%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG225+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:22 AM UTC 2026
% Result : Theorem 138.83s 38.18s
% Output : Refutation 140.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 402
% Syntax : Number of formulae : 1954 ( 517 unt; 0 typ; 17 def)
% Number of atoms : 5888 (1554 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 21379 (2128 ~;1114 |; 742 &;15726 @)
% ( 60 <=>;1609 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 75 usr; 15 con; 0-4 aty)
% Number of variables : 3619 ( 11 ^;3516 !; 75 ?;3619 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v2_relat_1_decl,type,
v2_relat_1: $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(k1_pboole_decl,type,
k1_pboole: $i > $i ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(k1_closure3_decl,type,
k1_closure3: $i > $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(r6_pboole_decl,type,
r6_pboole: $i > $i > $i > $o ).
thf(k2_mboolean_decl,type,
k2_mboolean: $i > $i > $i ).
thf(k2_pre_circ_decl,type,
k2_pre_circ: $i > $i > $i ).
thf(k1_mboolean_decl,type,
k1_mboolean: $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k4_pboole_decl,type,
k4_pboole: $i > $i > $i > $i ).
thf(k2_pboole_decl,type,
k2_pboole: $i > $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k3_pboole_decl,type,
k3_pboole: $i > $i > $i > $i ).
thf(r5_pboole_decl,type,
r5_pboole: $i > $i > $i > $o ).
thf(k5_pboole_decl,type,
k5_pboole: $i > $i > $i > $i ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(r2_pboole_decl,type,
r2_pboole: $i > $i > $i > $o ).
thf(v1_pre_circ_decl,type,
v1_pre_circ: $i > $i > $o ).
thf(k4_zfmisc_1_decl,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(r1_pboole_decl,type,
r1_pboole: $i > $i > $i > $o ).
thf(r4_pboole_decl,type,
r4_pboole: $i > $i > $i > $o ).
thf(k10_funct_6_decl,type,
k10_funct_6: $i > $i ).
thf(r2_subset_1_decl,type,
r2_subset_1: $i > $i > $o ).
thf(m1_finseq_2_decl,type,
m1_finseq_2: $i > $i > $o ).
thf(m2_finseq_2_decl,type,
m2_finseq_2: $i > $i > $i > $o ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(r1_subset_1_decl,type,
r1_subset_1: $i > $i > $o ).
thf(k11_pboole_decl,type,
k11_pboole: $i > $i > $i > $i ).
thf(k3_numbers_decl,type,
k3_numbers: $i ).
thf(k2_numbers_decl,type,
k2_numbers: $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(m3_pboole_decl,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(r3_pboole_decl,type,
r3_pboole: $i > $i > $i > $o ).
thf(r7_pboole_decl,type,
r7_pboole: $i > $i > $i > $o ).
thf(v3_relat_1_decl,type,
v3_relat_1: $i > $o ).
thf(k12_pboole_decl,type,
k12_pboole: $i > $i > $i > $i ).
thf(a_2_1_closure3_decl,type,
a_2_1_closure3: $i > $i > $i ).
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
thf(m2_pboole_decl,type,
m2_pboole: $i > $i > $i > $o ).
thf(a_2_0_closure3_decl,type,
a_2_0_closure3: $i > $i > $i ).
thf(v2_pboole_decl,type,
v2_pboole: $i > $i > $o ).
thf(v1_pboole_decl,type,
v1_pboole: $i > $i > $o ).
thf(f1_s2_pboole_decl,type,
f1_s2_pboole: $i ).
thf(f2_s2_pboole_decl,type,
f2_s2_pboole: $i ).
thf(p1_s2_pboole_decl,type,
p1_s2_pboole: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk39_decl,type,
sk39: $i ).
thf(sk57_decl,type,
sk57: $i > $i ).
thf(sk79_decl,type,
sk79: $i > $i ).
thf(sk80_decl,type,
sk80: $i ).
thf(sk82_decl,type,
sk82: $i ).
thf(sk83_decl,type,
sk83: $i > $i ).
