TSTP Solution File: SEU430+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:59:04 EDT 2023
% Result : Theorem 7.48s 2.63s
% Output : Refutation 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 45
% Syntax : Number of formulae : 134 ( 37 unt; 20 typ; 0 def)
% Number of atoms : 262 ( 61 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 576 ( 95 ~; 45 |; 42 &; 349 @)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 142 ( 0 ^; 120 !; 22 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v3_relat_1_type,type,
v3_relat_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(44,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,plain,
~ ? [A: $i] :
( ( v1_xboole_0 @ A )
& ? [B: $i] :
( ( A != B )
& ( v1_xboole_0 @ B ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A = B )
| ~ ( v1_xboole_0 @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ B ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) )
=> ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
( ( sk4 != k1_xboole_0 )
| ~ sk3 ),
inference(cnf,[status(esa)],[27]) ).
thf(36,plain,
( ( sk4 != k1_xboole_0 )
| ~ sk3 ),
inference(lifteq,[status(thm)],[30]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ B )
| ( B != k1_xboole_0 )
| ~ sk3
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[47,36]) ).
thf(385,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk4 )
| ~ ( v1_xboole_0 @ A )
| ( A != k1_xboole_0 )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( sk4 ))]]) ).
thf(395,plain,
( ~ ( v1_xboole_0 @ sk4 )
| ~ ( v1_xboole_0 @ k1_xboole_0 )
| ~ sk3 ),
inference(simp,[status(thm)],[385]) ).
thf(16,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(73,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[73]) ).
thf(627,plain,
( ~ ( v1_xboole_0 @ sk4 )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[395,76]) ).
thf(628,plain,
( ~ ( v1_xboole_0 @ sk4 )
| ~ sk3 ),
inference(simp,[status(thm)],[627]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,plain,
v3_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[73]) ).
thf(4,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(41,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
( sk3
| ( ( k5_setfam_1 @ sk1 @ sk2 )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[27]) ).
thf(34,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
!= k1_xboole_0 )
| sk3 ),
inference(lifteq,[status(thm)],[29]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(43,plain,
v1_xboole_0 @ sk6,
inference(cnf,[status(esa)],[41]) ).
thf(18,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(79,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(55,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(56,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk8 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(23,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(117,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(118,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( r2_hidden @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[117]) ).
thf(119,plain,
! [A: $i] :
( ( r2_hidden @ ( sk15 @ A ) @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[118]) ).
thf(121,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( r2_hidden @ ( sk15 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(122,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( r2_hidden @ ( sk15 @ A ) @ A ) ),
inference(simp,[status(thm)],[121]) ).
thf(8,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(52,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,plain,
~ ( v1_xboole_0 @ sk7 ),
inference(cnf,[status(esa)],[52]) ).
thf(136,plain,
( ( v1_xboole_0 @ sk7 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[76,54]) ).
thf(137,plain,
sk7 != k1_xboole_0,
inference(simp,[status(thm)],[136]) ).
thf(549,plain,
! [A: $i] :
( ( r2_hidden @ ( sk15 @ A ) @ A )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[122,137]) ).
thf(550,plain,
r2_hidden @ ( sk15 @ sk7 ) @ sk7,
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( sk7 ))]]) ).
thf(11,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(60,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(61,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[60]) ).
thf(62,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[61]) ).
thf(140,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[76,62]) ).
thf(142,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[140]) ).
thf(42,plain,
v1_relat_1 @ sk6,
inference(cnf,[status(esa)],[41]) ).
thf(28,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
= k1_xboole_0 )
| ~ sk3 ),
inference(cnf,[status(esa)],[27]) ).
thf(37,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
= k1_xboole_0 )
| ~ sk3 ),
inference(lifteq,[status(thm)],[28]) ).
thf(24,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(125,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,plain,
! [A: $i] :
( sk3
| ~ ( r2_hidden @ A @ sk2 )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[27]) ).
thf(35,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| sk3
| ~ ( r2_hidden @ A @ sk2 ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(188,plain,
! [A: $i] :
( sk3
| ~ ( r2_hidden @ A @ sk2 )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[35,137]) ).
