TSTP Solution File: GRP631+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 11:14:39 EDT 2023
% Result : Theorem 5.90s 2.53s
% Output : Refutation 6.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 193 ( 25 unt; 41 typ; 0 def)
% Number of atoms : 579 ( 30 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1797 ( 69 ~; 2 |; 302 &;1301 @)
% ( 3 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 2 con; 0-6 aty)
% Number of variables : 315 ( 0 ^; 269 !; 46 ?; 315 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v1_group_1_type,type,
v1_group_1: $i > $o ).
thf(v3_group_1_type,type,
v3_group_1: $i > $o ).
thf(v4_group_1_type,type,
v4_group_1: $i > $o ).
thf(l1_group_1_type,type,
l1_group_1: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k6_autgroup_type,type,
k6_autgroup: $i > $i > $i ).
thf(k2_group_1_type,type,
k2_group_1: $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $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(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(v3_relat_2_type,type,
v3_relat_2: $i > $o ).
thf(v8_relat_2_type,type,
v8_relat_2: $i > $o ).
thf(v1_relat_2_type,type,
v1_relat_2: $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(m1_fraenkel_type,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(v1_fraenkel_type,type,
v1_fraenkel: $i > $o ).
thf(v4_relat_2_type,type,
v4_relat_2: $i > $o ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(k7_relset_1_type,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v3_funct_2_type,type,
v3_funct_2: $i > $i > $i > $o ).
thf(v2_funct_2_type,type,
v2_funct_2: $i > $i > $i > $o ).
thf(m2_fraenkel_type,type,
m2_fraenkel: $i > $i > $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v2_group_1_type,type,
v2_group_1: $i > $o ).
thf(k4_autgroup_type,type,
k4_autgroup: $i > $i ).
thf(u1_group_1_type,type,
u1_group_1: $i > $i ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_fraenkel @ C @ A @ B )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_fraenkel @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
thf(142,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_fraenkel @ C @ A @ B )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_fraenkel @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(185,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_fraenkel @ ( k4_autgroup @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
thf(292,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_fraenkel @ ( k4_autgroup @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(188,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(129,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(86,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_1) ).
thf(262,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( ( v1_funct_1 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( v1_relat_2 @ B )
& ( v1_funct_2 @ B @ A @ A ) )
=> ( ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v2_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( ( v1_funct_1 @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( v1_relat_2 @ B )
& ( v1_funct_2 @ B @ A @ A ) )
=> ( ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v2_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(68,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(308,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(120,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(110,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(125,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(58,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_fraenkel) ).
thf(284,plain,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
<=> ( m1_subset_1 @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( m2_fraenkel @ D @ A @ B @ C )
=> ( m1_subset_1 @ D @ C ) )
& ( ( m1_subset_1 @ D @ C )
=> ( m2_fraenkel @ D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(289,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)],[60]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(265,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(206,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(116,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)],[12]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(65,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(302,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(260,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)],[50]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(160,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(256,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)],[48]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) @ ( k6_autgroup @ A @ B ) )
= ( k6_autgroup @ A @ B ) )
& ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ B ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) )
= ( k6_autgroup @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_autgroup) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) @ ( k6_autgroup @ A @ B ) )
= ( k6_autgroup @ A @ B ) )
& ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ B ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) )
= ( k6_autgroup @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(77,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) @ ( k6_autgroup @ A @ B ) )
= ( k6_autgroup @ A @ B ) )
& ( ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k6_autgroup @ A @ B ) @ ( k6_autgroup @ A @ ( k2_group_1 @ A ) ) )
= ( k6_autgroup @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_relat_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(96,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_2 @ A )
& ( v8_relat_2 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_relat_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(134,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_group_1) ).
thf(311,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(279,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v3_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v2_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(180,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v3_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v2_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_group_1 @ ( g1_group_1 @ A @ B ) )
& ( l1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_group_1) ).
thf(296,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_group_1 @ ( g1_group_1 @ A @ B ) )
& ( l1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(191,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(57,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_group_1) ).
thf(281,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_funct_1 @ ( u1_group_1 @ A ) )
& ( v1_funct_2 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_group_1) ).
thf(318,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_funct_1 @ ( u1_group_1 @ A ) )
& ( v1_funct_2 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(19,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_fraenkel) ).
thf(140,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
thf(213,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ? [D: $i] : ( m2_fraenkel @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_fraenkel) ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ? [D: $i] : ( m2_fraenkel @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(108,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_group_1 @ A )
=> ( A
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
thf(330,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_group_1 @ A )
=> ( A
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(40,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(223,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_fraenkel @ ( k6_autgroup @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_autgroup) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_fraenkel @ ( k6_autgroup @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(64,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_autgroup @ A @ ( k2_group_1 @ A ) )
= ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_autgroup) ).