thf(sk84_decl,type,
sk84: $i ).
thf(sk86_decl,type,
sk86: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( B
= ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( sk1 @ ( A @ m1_pboole ) )
& ( A @ v2_relat_1 ) )
=> ( A
= ( A @ ( sk1 @ k1_closure3 ) @ ( A @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C != A )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( @+[A: $i] :
~ ( A @ v2_setfam_1 ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_finseq_2 ) ) ) ) ).
thf(sk79_def,definition,
( sk79
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk82_def,definition,
( sk82
= ( @+[A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk83_def,definition,
( sk83
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_pboole ) ) ) ) ).
thf(sk84_def,definition,
( sk84
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ( ! [C: $i] :
( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ) ) ) ).
thf(sk86_def,definition,
( sk86
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(148,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(892,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(37,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(541,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(542,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[541]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(486,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[486]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[487]) ).
thf(228,axiom,
k3_numbers != k2_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_numbers) ).
thf(1177,plain,
k3_numbers != k2_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1178,plain,
k3_numbers != k2_numbers,
inference(polarity_switch,[status(thm)],[1177]) ).
thf(1179,plain,
k2_numbers != k3_numbers,
inference(lifteq,[status(thm)],[1178]) ).
thf(19195,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k3_numbers )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1179]) ).
thf(19196,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( k2_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19195:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(21335,plain,
~ ( k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19196]) ).
thf(24750,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21335]) ).
thf(24751,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[24750]) ).
thf(24863,plain,
! [A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( ( k3_numbers @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[24751]) ).
thf(24878,plain,
( ( k3_numbers @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24863]) ).
thf(361,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(1716,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1717,plain,
( ( sk82 @ v1_setfam_1 )
& ~ ( sk82 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1716]) ).
thf(1718,plain,
~ ( sk82 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1717]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
| ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_mboolean) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
| ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(1024,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(225,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(1167,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1168,plain,
! [A: $i] : ( A @ ( A @ sk25 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[1167]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
<=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
& ( C @ ( E @ ( A @ r2_pboole ) ) ) )
=> ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_pboole) ).
thf(1633,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
& ( C @ ( E @ ( A @ r2_pboole ) ) ) )
=> ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
& ( C @ ( E @ ( A @ r2_pboole ) ) ) )
=> ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mboolean) ).
thf(1767,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(1105,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(365,axiom,
~ ( k3_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_numbers) ).
thf(1729,plain,
~ ( k3_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(63,axiom,
! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_mboolean) ).
thf(628,plain,
! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(403,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(404,plain,
~ ? [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(miniscope,[status(thm)],[403]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( ( ( A @ ( B @ sk3 ) )
!= B )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) )
& ( ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[405]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[406]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(431,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(432,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[431]) ).
thf(433,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk4 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( F @ ( E @ ( F @ sk4 ) @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
| ( D != A )
| ( B
!= ( A @ k1_tarski ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k1_tarski ) ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(441,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[440]) ).
thf(1719,plain,
sk82 @ v1_setfam_1,
inference(cnfConj,[status(thm)],[1717]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
<=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(756,plain,
! [A: $i] :
( ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v1_setfam_1 ) )
& ( ( A @ v1_setfam_1 )
=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(757,plain,
( ! [A: $i] :
( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v1_setfam_1 ) )
& ! [A: $i] :
( ( A @ v1_setfam_1 )
=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[756]) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_setfam_1 )
| ( B @ ( k1_xboole_0 @ r2_hidden ) ) )
& ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( A @ v1_setfam_1 ) ) ),
inference(cnf,[status(esa)],[757]) ).
thf(759,plain,
! [A: $i] :
( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
| ~ ( A @ v1_setfam_1 ) ),
inference(cnfConj,[status(thm)],[758]) ).
thf(2286,plain,
! [A: $i] :
( ( ( sk82 @ v1_setfam_1 )
!= ( A @ v1_setfam_1 ) )
| ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1719,759]) ).