thf(189,plain,
( sk3
| ~ ( r2_hidden @ sk7 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( sk7 ))]]) ).
thf(57,plain,
! [A: $i] : ( m1_subset_1 @ ( sk8 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(77,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,plain,
! [A: $i] : ( m1_subset_1 @ ( sk9 @ A ) @ A ),
inference(cnf,[status(esa)],[77]) ).
thf(3,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(38,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,plain,
( ( r2_hidden @ sk4 @ sk2 )
| ~ sk3 ),
inference(cnf,[status(esa)],[27]) ).
thf(53,plain,
v1_relat_1 @ sk7,
inference(cnf,[status(esa)],[52]) ).
thf(139,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[43,62]) ).
thf(141,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk6 ),
inference(simp,[status(thm)],[139]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[118]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(124,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[123]) ).
thf(208,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk8 @ A ) )
!= ( v1_xboole_0 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[56,54]) ).
thf(212,plain,
! [A: $i] :
( ( sk8 @ A )
!= sk7 ),
inference(simp,[status(thm)],[208]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(128,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(48,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ A ) ),
inference(cnf,[status(esa)],[48]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(39,plain,
v3_relat_1 @ sk5,
inference(cnf,[status(esa)],[38]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk8 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,62]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( sk8 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[209]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(134,plain,
( ( v1_xboole_0 @ sk7 )
!= ( v1_xboole_0 @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[43,54]) ).
thf(135,plain,
sk7 != sk6,
inference(simp,[status(thm)],[134]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(629,plain,
( ~ sk3
| ( ( v1_xboole_0 @ sk6 )
!= ( v1_xboole_0 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,628]) ).
thf(640,plain,
( ~ sk3
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[629]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(50,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
m1_subset_1 @ sk2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ sk1 ) ),
inference(cnf,[status(esa)],[27]) ).
thf(40,plain,
v1_relat_1 @ sk5,
inference(cnf,[status(esa)],[38]) ).
thf(75,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[73]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(51,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(cnf,[status(esa)],[50]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(131,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(215,plain,
! [A: $i] :
( ~ sk3
| ( ( r2_hidden @ sk4 @ sk2 )
!= ( r2_hidden @ A @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[33,124]) ).
thf(220,plain,
! [A: $i] :
( ~ sk3
| ( sk4 != A )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[215]) ).
thf(222,plain,
( ~ sk3
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[220]) ).
thf(898,plain,
$false,
inference(e,[status(thm)],[628,84,74,41,34,112,43,79,56,550,142,42,37,52,125,189,57,78,60,117,38,70,137,33,53,141,124,77,212,73,128,44,27,54,49,86,76,39,213,66,135,35,48,63,640,50,31,40,55,75,58,82,36,51,68,62,131,47,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 13:37:51 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.85/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (142ms).
% 1.22/0.99 % [INFO] Running in sequential loop mode.
% 1.71/1.21 % [INFO] eprover registered as external prover.
% 1.71/1.21 % [INFO] cvc4 registered as external prover.
% 1.81/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.28 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 1.91/1.32 % [INFO] Axiom selection finished. Selected 24 axioms (removed 4 axioms).
% 2.16/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.36 % [INFO] Type checking passed.
% 2.16/1.36 % [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 ...
% 7.48/2.63 % External prover 'e' found a proof!
% 7.48/2.63 % [INFO] Killing All external provers ...
% 7.48/2.63 % Time passed: 2107ms (effective reasoning time: 1636ms)
% 7.48/2.63 % 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)>
% 7.48/2.63 % Axioms used in derivation (24): cc1_relat_1, d1_xboole_0, t5_subset, redefinition_k5_setfam_1, rc1_subset_1, rc2_relat_1, dt_k5_setfam_1, t8_boole, antisymmetry_r2_hidden, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t4_subset, d4_tarski, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, rc1_relat_1, reflexivity_r1_tarski, t2_subset, fc12_relat_1
% 7.48/2.63 % No. of inferences in proof: 114
% 7.48/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2107 ms resp. 1636 ms w/o parsing
% 7.48/2.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.48/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------