TSTP Solution File: GRP637+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP637+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:14:41 EDT 2023
% Result : Theorem 4.63s 2.18s
% Output : Refutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 72
% Syntax : Number of formulae : 120 ( 21 unt; 26 typ; 0 def)
% Number of atoms : 366 ( 15 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1105 ( 68 ~; 2 |; 158 &; 765 @)
% ( 4 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 2 con; 0-4 aty)
% Number of variables : 218 ( 0 ^; 188 !; 30 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $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(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v1_group_6_type,type,
v1_group_6: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_group_2_type,type,
m1_group_2: $i > $i > $o ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(m1_group_6_type,type,
m1_group_6: $i > $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $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(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(u1_group_1_type,type,
u1_group_1: $i > $i ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(10,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(88,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_6) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(19,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(110,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,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(78,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)],[6]) ).
thf(15,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(102,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(160,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,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(97,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)],[13]) ).
thf(35,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(166,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)],[35]) ).
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(80,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(24,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(123,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(41,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
thf(182,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(99,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,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(90,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)],[11]) ).
thf(21,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(115,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,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(120,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)],[23]) ).
thf(34,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(164,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)],[34]) ).
thf(8,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(84,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,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(147,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)],[30]) ).
thf(26,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(132,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)],[26]) ).
thf(32,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(156,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)],[32]) ).
thf(43,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_2) ).
thf(188,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,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(169,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(27,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(134,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)],[27]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(73,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)],[4]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(105,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)],[17]) ).
thf(39,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(176,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(118,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(144,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(86,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(113,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)],[20]) ).
thf(5,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(76,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)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(46,axiom,
? [A: $i] : ( l1_group_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(198,plain,
? [A: $i] : ( l1_group_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(108,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ B )
=> ! [G: $i] :
( ( m1_group_2 @ G @ B )
=> ( ( ( ( u1_struct_0 @ F )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ A @ E ) )
=> ( m1_group_6 @ F @ B @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_latsubgr) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ B )
=> ! [G: $i] :
( ( m1_group_2 @ G @ B )
=> ( ( ( ( u1_struct_0 @ F )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ A @ E ) )
=> ( m1_group_6 @ F @ B @ G ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ B )
=> ! [G: $i] :
( ( m1_group_2 @ G @ B )
=> ( ( ( ( u1_struct_0 @ F )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ A @ E ) )
=> ( m1_group_6 @ F @ B @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] : ( m1_group_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_group_2) ).
thf(186,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] : ( m1_group_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
<=> ( m1_group_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ B ) )
& ( ( m1_group_2 @ C @ B )
=> ( m1_group_6 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,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(151,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)],[31]) ).
thf(44,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(190,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)],[44]) ).
thf(25,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( m1_group_2 @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_2) ).
thf(126,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( m1_group_2 @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_group_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,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(195,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)],[45]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ? [C: $i] : ( m1_group_6 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_group_6) ).
thf(200,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ? [C: $i] : ( m1_group_6 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(40,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(178,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)],[40]) ).
thf(202,plain,
$false,
inference(e,[status(thm)],[88,174,110,78,102,160,97,166,80,123,182,99,90,115,120,164,84,147,132,156,188,169,134,73,105,176,118,71,144,86,113,76,103,198,108,48,95,186,171,139,151,190,126,195,200,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP637+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n004.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 : Fri May 19 01:32:55 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.05 % [INFO] Parsing done (159ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.88/1.26 % [INFO] eprover registered as external prover.
% 1.88/1.26 % [INFO] cvc4 registered as external prover.
% 1.88/1.26 % [INFO] Scanning for conjecture ...
% 2.15/1.34 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.32/1.40 % [INFO] Axiom selection finished. Selected 45 axioms (removed 9 axioms).
% 2.32/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.46 % [INFO] Type checking passed.
% 2.58/1.46 % [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 ...
% 4.63/2.18 % External prover 'e' found a proof!
% 4.63/2.18 % [INFO] Killing All external provers ...
% 4.63/2.18 % Time passed: 1656ms (effective reasoning time: 1113ms)
% 4.63/2.18 % 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)>
% 4.63/2.18 % Axioms used in derivation (45): redefinition_m2_relset_1, dt_m1_group_6, existence_m1_group_6, fc4_subset_1, rc2_partfun1, existence_m1_relset_1, dt_k2_funct_2, existence_m2_relset_1, redefinition_m1_group_6, existence_l1_group_1, fc1_xboole_0, t1_subset, dt_m2_relset_1, dt_u1_group_1, redefinition_k2_funct_2, existence_m1_group_2, dt_l1_group_1, t6_boole, rc2_subset_1, dt_m1_group_2, t5_subset, t4_subset, cc1_funct_2, t7_boole, rc3_struct_0, fc1_subset_1, rc1_subset_1, rc1_funct_2, t3_subset, cc1_relset_1, existence_m1_subset_1, fc1_struct_0, cc6_funct_2, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, t156_relat_1, existence_l1_struct_0, cc5_funct_2, rc2_xboole_0, d5_group_2, t66_group_2, antisymmetry_r2_hidden
% 4.63/2.18 % No. of inferences in proof: 94
% 4.63/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1656 ms resp. 1113 ms w/o parsing
% 5.12/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.12/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------