thf(2287,plain,
! [A: $i] :
( ( ( sk82 @ v1_setfam_1 )
!= ( A @ v1_setfam_1 ) )
| ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[2286]) ).
thf(2288,plain,
~ ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[2287:[bind(A,$thf( sk82 ))]]) ).
thf(3230,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,2288]) ).
thf(3231,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[3230]) ).
thf(3240,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= sk82 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[3231]) ).
thf(3249,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk82 ),
inference(simp,[status(thm)],[3240]) ).
thf(3275,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk82 )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[408,3249]) ).
thf(3276,plain,
! [A: $i] :
( ( A != sk82 )
| ( A @ ( A @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3275:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(3289,plain,
( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
| ( sk82 = k1_xboole_0 ) ),
inference(simp,[status(thm)],[3276]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(936,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(937,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[936]) ).
thf(938,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[937]) ).
thf(940,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[938]) ).
thf(942,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[940]) ).
thf(943,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[942]) ).
thf(1819,plain,
( ( ( sk82 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,1718]) ).
thf(1820,plain,
( ( sk82 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1819]) ).
thf(1822,plain,
sk82 != k1_xboole_0,
inference(simp,[status(thm)],[1820]) ).
thf(3356,plain,
sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ),
inference(simplifyReflect,[status(thm)],[3289,1822]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(400,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
| ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[401]) ).
thf(3362,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ $true
| ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3356,402]) ).
thf(3363,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(simp,[status(thm)],[3362]) ).
thf(3364,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[3363:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) )),bind(B,$thf( sk82 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(394,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ r2_hidden ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ r2_hidden ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(3223,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[396,2288]) ).
thf(3224,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(simp,[status(thm)],[3223]) ).
thf(3225,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[3224:[bind(A,$thf( sk82 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(4744,plain,
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k3_xboole_0 ) ) )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3364,3225]) ).
thf(4787,plain,
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk82 != sk82 )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[4744]) ).
thf(4820,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[4787]) ).
thf(4877,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[408,4820]) ).
thf(4878,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ ( A @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[4877:[bind(A,$thf( A )),bind(B,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) ))]]) ).
thf(4920,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) @ r2_hidden ) )
| ( ( k1_xboole_0 @ k1_tarski )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[4878]) ).
thf(91,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(714,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(715,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[714]) ).
thf(716,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[715]) ).
thf(3318,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k3_xboole_0 ) ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[716,3225]) ).
thf(3319,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 )
| ( A != sk82 )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[3318]) ).
thf(3332,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[3319]) ).
thf(5080,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) @ r2_hidden ),
inference(simplifyReflect,[status(thm)],[4920,3332]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
| ( C = A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[437]) ).
thf(451,plain,
! [B: $i,A: $i] :
( ~ ( A @ k1_tarski @ ( B @ r2_hidden ) )
| ( B = A ) ),
inference(simp,[status(thm)],[450]) ).
thf(8281,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) @ r2_hidden ) )
!= ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[5080,451]) ).
thf(8282,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) @ r2_hidden ) )
!= ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[8281]) ).
thf(8283,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[8282:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ sk3 ) ))]]) ).
thf(893,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[892]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ v2_setfam_1 )
<=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_setfam_1) ).
thf(1554,plain,
! [A: $i] :
( ( ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v2_setfam_1 ) )
& ( ( A @ v2_setfam_1 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(3365,plain,
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3356,2288]) ).
thf(3366,plain,
( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( sk82 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[3365]) ).
thf(3388,plain,
( ( sk82 != sk82 )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[3366]) ).
thf(3399,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[3388]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( B
= ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( B
= ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(387,plain,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( B
= ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(388,plain,
( ( sk2
!= ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) )
& ( sk1 @ ( sk2 @ m1_pboole ) )
& ( sk2 @ v2_relat_1 )
& ~ ( sk1 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
~ ( sk1 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[388]) ).
thf(1798,plain,
( ( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,389]) ).
thf(1799,plain,
( ( sk1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1798]) ).
thf(1802,plain,
sk1 != k1_xboole_0,
inference(simp,[status(thm)],[1799]) ).
