TSTP Solution File: SEU439+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU439+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:59:11 EDT 2023
% Result : Theorem 114.02s 20.63s
% Output : Refutation 114.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 89
% Syntax : Number of formulae : 251 ( 100 unt; 39 typ; 0 def)
% Number of atoms : 433 ( 91 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1409 ( 125 ~; 36 |; 60 &;1095 @)
% ( 7 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 10 con; 0-4 aty)
% Number of variables : 386 ( 0 ^; 353 !; 33 ?; 386 :)
% 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(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
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(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k7_relset_2_type,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $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 > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk19_type,type,
sk19: $i > $i ).
thf(32,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(139,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)],[32]) ).
thf(142,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[139]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(105,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(106,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[106]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[142,107]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[252]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(85,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(cnf,[status(esa)],[85]) ).
thf(7,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(67,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,plain,
v1_relat_1 @ sk7,
inference(cnf,[status(esa)],[67]) ).
thf(17,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(100,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(101,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ A ) ),
inference(cnf,[status(esa)],[100]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(132,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(133,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(cnf,[status(esa)],[132]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C != k1_xboole_0 )
=> ( r1_tarski @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C != k1_xboole_0 )
=> ( r1_tarski @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(52,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C != k1_xboole_0 )
=> ( r1_tarski @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
~ ( r1_tarski @ ( k8_relset_2 @ sk1 @ sk2 @ sk3 @ sk4 ) @ ( k9_relat_1 @ sk4 @ sk3 ) ),
inference(cnf,[status(esa)],[52]) ).
thf(247,plain,
! [A: $i] :
( ( r1_tarski @ A @ A )
!= ( r1_tarski @ ( k8_relset_2 @ sk1 @ sk2 @ sk3 @ sk4 ) @ ( k9_relat_1 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[133,53]) ).
thf(248,plain,
! [A: $i] :
( ( A
!= ( k8_relset_2 @ sk1 @ sk2 @ sk3 @ sk4 ) )
| ( A
!= ( k9_relat_1 @ sk4 @ sk3 ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
( ( k8_relset_2 @ sk1 @ sk2 @ sk3 @ sk4 )
!= ( k9_relat_1 @ sk4 @ sk3 ) ),
inference(simp,[status(thm)],[248]) ).
thf(10,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(76,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(78,plain,
~ ( v1_xboole_0 @ sk9 ),
inference(cnf,[status(esa)],[76]) ).
thf(232,plain,
( ( v1_xboole_0 @ sk9 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[142,78]) ).
thf(234,plain,
sk9 != k1_xboole_0,
inference(simp,[status(thm)],[232]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(115,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(199,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)],[45]) ).
thf(200,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)],[199]) ).
thf(201,plain,
! [A: $i] :
( ( r2_hidden @ ( sk19 @ A ) @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[200]) ).
thf(203,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( r2_hidden @ ( sk19 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(204,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( r2_hidden @ ( sk19 @ A ) @ A ) ),
inference(simp,[status(thm)],[203]) ).
thf(537,plain,
! [A: $i] :
( ( r2_hidden @ ( sk19 @ A ) @ A )
| ( A != sk9 ) ),
inference(paramod_ordered,[status(thm)],[204,234]) ).
thf(538,plain,
r2_hidden @ ( sk19 @ sk9 ) @ sk9,
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( sk9 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[65]) ).
thf(740,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ B @ A )
| ( ( r2_hidden @ ( sk19 @ sk9 ) @ sk9 )
!= ( r2_hidden @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[538,66]) ).
thf(741,plain,
~ ( r2_hidden @ sk9 @ ( sk19 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[740:[bind(A,$thf( sk19 @ sk9 )),bind(B,$thf( sk9 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k2_tarski @ B @ A )
!= k1_xboole_0 )
| ( ( k2_tarski @ A @ B )
!= ( k2_tarski @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[60,257]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ B @ A )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(56,plain,
m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ sk1 ),
inference(cnf,[status(esa)],[52]) ).
thf(21,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(110,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)],[21]) ).
thf(112,plain,
! [A: $i] : ( m1_subset_1 @ ( sk12 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[110]) ).
thf(111,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk12 @ A ) ),
inference(cnf,[status(esa)],[110]) ).
thf(36,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(151,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(152,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( v1_xboole_0 @ ( sk12 @ A ) )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[111,153]) ).
thf(301,plain,
! [A: $i] :
( ( sk12 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( C )),bind(B,$thf( sk12 @ C ))]]) ).
thf(437,plain,
! [A: $i] :
( ( sk12 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[301]) ).
thf(472,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(rewrite,[status(thm)],[112,437]) ).
thf(40,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(184,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(185,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[185]) ).
thf(243,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[142,186]) ).
thf(246,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[243]) ).
thf(644,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ ( sk19 @ A ) @ A )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[204,246]) ).
