TSTP Solution File: SEU414+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU414+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:58:51 EDT 2023
% Result : Theorem 192.86s 37.20s
% Output : Refutation 192.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 88
% Syntax : Number of formulae : 275 ( 85 unt; 40 typ; 0 def)
% Number of atoms : 620 ( 147 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 2101 ( 139 ~; 127 |; 111 &;1605 @)
% ( 7 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 9 con; 0-6 aty)
% Number of variables : 423 ( 0 ^; 402 !; 21 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(r1_latsum_1_type,type,
r1_latsum_1: $i > $i > $o ).
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(v12_waybel_0_type,type,
v12_waybel_0: $i > $i > $o ).
thf(v3_orders_2_type,type,
v3_orders_2: $i > $o ).
thf(v4_orders_2_type,type,
v4_orders_2: $i > $o ).
thf(k1_latsum_1_type,type,
k1_latsum_1: $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $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(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(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(r4_relat_2_type,type,
r4_relat_2: $i > $i > $o ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_orders_2_type,type,
v1_orders_2: $i > $o ).
thf(u1_orders_2_type,type,
u1_orders_2: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $i > $o ).
thf(sk4_type,type,
sk4: $i > $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ( ( ( r1_latsum_1 @ A @ B )
& ( 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 ) ) )
& ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B ) )
=> ( v4_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_latsum_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ( ( ( r1_latsum_1 @ A @ B )
& ( 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 ) ) )
& ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B ) )
=> ( v4_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ( ( ( r1_latsum_1 @ A @ B )
& ( 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 ) ) )
& ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( v3_orders_2 @ A )
& ( v4_orders_2 @ A )
& ( v3_orders_2 @ B )
& ( v4_orders_2 @ B ) )
=> ( v4_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,plain,
v3_orders_2 @ sk1,
inference(cnf,[status(esa)],[50]) ).
thf(4,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(68,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)],[4]) ).
thf(69,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 ) ) )
& ! [D: $i] :
( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ! [D: $i] :
( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( sk3 @ A @ B @ C )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ A )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ B )
| ( C
= ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ( sk3 @ A @ B @ C )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ A )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ( sk3 @ A @ B @ C )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ A )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[80]) ).
thf(9,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(105,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(106,plain,
v1_xboole_0 @ sk8,
inference(cnf,[status(esa)],[105]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(120,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(121,plain,
~ ? [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(miniscope,[status(thm)],[120]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( v1_xboole_0 @ B ) ),
inference(cnf,[status(esa)],[121]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ( ( v1_xboole_0 @ sk8 )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[106,122]) ).
thf(254,plain,
! [A: $i] :
~ ( r2_hidden @ A @ sk8 ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ( sk3 @ A @ B @ C )
| ( r2_hidden @ ( sk5 @ C @ B @ A ) @ B )
| ( ( r2_hidden @ ( sk5 @ C @ B @ A ) @ A )
!= ( r2_hidden @ D @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[81,254]) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( A
= ( k2_xboole_0 @ sk8 @ B ) )
| ( sk3 @ sk8 @ B @ A )
| ( r2_hidden @ ( sk5 @ A @ B @ sk8 ) @ B ) ),
inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( sk8 )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( sk5 @ E @ F @ sk8 ))]]) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( A
= ( k2_xboole_0 @ sk8 @ B ) )
| ( sk3 @ sk8 @ B @ A )
| ( r2_hidden @ ( sk5 @ A @ B @ sk8 ) @ B ) ),
inference(simp,[status(thm)],[791]) ).
thf(16,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(123,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ( ( v1_xboole_0 @ k1_xboole_0 )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[123,122]) ).
thf(252,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( k2_xboole_0 @ sk8 @ B ) )
| ( sk3 @ sk8 @ B @ A )
| ( ( r2_hidden @ ( sk5 @ A @ B @ sk8 ) @ B )
!= ( r2_hidden @ C @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[816,252]) ).
thf(965,plain,
! [A: $i] :
( ( A
= ( k2_xboole_0 @ sk8 @ k1_xboole_0 ) )
| ( sk3 @ sk8 @ k1_xboole_0 @ A ) ),
inference(pattern_uni,[status(thm)],[964:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( sk5 @ D @ k1_xboole_0 @ sk8 ))]]) ).
