TSTP Solution File: SEU429+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU429+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 11:59:01 EDT 2023
% Result : Theorem 4.28s 2.03s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 67
% Syntax : Number of formulae : 113 ( 17 unt; 23 typ; 0 def)
% Number of atoms : 223 ( 17 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 822 ( 33 ~; 2 |; 62 &; 656 @)
% ( 4 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 2 con; 0-4 aty)
% Number of variables : 216 ( 0 ^; 193 !; 23 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(a_4_1_relset_2_type,type,
a_4_1_relset_2: $i > $i > $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v3_relat_1_type,type,
v3_relat_1: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
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(43,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(174,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)],[43]) ).
thf(45,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(179,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)],[45]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( r2_hidden @ A @ ( a_4_1_relset_2 @ B @ C @ D @ E ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k8_relset_2 @ B @ C @ F @ E ) )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_relset_2) ).
thf(85,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_4_1_relset_2 @ B @ C @ D @ E ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k8_relset_2 @ B @ C @ F @ E ) )
& ( r2_hidden @ F @ D ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k8_relset_2 @ B @ C @ F @ E ) )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_4_1_relset_2 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(39,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(160,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(54,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,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(145,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)],[33]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(150,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,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(72,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(51,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(142,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_38__relset_2) ).
thf(153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,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(93,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)],[15]) ).
thf(34,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(147,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,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(132,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)],[29]) ).
thf(23,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,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(74,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)],[9]) ).
thf(21,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(109,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(77,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(128,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(19,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(105,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)],[19]) ).
thf(41,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(166,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)],[41]) ).
thf(5,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(64,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,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(176,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)],[44]) ).
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(118,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(22,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(113,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)],[22]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(81,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,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(98,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)],[16]) ).
thf(18,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(103,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)],[18]) ).
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(66,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(155,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(28,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(130,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)],[28]) ).
thf(30,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(135,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)],[30]) ).
thf(38,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(158,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(42,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(171,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)],[42]) ).
thf(31,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(139,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)],[31]) ).
thf(20,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(107,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)],[20]) ).
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(126,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(79,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(163,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,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(68,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)],[7]) ).
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(122,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(13,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(83,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,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(100,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)],[17]) ).
thf(182,plain,
$false,
inference(e,[status(thm)],[174,179,85,160,54,145,150,72,51,142,153,46,93,147,132,116,74,109,77,128,105,166,64,176,118,113,81,98,103,66,155,130,135,158,171,139,107,126,79,163,68,122,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU429+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 13:56:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (143ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.82/1.19 % [INFO] eprover registered as external prover.
% 1.82/1.19 % [INFO] cvc4 registered as external prover.
% 1.82/1.20 % [INFO] Scanning for conjecture ...
% 1.96/1.26 % [INFO] Found a conjecture and 50 axioms. Running axiom selection ...
% 1.96/1.31 % [INFO] Axiom selection finished. Selected 43 axioms (removed 7 axioms).
% 2.27/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.37 % [INFO] Type checking passed.
% 2.27/1.37 % [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 ...
% 4.28/2.03 % External prover 'e' found a proof!
% 4.28/2.03 % [INFO] Killing All external provers ...
% 4.28/2.03 % Time passed: 1509ms (effective reasoning time: 1031ms)
% 4.28/2.03 % 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)>
% 4.28/2.03 % Axioms used in derivation (43): redefinition_m2_relset_1, redefinition_k8_relset_2, fc4_subset_1, rc2_partfun1, dt_k8_relset_2, dt_m1_eqrel_1, existence_m1_relset_1, t4_subset, 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, fc4_relat_1, t1_subset, dt_m2_relset_1, cc1_relat_1, rc3_relat_1, t6_boole, rc2_subset_1, redefinition_k4_relset_2, t5_subset, d4_relset_2, t2_tarski, s8_domain_1__e1_38__relset_2, dt_k6_relset_2, t7_boole, fc1_subset_1, dt_k3_pua2mss1, dt_k8_setfam_1, t3_subset, cc1_relset_1, existence_m1_subset_1, fraenkel_a_4_1_relset_2, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, reflexivity_r1_tarski, t2_subset, fc12_relat_1
% 4.28/2.03 % No. of inferences in proof: 90
% 4.28/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1509 ms resp. 1031 ms w/o parsing
% 4.64/2.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.64/2.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------