thf(20665,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1802]) ).
thf(20666,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20665:[bind(A,$thf( sk1 ))]]) ).
thf(21164,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20666]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(587,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(miniscope,[status(thm)],[586]) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) ) )
& ( ( A @ ( B @ r1_tarski ) )
| ( A != B ) )
& ( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[587]) ).
thf(589,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[588]) ).
thf(592,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[589]) ).
thf(593,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[592]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(583,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(584,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[583]) ).
thf(585,plain,
! [A: $i] :
( ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[584]) ).
thf(96,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(725,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(726,plain,
( ( sk10 @ v1_finset_1 )
& ~ ( sk10 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[725]) ).
thf(727,plain,
~ ( sk10 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[726]) ).
thf(1800,plain,
( ( ( sk10 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,727]) ).
thf(1801,plain,
( ( sk10 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1803,plain,
sk10 != k1_xboole_0,
inference(simp,[status(thm)],[1801]) ).
thf(64839,plain,
! [A: $i] :
( ( A != sk10 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[585,1803]) ).
thf(64840,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[64839]) ).
thf(64841,plain,
~ ( sk10 @ ( sk10 @ k2_zfmisc_1 ) @ ( sk10 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[64840:[bind(A,$thf( sk10 ))]]) ).
thf(75928,plain,
! [A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( sk10 @ ( sk10 @ k2_zfmisc_1 ) @ ( sk10 @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,64841]) ).
thf(75929,plain,
! [A: $i] :
( ( A @ ( A @ r1_tarski ) )
!= ( sk10 @ ( sk10 @ k2_zfmisc_1 ) @ ( sk10 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[75928]) ).
thf(76061,plain,
! [A: $i] :
( ( A
!= ( sk10 @ ( sk10 @ k2_zfmisc_1 ) ) )
| ( A != sk10 ) ),
inference(simp,[status(thm)],[75929]) ).
thf(76079,plain,
( ( sk10 @ ( sk10 @ k2_zfmisc_1 ) )
!= sk10 ),
inference(simp,[status(thm)],[76061]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_pboole) ).
thf(517,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[517]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r1_subset_1) ).
thf(1686,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(478,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(479,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[478]) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ k1_tarski @ r1_tarski ) )
| ~ ( D @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
| ~ ( B @ ( A @ k1_tarski @ r1_tarski ) ) ) ),
inference(cnf,[status(esa)],[479]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2_hidden ) )
| ~ ( B @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[480]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r7_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_pboole) ).
thf(1200,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r1_pboole ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r7_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r1_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k4_pboole ) ) @ ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mboolean) ).
thf(1005,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k4_pboole ) ) @ ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(1068,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[455]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[456]) ).
thf(11087,plain,
! [B: $i,A: $i] :
( ( A != sk82 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1822]) ).
thf(11088,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk82 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11087:[bind(A,$thf( sk82 ))]]) ).
thf(11571,plain,
k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11088]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_pboole) ).
thf(1443,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pboole) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
<=> ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_mboolean) ).
thf(741,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
& ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(1142,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(510,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ r1_tarski ) )
| ~ ( C @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[510]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_pboole) ).
thf(677,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[588]) ).
thf(596,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[591]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) )
| ( A = B ) ),
inference(simp,[status(thm)],[596]) ).
thf(8030,plain,
! [B: $i,A: $i] :
( ( B != sk10 )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1803]) ).
thf(8031,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk10 @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8030:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(9302,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk10 @ r2_hidden ) ),
inference(simp,[status(thm)],[8031]) ).
thf(12139,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9302]) ).
thf(12140,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12139]) ).
thf(12158,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk10 ) ),
inference(simp,[status(thm)],[12140]) ).
thf(12181,plain,
( ( sk10 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[12158]) ).
thf(14359,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,12181]) ).
thf(14360,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14359:[bind(A,$thf( sk10 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14399,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14360]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1045,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1046,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[1045]) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1046]) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1047]) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1049]) ).