thf(1128,plain,
! [A: $i] :
( ( A
= ( k2_xboole_0 @ sk8 @ k1_xboole_0 ) )
| ( sk3 @ sk8 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[965]) ).
thf(18,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(127,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(128,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(1584,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk8 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,129]) ).
thf(1585,plain,
sk8 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[1584:[bind(A,$thf( sk8 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(107,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(108,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[107]) ).
thf(109,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[108]) ).
thf(1900,plain,
! [A: $i] :
( ( A = sk8 )
| ( sk3 @ k1_xboole_0 @ k1_xboole_0 @ A ) ),
inference(rewrite,[status(thm)],[1128,1585,109]) ).
thf(22,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(138,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)],[22]) ).
thf(58,plain,
v4_orders_2 @ sk2,
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
~ ( v4_orders_2 @ ( k1_latsum_1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[50]) ).
thf(232,plain,
( ( v4_orders_2 @ ( k1_latsum_1 @ sk1 @ sk2 ) )
!= ( v4_orders_2 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[58,52]) ).
thf(234,plain,
( ( k1_latsum_1 @ sk1 @ sk2 )
!= sk2 ),
inference(simp,[status(thm)],[232]) ).
thf(44,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(215,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(cnf,[status(esa)],[215]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(31,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(181,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(182,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[182]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ B @ A )
= k1_xboole_0 )
| ( ( k3_xboole_0 @ A @ B )
!= ( k3_xboole_0 @ C @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[217,183]) ).
thf(511,plain,
! [A: $i] :
( ( k3_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(61,plain,
v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) @ sk2,
inference(cnf,[status(esa)],[50]) ).
thf(241,plain,
! [A: $i] :
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( ( k3_xboole_0 @ A @ k1_xboole_0 )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[183,61]) ).
thf(244,plain,
! [A: $i] :
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[241]) ).
thf(247,plain,
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[244]) ).
thf(32,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(184,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)],[32]) ).
thf(11,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(110,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)],[11]) ).
thf(1510,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v3_orders_2 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[129,56]) ).
thf(1511,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( v3_orders_2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1510:[bind(A,$thf( sk1 ))]]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(196,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(34,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(189,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)],[34]) ).
thf(60,plain,
l1_orders_2 @ sk2,
inference(cnf,[status(esa)],[50]) ).
thf(1608,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_orders_2 @ k1_xboole_0 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[129,60]) ).
thf(1609,plain,
( ~ ( v1_xboole_0 @ sk2 )
| ( l1_orders_2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1608:[bind(A,$thf( sk2 ))]]) ).
thf(49,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_latsum_1) ).
thf(228,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
& ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(57,plain,
m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ),
inference(cnf,[status(esa)],[50]) ).
thf(27,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(164,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)],[27]) ).
thf(13,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(114,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(115,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[114]) ).
thf(116,plain,
~ ( v1_xboole_0 @ sk9 ),
inference(cnf,[status(esa)],[115]) ).
thf(237,plain,
( ( v1_xboole_0 @ sk9 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[123,116]) ).
thf(238,plain,
sk9 != k1_xboole_0,
inference(simp,[status(thm)],[237]) ).
thf(25,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r4_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
thf(147,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r4_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( C = D ) )
=> ( r4_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[96]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ( ( r2_hidden @ B @ A )
!= ( r2_hidden @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[97]) ).
thf(279,plain,
! [A: $i] :
~ ( r2_hidden @ A @ A ),
inference(pattern_uni,[status(thm)],[278:[bind(A,$thf( B ))]]) ).
thf(280,plain,
! [A: $i] :
~ ( r2_hidden @ A @ A ),
inference(simp,[status(thm)],[279]) ).
thf(46,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( 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 ) )
& ( r1_latsum_1 @ A @ B )
& ( v3_orders_2 @ B ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_latsum_1) ).
thf(221,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( 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 ) )
& ( r1_latsum_1 @ A @ B )
& ( v3_orders_2 @ B ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(54,plain,
v4_orders_2 @ sk1,
inference(cnf,[status(esa)],[50]) ).
thf(231,plain,
( ( v4_orders_2 @ ( k1_latsum_1 @ sk1 @ sk2 ) )
!= ( v4_orders_2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[54,52]) ).
thf(233,plain,
( ( k1_latsum_1 @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[231]) ).
thf(14,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(117,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)],[14]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ A )
| ~ ( sk3 @ A @ B @ C )
| ( C
= ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ A )
| ~ ( sk3 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ A )
| ~ ( sk3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[84]) ).