thf(299,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_autgroup @ A @ ( k2_group_1 @ A ) )
= ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(25,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ A @ A )
& ( v1_relat_1 @ B )
& ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v4_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(167,plain,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ A @ A )
& ( v1_relat_1 @ B )
& ( v1_relat_2 @ B )
& ( v3_relat_2 @ B )
& ( v4_relat_2 @ B )
& ( v8_relat_2 @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(24,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(162,plain,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(112,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(194,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) )
& ( v1_relat_2 @ ( k6_relat_1 @ A ) )
& ( v3_relat_2 @ ( k6_relat_1 @ A ) )
& ( v4_relat_2 @ ( k6_relat_1 @ A ) )
& ( v8_relat_2 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(145,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) )
& ( v1_relat_2 @ ( k6_relat_1 @ A ) )
& ( v3_relat_2 @ ( k6_relat_1 @ A ) )
& ( v4_relat_2 @ ( k6_relat_1 @ A ) )
& ( v8_relat_2 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(127,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(338,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(75,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_subset_1 @ ( k2_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
thf(336,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_subset_1 @ ( k2_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(250,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(99,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)],[6]) ).
thf(34,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_fraenkel) ).
thf(203,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_fraenkel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(104,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(66,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(304,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(258,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)],[49]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v2_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v3_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(235,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v2_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( v3_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(207,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(272,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)],[54]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(287,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)],[59]) ).
thf(37,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(210,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(239,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(53,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_group_1) ).
thf(268,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(62,axiom,
? [A: $i] : ( l1_group_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(294,plain,
? [A: $i] : ( l1_group_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(136,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(200,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(277,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ A @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v2_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(227,plain,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ A @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v2_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_group_1 @ A @ B ) )
& ( v1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_group_1) ).
thf(322,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_group_1 @ A @ B ) )
& ( v1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(354,plain,
$false,
inference(cvc4,[status(thm)],[333,142,185,253,292,188,129,86,262,217,308,120,110,125,284,325,289,265,206,116,243,302,260,160,256,77,96,134,311,279,180,296,191,281,245,318,140,213,91,198,108,330,223,306,299,167,162,112,194,145,127,338,336,175,250,99,203,104,304,258,158,114,235,207,272,287,210,239,268,294,136,200,277,227,322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 01:51:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/1.13 % [INFO] Parsing done (209ms).
% 1.68/1.14 % [INFO] Running in sequential loop mode.
% 2.10/1.38 % [INFO] eprover registered as external prover.
% 2.10/1.39 % [INFO] cvc4 registered as external prover.
% 2.10/1.39 % [INFO] Scanning for conjecture ...
% 2.33/1.48 % [INFO] Found a conjecture and 81 axioms. Running axiom selection ...
% 2.55/1.55 % [INFO] Axiom selection finished. Selected 74 axioms (removed 7 axioms).
% 2.68/1.63 % [INFO] Problem is first-order (TPTP FOF).
% 2.68/1.64 % [INFO] Type checking passed.
% 2.68/1.64 % [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 ...
% 5.90/2.52 % External prover 'cvc4' found a proof!
% 5.90/2.52 % [INFO] Killing All external provers ...
% 5.90/2.52 % Time passed: 1989ms (effective reasoning time: 1375ms)
% 5.90/2.52 % 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)>
% 5.90/2.53 % Axioms used in derivation (74): cc4_funct_2, dt_k7_relset_1, dt_m2_fraenkel, dt_m1_fraenkel, existence_m2_relset_1, dt_k6_relat_1, redefinition_k7_relset_1, rc2_xboole_0, t23_funct_2, rc3_group_1, redefinition_m2_relset_1, free_g1_group_1, fc2_partfun1, fc1_xboole_0, t1_subset, redefinition_k7_funct_2, rc2_partfun1, rc3_funct_1, cc1_fraenkel, fc1_funct_1, rc1_fraenkel, dt_k6_partfun1, dt_m2_relset_1, dt_u1_group_1, dt_k7_funct_2, existence_m2_fraenkel, rc1_funct_1, dt_l1_group_1, cc2_funct_2, t6_boole, rc3_partfun1, t5_subset, dt_k6_autgroup, existence_m1_relset_1, cc3_funct_2, fc2_funct_1, t4_subset, cc1_funct_2, cc1_partfun1, dt_k4_autgroup, t7_boole, cc1_funct_1, rc3_struct_0, redefinition_k6_partfun1, cc1_group_1, rc2_funct_1, redefinition_m2_fraenkel, rc1_funct_2, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, fc1_struct_0, cc6_funct_2, dt_k5_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, existence_m1_fraenkel, rc5_struct_0, t2_subset, fc1_group_1, dt_k2_group_1, existence_l1_group_1, rc1_group_1, existence_l1_struct_0, rc2_group_1, rc1_partfun1, cc5_funct_2, t24_autgroup, antisymmetry_r2_hidden, rc2_funct_2, dt_g1_group_1, abstractness_v1_group_1
% 5.90/2.53 % No. of inferences in proof: 152
% 5.90/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1989 ms resp. 1375 ms w/o parsing
% 6.30/2.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.30/2.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------