thf(1053,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1052]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ! [C: $i,D: $i] : ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ! [C: $i,D: $i] : ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[413]) ).
thf(415,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ k1_tarski @ ( F @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( E @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) )
& ( ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[414]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[415]) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ),
inference(simp,[status(thm)],[419]) ).
thf(349,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(1689,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(1690,plain,
sk80 @ v1_xboole_0,
inference(cnf,[status(esa)],[1689]) ).
thf(1808,plain,
( ( ( sk80 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1690,389]) ).
thf(1809,plain,
( ( sk80 @ v1_xboole_0 )
!= ( sk1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1808]) ).
thf(1814,plain,
sk80 != sk1,
inference(simp,[status(thm)],[1809]) ).
thf(3750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != sk80 )
| ( B != sk1 )
| ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[420,1814]) ).
thf(3751,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( sk80 @ k1_tarski @ ( B @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[3750:[bind(A,$thf( sk80 ))]]) ).
thf(4293,plain,
! [B: $i,A: $i] : ( sk1 @ k1_tarski @ ( B @ k2_zfmisc_1 ) @ ( sk80 @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[3751]) ).
thf(12,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(452,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(453,plain,
~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[452]) ).
thf(454,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnf,[status(esa)],[453]) ).
thf(1838,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1690,454]) ).
thf(1839,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1842,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk80 ),
inference(simp,[status(thm)],[1839]) ).
thf(1929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ k1_tarski )
!= ( C @ k1_tarski ) )
| ( A != sk80 )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[408,1842]) ).
thf(1930,plain,
! [B: $i,A: $i] :
( ( A != sk80 )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1982,plain,
! [A: $i] :
( ( sk80 @ ( sk80 @ ( A @ sk3 ) @ r2_hidden ) )
| ( sk80 = k1_xboole_0 ) ),
inference(simp,[status(thm)],[1930]) ).
thf(324,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(1599,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1600,plain,
~ ? [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[1599]) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ~ ( B @ v1_xboole_0 )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1600]) ).
thf(7411,plain,
! [B: $i,A: $i] :
( ( ( sk80 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[1690,1601]) ).
thf(7412,plain,
! [B: $i,A: $i] :
( ( ( sk80 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[7411]) ).
thf(7413,plain,
! [A: $i] :
~ ( sk80 @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[7412:[bind(A,$thf( A )),bind(B,$thf( sk80 ))]]) ).
thf(7601,plain,
( $false
| ( sk80 = k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[1982,7413]) ).
thf(7602,plain,
sk80 = k1_xboole_0,
inference(simp,[status(thm)],[7601]) ).
thf(7782,plain,
! [B: $i,A: $i] : ( sk1 @ k1_tarski @ ( B @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(rewrite,[status(thm)],[4293,7602]) ).
thf(7841,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( k1_xboole_0 @ k1_tarski @ ( B @ k2_zfmisc_1 ) ) )
| ( sk1 @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1053,7782]) ).
thf(7842,plain,
! [A: $i] : ( sk1 @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(7886,plain,
! [A: $i] : ( sk1 @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[7842]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_pboole) ).
thf(762,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ~ ( ( C @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( D @ ( E @ ( A @ r2_pboole ) ) )
& ( A @ ( E @ v1_pre_circ ) ) ) )
& ( C @ ( D @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( A @ ( C @ v1_pre_circ ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_mssubfam) ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ~ ( ( C @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( D @ ( E @ ( A @ r2_pboole ) ) )
& ( A @ ( E @ v1_pre_circ ) ) ) )
& ( C @ ( D @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( A @ ( C @ v1_pre_circ ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(19365,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1803]) ).
thf(19366,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19365:[bind(A,$thf( sk10 ))]]) ).
thf(21393,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19366]) ).
thf(24990,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21393]) ).
thf(24991,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[24990]) ).
thf(25105,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk10 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[24991]) ).
thf(25115,plain,
( ( sk10 @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25105]) ).
thf(25186,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,25115]) ).