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(201,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(197,plain,
! [A: $i] : ( m1_subset_1 @ ( sk15 @ A ) @ A ),
inference(cnf,[status(esa)],[196]) ).
thf(7,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(98,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk7 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[98]) ).
thf(3,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(63,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)],[3]) ).
thf(64,plain,
( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(miniscope,[status(thm)],[63]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_relset_1 @ C @ A @ B )
| ( m2_relset_1 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[64]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_relset_1 @ C @ A @ B )
| ( m2_relset_1 @ C @ A @ B ) ),
inference(simp,[status(thm)],[65]) ).
thf(283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( m2_relset_1 @ E @ C @ D )
| ( ( m1_relset_1 @ ( sk7 @ B @ A ) @ A @ B )
!= ( m1_relset_1 @ E @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[99,67]) ).
thf(284,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk7 @ A @ B ) @ B @ A ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( sk7 @ F @ G ))]]) ).
thf(285,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk7 @ A @ B ) @ B @ A ),
inference(simp,[status(thm)],[284]) ).
thf(53,plain,
r1_latsum_1 @ sk1 @ sk2,
inference(cnf,[status(esa)],[50]) ).
thf(23,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(141,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( m1_relset_1 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[64]) ).
thf(861,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( m1_relset_1 @ E @ C @ D )
| ( ( m2_relset_1 @ ( sk7 @ A @ B ) @ B @ A )
!= ( m2_relset_1 @ E @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[285,66]) ).
thf(862,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk7 @ A @ B ) @ B @ A ),
inference(pattern_uni,[status(thm)],[861:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( sk7 @ F @ G ))]]) ).
thf(869,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk7 @ A @ B ) @ B @ A ),
inference(simp,[status(thm)],[862]) ).
thf(55,plain,
m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ),
inference(cnf,[status(esa)],[50]) ).
thf(527,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( ( k3_xboole_0 @ k1_xboole_0 @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,55]) ).
thf(549,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(554,plain,
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[549]) ).
thf(36,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(193,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)],[36]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(124,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,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)],[48]) ).
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(205,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(206,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(cnf,[status(esa)],[205]) ).
thf(207,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[206]) ).
thf(262,plain,
! [A: $i] :
( ( v12_waybel_0 @ A @ sk2 )
| ( ( k3_xboole_0 @ A @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[207,61]) ).
thf(270,plain,
! [A: $i] :
( ( v12_waybel_0 @ A @ sk2 )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(274,plain,
( ( v12_waybel_0 @ ( u1_struct_0 @ sk1 ) @ sk2 )
| ( ( u1_struct_0 @ sk2 )
!= ( u1_struct_0 @ sk1 ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(1150,plain,
( ( v12_waybel_0 @ ( u1_struct_0 @ sk1 ) @ sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[274]) ).
thf(28,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(173,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)],[28]) ).
thf(20,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(134,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(62,plain,
v13_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) @ sk1,
inference(cnf,[status(esa)],[50]) ).
thf(261,plain,
! [A: $i] :
( ( v13_waybel_0 @ A @ sk1 )
| ( ( k3_xboole_0 @ A @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[207,62]) ).
thf(267,plain,
! [A: $i] :
( ( v13_waybel_0 @ A @ sk1 )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(271,plain,
( ( v13_waybel_0 @ ( u1_struct_0 @ sk1 ) @ sk1 )
| ( ( u1_struct_0 @ sk2 )
!= ( u1_struct_0 @ sk1 ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(343,plain,
( ( v13_waybel_0 @ ( u1_struct_0 @ sk1 ) @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[271]) ).
thf(526,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( ( k3_xboole_0 @ k1_xboole_0 @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,57]) ).
thf(552,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[526]) ).
thf(558,plain,
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[552]) ).
thf(29,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(175,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(176,plain,
l1_orders_2 @ sk13,
inference(cnf,[status(esa)],[175]) ).
thf(35,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(191,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)],[35]) ).
thf(135,plain,
l1_struct_0 @ sk10,
inference(cnf,[status(esa)],[134]) ).
thf(1534,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[129,135]) ).