thf(645,plain,
! [A: $i] : ( r2_hidden @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) @ ( k1_zfmisc_1 @ A ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(659,plain,
! [A: $i] : ( r2_hidden @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) @ ( k1_zfmisc_1 @ A ) ),
inference(simp,[status(thm)],[645]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ( ( r2_hidden @ B @ A )
!= ( r2_hidden @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[66]) ).
thf(460,plain,
! [A: $i] :
~ ( r2_hidden @ A @ A ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( B ))]]) ).
thf(461,plain,
! [A: $i] :
~ ( r2_hidden @ A @ A ),
inference(simp,[status(thm)],[460]) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) @ ( k1_zfmisc_1 @ A ) )
!= ( r2_hidden @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[659,461]) ).
thf(825,plain,
! [B: $i,A: $i] :
( ( ( sk19 @ ( k1_zfmisc_1 @ A ) )
!= B )
| ( ( k1_zfmisc_1 @ A )
!= B ) ),
inference(simp,[status(thm)],[814]) ).
thf(838,plain,
! [A: $i] :
( ( sk19 @ ( k1_zfmisc_1 @ A ) )
!= ( k1_zfmisc_1 @ A ) ),
inference(simp,[status(thm)],[825]) ).
thf(54,plain,
sk3 != k1_xboole_0,
inference(cnf,[status(esa)],[52]) ).
thf(57,plain,
sk3 != k1_xboole_0,
inference(lifteq,[status(thm)],[54]) ).
thf(565,plain,
! [A: $i] :
( ( r2_hidden @ ( sk19 @ A ) @ A )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[204,57]) ).
thf(566,plain,
r2_hidden @ ( sk19 @ sk3 ) @ sk3,
inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( sk3 ))]]) ).
thf(701,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ B @ A )
| ( ( r2_hidden @ ( sk19 @ sk3 ) @ sk3 )
!= ( r2_hidden @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[566,66]) ).
thf(702,plain,
~ ( r2_hidden @ sk3 @ ( sk19 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( sk19 @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ C )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(320,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[153,56]) ).
thf(321,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( sk1 ))]]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(121,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(82,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,plain,
~ ? [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(miniscope,[status(thm)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( v1_xboole_0 @ B ) ),
inference(cnf,[status(esa)],[83]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(61,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(50,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(221,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)],[50]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[200]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(206,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[205]) ).
thf(11,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(79,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(80,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(miniscope,[status(thm)],[79]) ).
thf(81,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[80]) ).
thf(231,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[142,81]) ).
thf(233,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[231]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(733,plain,
! [A: $i] :
( ( r2_hidden @ ( sk19 @ sk9 ) @ sk9 )
!= ( r2_hidden @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[538,461]) ).
thf(744,plain,
! [A: $i] :
( ( ( sk19 @ sk9 )
!= A )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[733]) ).
thf(746,plain,
( ( sk19 @ sk9 )
!= sk9 ),
inference(simp,[status(thm)],[744]) ).
thf(8,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(70,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,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(192,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)],[43]) ).
thf(15,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(92,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relset_2) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(96,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(97,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk10 @ B @ A ) ),
inference(cnf,[status(esa)],[96]) ).
thf(328,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[153,57]) ).
thf(329,plain,
~ ( v1_xboole_0 @ sk3 ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( sk3 ))]]) ).
thf(38,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(156,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)],[38]) ).
thf(141,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[139]) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(108,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(109,plain,
! [A: $i] : ( m1_eqrel_1 @ ( sk11 @ A ) @ A ),
inference(cnf,[status(esa)],[108]) ).
thf(575,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ ( sk19 @ A ) @ A )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[204,233]) ).
thf(576,plain,
! [A: $i] : ( r2_hidden @ ( sk19 @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) ),
inference(pattern_uni,[status(thm)],[575:[bind(A,$thf( k1_tarski @ C )),bind(B,$thf( C ))]]) ).
thf(674,plain,
! [A: $i] : ( r2_hidden @ ( sk19 @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[576]) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ ( sk19 @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
!= ( r2_hidden @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[674,461]) ).
thf(875,plain,
! [B: $i,A: $i] :
( ( ( sk19 @ ( k1_tarski @ A ) )
!= B )
| ( ( k1_tarski @ A )
!= B ) ),
inference(simp,[status(thm)],[863]) ).
thf(884,plain,
! [A: $i] :
( ( sk19 @ ( k1_tarski @ A ) )
!= ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[875]) ).
thf(77,plain,
v1_relat_1 @ sk9,
inference(cnf,[status(esa)],[76]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(63,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(64,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk6 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[63]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(149,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(190,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(191,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(cnf,[status(esa)],[190]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(187,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(98,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk10 @ B @ A ) ),
inference(cnf,[status(esa)],[96]) ).
thf(140,plain,
v3_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[139]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(88,plain,
( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(miniscope,[status(thm)],[87]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_relset_1 @ C @ A @ B )
| ( m2_relset_1 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_relset_1 @ C @ A @ B )
| ( m2_relset_1 @ C @ A @ B ) ),
inference(simp,[status(thm)],[89]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ C @ B )
| ( ( r2_hidden @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) @ ( k1_zfmisc_1 @ A ) )
!= ( r2_hidden @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[659,66]) ).