thf(25187,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk10 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[25186:[bind(A,$thf( sk10 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(25211,plain,
~ ( sk10 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[25187]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pboole) ).
thf(873,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(lifteq,[status(thm)],[438]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[448]) ).
thf(8018,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk82 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3249]) ).
thf(8019,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8018:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(9297,plain,
~ ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[8019]) ).
thf(15213,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9297]) ).
thf(15214,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[15213]) ).
thf(15234,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( sk82 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[15214]) ).
thf(15239,plain,
( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( sk82 @ k1_tarski ) ),
inference(simp,[status(thm)],[15234]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_pboole) ).
thf(1041,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pboole) ).
thf(1705,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(384,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B
= ( A @ k1_pboole ) )
& ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_pboole) ).
thf(1788,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B
= ( A @ k1_pboole ) )
& ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(25166,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,25115]) ).
thf(25167,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[25166:[bind(A,$thf( sk10 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(25204,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[25167]) ).
thf(8829,plain,
! [B: $i,A: $i] :
( ( B != sk82 )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1822]) ).
thf(8830,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8829:[bind(A,$thf( A )),bind(B,$thf( sk82 ))]]) ).
thf(9195,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ r2_hidden ) ),
inference(simp,[status(thm)],[8830]) ).
thf(11739,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9195]) ).
thf(11740,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11739]) ).
thf(11758,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk82 ) ),
inference(simp,[status(thm)],[11740]) ).
thf(11779,plain,
( ( sk82 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[11758]) ).
thf(14233,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,11779]) ).
thf(14234,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14233:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski ))]]) ).
thf(14264,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14234]) ).
thf(8727,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1802]) ).
thf(8728,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8727:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(9158,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ r2_hidden ) ),
inference(simp,[status(thm)],[8728]) ).
thf(9397,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ r2_hidden ) ) )
| ~ $true
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[396,9158]) ).
thf(9398,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ r2_hidden ) ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(simp,[status(thm)],[9397]) ).
thf(9399,plain,
( ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k3_xboole_0 ) )
!= ( sk1 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[9398:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( sk1 ))]]) ).
thf(16602,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
!= ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k3_xboole_0 ) ) )
| ( ( sk1 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[716,9399]) ).
thf(16608,plain,
! [A: $i] :
( ( ( sk1 @ k1_tarski )
!= k1_xboole_0 )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk1 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[16602]) ).
thf(16643,plain,
( ( sk1 @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16608]) ).
thf(16747,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,16643]) ).
thf(16748,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[16747:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(16777,plain,
k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[16748]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(346,axiom,
~ ( k2_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_numbers) ).
thf(1682,plain,
~ ( k2_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1683,plain,
~ ( k2_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[1682]) ).
thf(1805,plain,
( ( ( k2_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,1683]) ).
thf(1806,plain,
( ( k2_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1805]) ).
thf(1807,plain,
k2_numbers != k1_xboole_0,
inference(simp,[status(thm)],[1806]) ).
thf(20805,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1807]) ).
thf(20806,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20805:[bind(A,$thf( k2_numbers ))]]) ).
thf(21210,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20806]) ).
thf(22531,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21210]) ).
thf(22532,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22531]) ).
thf(22644,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( k2_numbers @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[22532]) ).
thf(22680,plain,
( ( k2_numbers @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[22644]) ).
thf(23398,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,22680]) ).
thf(23399,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23398:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23440,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23399]) ).
thf(37489,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,23440]) ).
thf(37490,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[37489]) ).
thf(37630,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( k2_numbers @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[37490]) ).
thf(37682,plain,
( ( k2_numbers @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[37630]) ).
thf(37753,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,37682]) ).
thf(37754,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[37753:[bind(A,$thf( k2_numbers @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(37798,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[37754]) ).
thf(1730,plain,
~ ( k3_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[1729]) ).
thf(1825,plain,
( ( ( k3_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,1730]) ).
thf(1826,plain,
( ( k3_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1825]) ).
thf(1828,plain,
k3_numbers != k1_xboole_0,
inference(simp,[status(thm)],[1826]) ).