thf(1535,plain,
( ~ ( v1_xboole_0 @ sk10 )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1534:[bind(A,$thf( sk10 ))]]) ).
thf(59,plain,
l1_orders_2 @ sk1,
inference(cnf,[status(esa)],[50]) ).
thf(24,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(144,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)],[24]) ).
thf(1674,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_orders_2 @ k1_xboole_0 )
| ( A != sk13 ) ),
inference(paramod_ordered,[status(thm)],[129,176]) ).
thf(1675,plain,
( ~ ( v1_xboole_0 @ sk13 )
| ( l1_orders_2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1674:[bind(A,$thf( sk13 ))]]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(112,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(113,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(cnf,[status(esa)],[112]) ).
thf(239,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( ( k3_xboole_0 @ A @ k1_xboole_0 )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[183,57]) ).
thf(242,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[239]) ).
thf(245,plain,
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[242]) ).
thf(42,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
& ( r1_latsum_1 @ A @ B )
& ( v3_orders_2 @ A ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_latsum_1) ).
thf(208,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( l1_orders_2 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
& ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
& ( r1_latsum_1 @ A @ B )
& ( v3_orders_2 @ A ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,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)],[5]) ).
thf(95,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk6 @ B @ A ) @ A @ B ),
inference(cnf,[status(esa)],[94]) ).
thf(275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( m1_relset_1 @ E @ C @ D )
| ( ( m2_relset_1 @ ( sk6 @ B @ A ) @ A @ B )
!= ( m2_relset_1 @ E @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[95,66]) ).
thf(276,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk6 @ A @ B ) @ B @ A ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( sk6 @ F @ G ))]]) ).
thf(277,plain,
! [B: $i,A: $i] : ( m1_relset_1 @ ( sk6 @ A @ B ) @ B @ A ),
inference(simp,[status(thm)],[276]) ).
thf(852,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( m2_relset_1 @ E @ C @ D )
| ( ( m1_relset_1 @ ( sk6 @ A @ B ) @ B @ A )
!= ( m1_relset_1 @ E @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[277,67]) ).
thf(853,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk6 @ A @ B ) @ B @ A ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( sk6 @ F @ G ))]]) ).
thf(858,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ ( sk6 @ A @ B ) @ B @ A ),
inference(simp,[status(thm)],[853]) ).
thf(38,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v4_orders_2 @ A )
<=> ( r4_relat_2 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
thf(198,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v4_orders_2 @ A )
=> ( r4_relat_2 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) ) )
& ( ( r4_relat_2 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) )
=> ( v4_orders_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(19,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(130,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(47,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)],[47]) ).
thf(26,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(162,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)],[26]) ).
thf(537,plain,
! [A: $i] :
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( ( k3_xboole_0 @ k1_xboole_0 @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,61]) ).
thf(551,plain,
! [A: $i] :
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[537]) ).
thf(557,plain,
( ( v12_waybel_0 @ k1_xboole_0 @ sk2 )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[551]) ).
thf(30,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v12_waybel_0 @ B @ A )
& ( v13_waybel_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(177,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v12_waybel_0 @ B @ A )
& ( v13_waybel_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(248,plain,
! [A: $i] :
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( ( k3_xboole_0 @ A @ k1_xboole_0 )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[183,62]) ).
thf(249,plain,
! [A: $i] :
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[249]) ).
thf(528,plain,
! [A: $i] :
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( ( k3_xboole_0 @ k1_xboole_0 @ A )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[511,62]) ).
thf(550,plain,
! [A: $i] :
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 )
| ( A
!= ( u1_struct_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[528]) ).
thf(556,plain,
( ( v13_waybel_0 @ k1_xboole_0 @ sk1 )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[550]) ).