thf(822,plain,
! [A: $i] :
~ ( r2_hidden @ ( k1_zfmisc_1 @ A ) @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[821:[bind(A,$thf( F )),bind(B,$thf( sk19 @ ( k1_zfmisc_1 @ F ) )),bind(C,$thf( k1_zfmisc_1 @ F ))]]) ).
thf(836,plain,
! [A: $i] :
~ ( r2_hidden @ ( k1_zfmisc_1 @ A ) @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[822]) ).
thf(72,plain,
v1_xboole_0 @ sk8,
inference(cnf,[status(esa)],[70]) ).
thf(294,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk8 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[72,153]) ).
thf(295,plain,
sk8 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( sk8 ))]]) ).
thf(150,plain,
! [A: $i] : ( m1_subset_1 @ ( sk13 @ A ) @ A ),
inference(cnf,[status(esa)],[149]) ).
thf(27,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(127,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)],[27]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relset_2) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(99,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk10 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[96]) ).
thf(39,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(158,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,plain,
m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[52]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(146,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,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(136,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)],[31]) ).
thf(68,plain,
v3_relat_1 @ sk7,
inference(cnf,[status(esa)],[67]) ).
thf(62,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk5 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[61]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk12 @ A ) )
!= ( v1_xboole_0 @ ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[111,107]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( sk12 @ A )
!= ( k2_tarski @ B @ C ) ),
inference(simp,[status(thm)],[251]) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[258,437]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( m1_relset_1 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(694,plain,
! [A: $i] :
( ( r2_hidden @ ( sk19 @ sk3 ) @ sk3 )
!= ( r2_hidden @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[566,461]) ).
thf(706,plain,
! [A: $i] :
( ( ( sk19 @ sk3 )
!= A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[694]) ).
thf(708,plain,
( ( sk19 @ sk3 )
!= sk3 ),
inference(simp,[status(thm)],[706]) ).
thf(45508,plain,
$false,
inference(cvc4,[status(thm)],[257,129,86,69,101,249,234,115,741,269,56,142,472,538,153,52,184,110,838,702,125,57,78,216,321,121,84,61,221,132,133,206,233,85,102,60,117,746,70,192,92,566,197,65,461,224,97,329,156,53,141,109,884,77,96,134,73,105,674,64,149,191,204,187,113,219,81,76,98,140,91,66,108,209,836,63,295,150,67,199,127,154,143,99,87,158,186,55,139,75,58,246,207,82,151,146,190,107,136,79,437,68,62,501,90,659,708,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU439+1 : TPTP v8.1.2. Released v3.4.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n027.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 13:38:51 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.01 % [INFO] Parsing done (140ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 1.88/1.23 % [INFO] eprover registered as external prover.
% 1.88/1.23 % [INFO] cvc4 registered as external prover.
% 1.88/1.24 % [INFO] Scanning for conjecture ...
% 1.95/1.31 % [INFO] Found a conjecture and 59 axioms. Running axiom selection ...
% 2.14/1.36 % [INFO] Axiom selection finished. Selected 49 axioms (removed 10 axioms).
% 2.31/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/1.42 % [INFO] Type checking passed.
% 2.31/1.42 % [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 ...
% 114.02/20.62 % External prover 'cvc4' found a proof!
% 114.02/20.62 % [INFO] Killing All external provers ...
% 114.02/20.63 % Time passed: 20105ms (effective reasoning time: 19600ms)
% 114.02/20.63 % 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)>
% 114.02/20.63 % Axioms used in derivation (49): redefinition_m2_relset_1, redefinition_k8_relset_2, fc4_subset_1, t24_relset_2, rc2_partfun1, dt_k8_relset_2, d4_relset_2, t4_subset, dt_k6_relset_2, rc1_subset_1, redefinition_k6_relset_2, dt_k4_relset_2, existence_m1_eqrel_1, t8_boole, dt_k5_relset_2, fc1_sysrel, antisymmetry_r2_hidden, d5_tarski, fc4_relat_1, t1_subset, dt_m2_relset_1, cc1_relat_1, d1_xboole_0, dt_m1_eqrel_1, d13_relat_1, rc3_relat_1, t6_boole, rc2_subset_1, redefinition_k4_relset_2, fc3_subset_1, t5_subset, existence_m1_relset_1, fc2_subset_1, t7_boole, fc1_subset_1, dt_k3_pua2mss1, t9_relset_2, dt_k8_setfam_1, t3_subset, cc1_relset_1, existence_m1_subset_1, commutativity_k2_tarski, rc2_relat_1, existence_m2_relset_1, d3_tarski, rc1_relat_1, reflexivity_r1_tarski, t2_subset, fc12_relat_1
% 114.02/20.63 % No. of inferences in proof: 212
% 114.02/20.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20105 ms resp. 19600 ms w/o parsing
% 114.02/20.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 114.02/20.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------