TSTP Solution File: SEU412+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU412+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:58:50 EDT 2023
% Result : Theorem 8.13s 2.94s
% Output : Refutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 70
% Syntax : Number of formulae : 118 ( 35 unt; 24 typ; 0 def)
% Number of atoms : 266 ( 45 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 955 ( 39 ~; 7 |; 79 &; 744 @)
% ( 8 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-6 aty)
% Number of variables : 215 ( 0 ^; 201 !; 14 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(u1_orders_2_type,type,
u1_orders_2: $i > $i ).
thf(k1_latsum_1_type,type,
k1_latsum_1: $i > $i > $i ).
thf(v13_waybel_0_type,type,
v13_waybel_0: $i > $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_orders_2_type,type,
g1_orders_2: $i > $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $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(k7_relset_1_type,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_orders_2_type,type,
v1_orders_2: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(69,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)],[7]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(174,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ A )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ C @ ( u1_struct_0 @ B ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_latsum_1) ).
thf(223,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ A )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ C @ ( u1_struct_0 @ B ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(203,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,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(168,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)],[34]) ).
thf(27,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(152,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
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(57,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,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(164,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)],[32]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(106,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,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(85,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)],[13]) ).
thf(44,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(220,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_orders_2 @ A )
=> ( A
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(29,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(156,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(25,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i] :
( ( ( v1_orders_2 @ C )
& ( l1_orders_2 @ C ) )
=> ( ( C
= ( k1_latsum_1 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= ( k2_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_orders_2 @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) @ ( k7_relset_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).
thf(141,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i] :
( ( ( v1_orders_2 @ C )
& ( l1_orders_2 @ C ) )
=> ( ( ( C
= ( k1_latsum_1 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= ( k2_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_orders_2 @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) @ ( k7_relset_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= ( k2_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_orders_2 @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) @ ( k7_relset_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ A ) @ ( u1_orders_2 @ B ) ) ) ) )
=> ( C
= ( k1_latsum_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(109,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ( l1_orders_2 @ B ) )
=> ( ( v1_orders_2 @ ( k1_latsum_1 @ A @ B ) )
& ( l1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
thf(225,plain,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ( l1_orders_2 @ B ) )
=> ( ( v1_orders_2 @ ( k1_latsum_1 @ A @ B ) )
& ( l1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,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(212,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)],[42]) ).
thf(16,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(96,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(73,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(205,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(166,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(64,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(71,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
& ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(76,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)],[10]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(98,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)],[17]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(66,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(162,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(209,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( l1_orders_2 @ C )
=> ! [D: $i] :
( ( l1_orders_2 @ D )
=> ~ ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( u1_orders_2 @ ( k1_latsum_1 @ C @ D ) ) )
& ( v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ C )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ C ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ D ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ D ) ) )
& ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) )
& ( r2_hidden @ B @ ( k4_xboole_0 @ ( u1_struct_0 @ D ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_latsum_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( l1_orders_2 @ C )
=> ! [D: $i] :
( ( l1_orders_2 @ D )
=> ~ ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( u1_orders_2 @ ( k1_latsum_1 @ C @ D ) ) )
& ( v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ C )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ C ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ D ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ D ) ) )
& ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) )
& ( r2_hidden @ B @ ( k4_xboole_0 @ ( u1_struct_0 @ D ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( l1_orders_2 @ C )
=> ! [D: $i] :
( ( l1_orders_2 @ D )
=> ~ ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( u1_orders_2 @ ( k1_latsum_1 @ C @ D ) ) )
& ( v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ C )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ C ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ C ) ) )
& ~ ( ( r2_hidden @ A @ ( u1_struct_0 @ D ) )
& ( r2_hidden @ B @ ( u1_struct_0 @ D ) ) )
& ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) )
& ( r2_hidden @ B @ ( k4_xboole_0 @ ( u1_struct_0 @ D ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,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(150,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)],[26]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(171,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
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(139,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(40,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(207,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)],[40]) ).
thf(12,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(82,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(136,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(79,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,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(94,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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(90,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(18,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(100,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(419,plain,
$false,
inference(cvc4,[status(thm)],[69,217,174,110,59,223,177,154,203,168,152,228,57,164,106,85,220,156,141,109,225,212,96,73,205,166,64,71,159,76,98,103,66,162,209,48,150,171,139,207,82,136,79,94,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU412+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 12:23:07 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.95/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.09 % [INFO] Parsing done (165ms).
% 1.35/1.09 % [INFO] Running in sequential loop mode.
% 1.76/1.32 % [INFO] eprover registered as external prover.
% 1.76/1.32 % [INFO] cvc4 registered as external prover.
% 1.76/1.32 % [INFO] Scanning for conjecture ...
% 2.09/1.40 % [INFO] Found a conjecture and 56 axioms. Running axiom selection ...
% 2.32/1.47 % [INFO] Axiom selection finished. Selected 45 axioms (removed 11 axioms).
% 2.49/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 2.49/1.52 % [INFO] Type checking passed.
% 2.49/1.53 % [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 ...
% 8.13/2.93 % External prover 'cvc4' found a proof!
% 8.13/2.93 % [INFO] Killing All external provers ...
% 8.13/2.94 % Time passed: 2382ms (effective reasoning time: 1838ms)
% 8.13/2.94 % 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)>
% 8.13/2.94 % Axioms used in derivation (45): redefinition_m2_relset_1, dt_k7_relset_1, t2_boole, dt_k1_latsum_1, t6_boole, existence_m1_relset_1, dt_g1_orders_2, abstractness_v1_orders_2, t106_zfmisc_1, existence_m2_relset_1, dt_l1_orders_2, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, t1_boole, fc1_xboole_0, t1_subset, dt_m2_relset_1, commutativity_k3_xboole_0, t17_latsum_1, fc2_xboole_0, dt_u1_orders_2, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, d2_xboole_0, t7_boole, existence_l1_orders_2, t3_subset, cc1_relset_1, existence_m1_subset_1, free_g1_orders_2, dt_k5_relat_1, reflexivity_r1_tarski, d4_xboole_0, redefinition_k7_relset_1, t8_boole, rc1_xboole_0, existence_l1_struct_0, d2_latsum_1, t3_boole
% 8.13/2.94 % No. of inferences in proof: 94
% 8.13/2.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2382 ms resp. 1838 ms w/o parsing
% 8.13/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.13/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------