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(203,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(45,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(218,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)],[45]) ).
thf(240,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( ( k3_xboole_0 @ A @ k1_xboole_0 )
!= ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[183,55]) ).
thf(243,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( A
!= ( u1_struct_0 @ sk1 ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[240]) ).
thf(246,plain,
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk1 ) ) )
| ( ( u1_struct_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[243]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k2_xboole_0 @ B @ A )
= C )
| ( ( k2_xboole_0 @ A @ B )
!= ( k2_xboole_0 @ C @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[143,109]) ).
thf(287,plain,
! [A: $i] :
( ( k2_xboole_0 @ k1_xboole_0 @ A )
= A ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(51,plain,
v3_orders_2 @ sk2,
inference(cnf,[status(esa)],[50]) ).
thf(43,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(210,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)],[43]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( sk3 @ A @ B @ C )
| ~ ( r2_hidden @ ( sk5 @ C @ B @ A ) @ C )
| ( C
= ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ( sk3 @ A @ B @ C )
| ~ ( r2_hidden @ ( sk5 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ( sk3 @ A @ B @ C )
| ~ ( r2_hidden @ ( sk5 @ C @ B @ A ) @ C ) ),
inference(simp,[status(thm)],[78]) ).
thf(194,plain,
~ ? [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
& ? [C: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ) ),
inference(miniscope,[status(thm)],[193]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
| ~ ( v1_xboole_0 @ C ) ),
inference(cnf,[status(esa)],[194]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ A @ B )
| ~ ( v1_xboole_0 @ C )
| ( ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk2 ) ) )
!= ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,195]) ).
thf(326,plain,
! [A: $i] :
( ~ ( r2_hidden @ A @ ( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) ) )
| ~ ( v1_xboole_0 @ ( u1_struct_0 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( A )),bind(B,$thf( k3_xboole_0 @ ( u1_struct_0 @ sk1 ) @ ( u1_struct_0 @ sk2 ) )),bind(C,$thf( u1_struct_0 @ sk2 ))]]) ).
thf(125,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[125]) ).
thf(21,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(136,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)],[21]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ B )
| ~ ( sk3 @ A @ B @ C )
| ( C
= ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ B )
| ~ ( sk3 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
| ~ ( r2_hidden @ ( sk4 @ C @ B @ A ) @ B )
| ~ ( sk3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[82]) ).
thf(8,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(100,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)],[8]) ).
thf(107809,plain,
$false,
inference(cvc4,[status(thm)],[56,1900,138,234,217,511,120,247,52,184,110,1511,196,189,1609,228,57,164,238,147,280,61,221,116,233,60,117,85,201,252,197,97,285,53,141,869,109,554,193,96,124,225,1150,173,129,134,343,105,205,558,176,191,1535,59,54,144,181,1675,187,113,274,81,245,98,271,208,858,66,198,130,223,135,162,112,123,557,63,95,50,67,177,127,143,1585,175,250,99,556,203,218,55,114,58,246,207,287,51,183,210,79,195,94,326,107,126,136,68,62,277,122,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU414+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n001.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 : Thu May 18 12:58:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.97/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.99 % [INFO] Parsing done (144ms).
% 1.45/1.00 % [INFO] Running in sequential loop mode.
% 1.80/1.19 % [INFO] eprover registered as external prover.
% 1.80/1.20 % [INFO] cvc4 registered as external prover.
% 1.80/1.20 % [INFO] Scanning for conjecture ...
% 1.99/1.27 % [INFO] Found a conjecture and 57 axioms. Running axiom selection ...
% 2.10/1.33 % [INFO] Axiom selection finished. Selected 47 axioms (removed 10 axioms).
% 2.42/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.40 % [INFO] Type checking passed.
% 2.42/1.40 % [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 ...
% 192.63/37.18 % External prover 'cvc4' found a proof!
% 192.63/37.18 % [INFO] Killing All external provers ...
% 192.86/37.19 % Time passed: 36682ms (effective reasoning time: 36194ms)
% 192.86/37.19 % 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)>
% 192.86/37.20 % Axioms used in derivation (47): redefinition_m2_relset_1, t2_boole, dt_k1_latsum_1, t6_boole, existence_m1_relset_1, t21_latsum_1, dt_g1_orders_2, abstractness_v1_orders_2, existence_m2_relset_1, dt_l1_orders_2, redefinition_k7_relset_1, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, t1_boole, fc1_xboole_0, t1_subset, dt_k7_relset_1, d6_orders_2, 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_subset, d2_xboole_0, fc3_xboole_0, t4_latsum_1, 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, t8_boole, rc1_xboole_0, existence_l1_struct_0, t5_latsum_1, rc7_waybel_0, d4_relat_2, d2_latsum_1
% 192.86/37.20 % No. of inferences in proof: 235
% 192.86/37.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36682 ms resp. 36194 ms w/o parsing
% 192.91/37.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 192.91/37.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------