
!= ( empty @ ( ordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[80,86]) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A )
!= ( ordered_pair @ B @ C ) ),
inference(simp,[status(thm)],[434]) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[443,1394,70]) ).
thf(1285,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_composition @ sk1 @ empty_set )
!= sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[65,359]) ).
thf(1286,plain,
( ~ ( empty @ sk2 )
| ( ( relation_composition @ sk1 @ empty_set )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1285:[bind(A,$thf( sk2 ))]]) ).
thf(6,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(43,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[44]) ).
thf(32,plain,
relation @ sk2,
inference(cnf,[status(esa)],[30]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(436,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,86]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[436]) ).
thf(1675,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[441,70]) ).
thf(156,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,56]) ).
thf(159,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[156]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[36,1700]) ).
thf(1722,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1721:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( (@) )),bind(D,$thf( A ))]]) ).
thf(15,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(66,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)],[15]) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk7 @ A ) @ A )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,90]) ).
thf(1835,plain,
! [A: $i] : ( subset @ ( sk7 @ ( powerset @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[1834:[bind(A,$thf( powerset @ E )),bind(B,$thf( sk7 @ ( powerset @ E ) )),bind(C,$thf( E ))]]) ).
thf(1841,plain,
! [A: $i] : ( subset @ ( sk7 @ ( powerset @ A ) ) @ A ),
inference(simp,[status(thm)],[1835]) ).
thf(1725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
!= empty_set )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[36,1700]) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1725:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( (@) ))]]) ).
thf(673,plain,
( ( ( relation_composition @ sk1 @ sk2 )
!= empty_set )
| ( ( empty @ sk3 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,518]) ).
thf(694,plain,
( ( ( relation_composition @ sk1 @ sk2 )
!= empty_set )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[673]) ).
thf(1605,plain,
( ( ( relation_composition @ sk1 @ sk2 )
!= empty_set )
| ( sk1 != empty_set ) ),
inference(rewrite,[status(thm)],[694,1106]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[66]) ).
thf(81,plain,
! [A: $i] : ( element @ ( sk6 @ A ) @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1517,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[81,1394]) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ empty_set @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1517,59]) ).
thf(1562,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[1561:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( powerset @ D ))]]) ).
thf(1585,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1636,plain,
! [A: $i] :
( $false
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[1585,75]) ).
thf(1637,plain,
! [A: $i] : ( in @ empty_set @ ( powerset @ A ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1283,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_composition @ empty_set @ sk2 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65,359]) ).
thf(1284,plain,
( ~ ( empty @ sk1 )
| ( ( relation_composition @ empty_set @ sk2 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1283:[bind(A,$thf( sk1 ))]]) ).
thf(2234,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[2233,1778]) ).
thf(2255,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[2234]) ).
thf(2266,plain,
! [A: $i] :
( ( powerset @ A )
!= A ),
inference(simp,[status(thm)],[2255]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[96]) ).
thf(496,plain,
( ~ ( empty @ ( relation_composition @ sk1 @ sk2 ) )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[57,395]) ).
thf(524,plain,
( ~ ( empty @ ( relation_composition @ sk1 @ sk2 ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[496]) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[36,429]) ).
thf(652,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ B @ A )
!= empty_set ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(150,plain,
( ( empty @ sk4 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,53]) ).
thf(151,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[150]) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( element @ B @ C )
| ( ( in @ ( sk7 @ A ) @ A )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[797,50]) ).
thf(1749,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk7 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1748:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(1757,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk7 @ A ) @ A ) ),
inference(simp,[status(thm)],[1749]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1848,plain,
! [A: $i] :
( ( subset @ ( sk7 @ ( powerset @ A ) ) @ A )
!= ( subset @ ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) @ ( relation_dom @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1841,31]) ).
thf(1857,plain,
! [A: $i] :
( ( ( sk7 @ ( powerset @ A ) )
!= ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) )
| ( A
!= ( relation_dom @ sk1 ) ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1859,plain,
( ( sk7 @ ( powerset @ ( relation_dom @ sk1 ) ) )
!= ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[1857]) ).
thf(62,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(1135,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( ( relation_composition @ empty_set @ sk2 )
!= empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65,518]) ).
thf(1136,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk1 )
| ( ( relation_composition @ empty_set @ sk2 )
!= empty_set ) ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( sk1 ))]]) ).
thf(1399,plain,
( ~ ( empty @ sk1 )
| ( ( relation_composition @ empty_set @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[1136]) ).
thf(27,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(122,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_composition @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_composition @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1203,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A
!= ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,916]) ).
thf(1204,plain,
~ ( empty @ ( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( relation_dom @ ( relation_composition @ sk1 @ sk2 ) ))]]) ).
thf(53898,plain,
$false,
inference(e,[status(thm)],[53,41,59,145,1840,518,1686,56,797,1386,37,46,57,78,1778,756,1450,2259,348,84,61,1394,60,2118,102,70,429,165,33,92,916,65,1106,537,1700,73,1286,45,32,34,71,54,144,49,1675,159,76,1722,1122,91,66,1841,1726,48,63,95,1605,50,67,1637,359,31,1284,72,43,2266,99,87,524,1517,40,652,75,58,82,151,36,30,51,1757,146,2233,1859,79,395,68,62,1399,90,122,83,1204,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 12:51:19 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (129ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.78/1.20 % [INFO] eprover registered as external prover.
% 1.78/1.20 % [INFO] cvc4 registered as external prover.
% 1.78/1.20 % [INFO] Scanning for conjecture ...
% 1.97/1.26 % [INFO] Found a conjecture and 34 axioms. Running axiom selection ...
% 2.05/1.31 % [INFO] Axiom selection finished. Selected 27 axioms (removed 7 axioms).
% 2.26/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.35 % [INFO] Type checking passed.
% 2.38/1.36 % [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 ...
% 123.63/20.91 % External prover 'e' found a proof!
% 123.63/20.91 % [INFO] Killing All external provers ...
% 123.63/20.91 % Time passed: 20389ms (effective reasoning time: 19924ms)
% 123.63/20.91 % 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)>
% 123.63/20.92 % Axioms used in derivation (27): fc1_zfmisc_1, t4_subset, rc1_subset_1, d8_relat_1, t2_subset, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, t1_subset, t6_boole, rc2_subset_1, fc3_subset_1, t5_subset, d4_relat_1, fc2_subset_1, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, commutativity_k2_tarski, d3_tarski, rc1_relat_1, dt_k5_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0
% 123.63/20.92 % No. of inferences in proof: 207
% 123.63/20.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20389 ms resp. 19924 ms w/o parsing
% 124.07/21.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 124.07/21.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------