TSTP Solution File: SEU449+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU449+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:59:16 EDT 2023
% Result : Theorem 4.37s 2.00s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 72
% Syntax : Number of formulae : 122 ( 17 unt; 24 typ; 0 def)
% Number of atoms : 230 ( 18 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 901 ( 26 ~; 2 |; 52 &; 743 @)
% ( 3 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-4 aty)
% Number of variables : 226 ( 0 ^; 206 !; 20 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_1_type,type,
k6_relset_1: $i > $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k4_relat_1_type,type,
k4_relat_1: $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(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k7_relset_2_type,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(34,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(138,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)],[34]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(115,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(46,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(174,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)],[46]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(44,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(167,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)],[44]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,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(55,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,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(119,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)],[27]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(136,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(14,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(83,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(110,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,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(125,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)],[29]) ).
thf(17,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(93,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(57,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(78,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,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(164,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)],[43]) ).
thf(48,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(179,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)],[48]) ).
thf(28,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(121,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)],[28]) ).
thf(16,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(89,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,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(133,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)],[32]) ).
thf(20,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(102,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(60,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_1) ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k6_relset_1 @ A @ B @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(73,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(105,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(42,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(161,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(149,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(71,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,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(159,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(45,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(172,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)],[45]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,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(81,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)],[13]) ).
thf(11,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(76,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,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(98,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)],[19]) ).
thf(35,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(140,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)],[35]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(66,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(108,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(63,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ A @ B )
=> ( ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k6_relset_1 @ A @ B @ E ) ) )
& ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ A @ B )
=> ( ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k6_relset_1 @ A @ B @ E ) ) )
& ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ A @ B )
=> ( ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k6_relset_1 @ A @ B @ E ) ) )
& ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,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(182,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)],[49]) ).
thf(40,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(154,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)],[40]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relset_2) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ C )
= ( k4_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_1) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k6_relset_1 @ A @ B @ C )
= ( k4_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ A @ B )
=> ( ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) )
<=> ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_relset_2) ).
thf(146,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ A @ B )
=> ( ( ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) )
=> ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ C @ E ) ) )
& ( ( r1_tarski @ D @ ( k8_relset_2 @ A @ B @ C @ E ) )
=> ( r1_tarski @ C @ ( k8_relset_2 @ B @ A @ D @ ( k6_relset_1 @ A @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,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(131,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)],[31]) ).
thf(8,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(68,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(185,plain,
$false,
inference(e,[status(thm)],[138,115,174,129,176,167,87,55,119,136,83,110,125,93,57,78,164,179,121,89,133,102,60,117,73,105,161,149,71,159,172,113,81,76,98,140,66,108,63,95,50,182,154,143,151,146,131,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU449+1 : TPTP v8.1.2. Released v3.4.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n016.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 13:55:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (139ms).
% 1.25/0.98 % [INFO] Running in sequential loop mode.
% 1.82/1.18 % [INFO] eprover registered as external prover.
% 1.82/1.18 % [INFO] cvc4 registered as external prover.
% 1.82/1.19 % [INFO] Scanning for conjecture ...
% 1.97/1.27 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.24/1.33 % [INFO] Axiom selection finished. Selected 47 axioms (removed 7 axioms).
% 2.24/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.24/1.38 % [INFO] Type checking passed.
% 2.24/1.38 % [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 ...
% 4.37/2.00 % External prover 'e' found a proof!
% 4.37/2.00 % [INFO] Killing All external provers ...
% 4.37/2.00 % Time passed: 1491ms (effective reasoning time: 1015ms)
% 4.37/2.00 % 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)>
% 4.37/2.00 % Axioms used in derivation (47): redefinition_m2_relset_1, dt_k6_relset_1, redefinition_k8_relset_2, fc4_subset_1, rc2_partfun1, dt_m1_eqrel_1, existence_m1_relset_1, d4_relset_2, rc1_subset_1, redefinition_k6_relset_2, dt_k4_relset_2, existence_m1_eqrel_1, t8_boole, dt_k5_relset_2, fc1_sysrel, antisymmetry_r2_hidden, fc4_relat_1, t1_subset, dt_m2_relset_1, cc1_relat_1, dt_k8_relset_2, redefinition_k6_relset_1, involutiveness_k6_relset_1, rc3_relat_1, t6_boole, rc2_subset_1, redefinition_k4_relset_2, t5_subset, dt_k4_relat_1, t4_subset, t61_relset_2, involutiveness_k4_relat_1, dt_k6_relset_2, t7_boole, fc1_subset_1, dt_k3_pua2mss1, dt_k8_setfam_1, t3_subset, cc1_relset_1, fc11_relat_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, reflexivity_r1_tarski, t2_subset, fc12_relat_1
% 4.37/2.00 % No. of inferences in proof: 98
% 4.37/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1491 ms resp. 1015 ms w/o parsing
% 4.37/2.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------