thf(8102,plain,
! [B: $i,A: $i] :
( ( B != k3_numbers )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1828]) ).
thf(8103,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k3_numbers @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8102:[bind(A,$thf( A )),bind(B,$thf( k3_numbers ))]]) ).
thf(9332,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ r2_hidden ) ),
inference(simp,[status(thm)],[8103]) ).
thf(12571,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9332]) ).
thf(12572,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ r2_hidden ) ) ),
inference(simp,[status(thm)],[12571]) ).
thf(12589,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != k3_numbers ) ),
inference(simp,[status(thm)],[12572]) ).
thf(12606,plain,
( ( k3_numbers @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[12589]) ).
thf(14803,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,12606]) ).
thf(14804,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14803:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(14829,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14804]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(1233,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( A @ r2_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_pboole) ).
thf(1260,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( A @ r2_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(9418,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9158]) ).
thf(9419,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9418]) ).
thf(9438,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[9419]) ).
thf(9450,plain,
( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[9438]) ).
thf(10060,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9450]) ).
thf(10061,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[10060:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(10100,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[10061]) ).
thf(13046,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,10100]) ).
thf(13047,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[13046]) ).
thf(13074,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( sk1 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[13047]) ).
thf(13083,plain,
( ( sk1 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[13074]) ).
thf(64874,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[585,13083]) ).
thf(64875,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[64874]) ).
thf(64876,plain,
~ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[64875:[bind(A,$thf( sk1 ))]]) ).
thf(68434,plain,
! [A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,64876]) ).
thf(68435,plain,
! [A: $i] :
( ( A @ ( A @ r1_tarski ) )
!= ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[68434]) ).
thf(68559,plain,
! [A: $i] :
( ( A
!= ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[68435]) ).
thf(68589,plain,
( ( sk1 @ ( sk1 @ k2_zfmisc_1 ) )
!= sk1 ),
inference(simp,[status(thm)],[68559]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_mboolean) ).
thf(930,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_pboole) ).
thf(1458,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(20653,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,16643]) ).
thf(20654,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20653:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(21160,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20654]) ).
thf(22889,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21160]) ).
thf(22890,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22889]) ).
thf(23031,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk1 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[22890]) ).
thf(23076,plain,
( ( sk1 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[23031]) ).
thf(23137,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,23076]) ).
thf(23138,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23137:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski @ k1_tarski ))]]) ).
thf(23179,plain,
sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23138]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_pboole) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(500,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(374,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(1764,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1765,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[1764]) ).
thf(1766,plain,
~ ( sk86 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[1765]) ).
thf(1831,plain,
( ( ( sk86 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,1766]) ).
thf(1832,plain,
( ( sk86 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1834,plain,
sk86 != k1_xboole_0,
inference(simp,[status(thm)],[1832]) ).
thf(20773,plain,
! [B: $i,A: $i] :
( ( A != sk86 )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1834]) ).
thf(20774,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20773:[bind(A,$thf( sk86 ))]]) ).
thf(21200,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20774]) ).
thf(22126,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21200]) ).
thf(22127,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22126]) ).
thf(22238,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk86 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[22127]) ).
thf(22271,plain,
( ( sk86 @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[22238]) ).
thf(22318,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,22271]) ).
thf(22319,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[22318:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski ))]]) ).
thf(22347,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[22319]) ).
thf(41042,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,25204]) ).
thf(41043,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[41042]) ).
thf(41191,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk10 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[41043]) ).
thf(41228,plain,
( ( sk10 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[41191]) ).
thf(41304,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,41228]) ).
thf(41305,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[41304:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski @ k1_tarski ))]]) ).
thf(41334,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[41305]) ).
thf(7975,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3399]) ).
thf(7976,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7975:[bind(A,$thf( A )),bind(B,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) ))]]) ).
thf(9278,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) ),
inference(simp,[status(thm)],[7976]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_pboole) ).
thf(535,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
| ~ ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) )
& ( ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) )
| ~ ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[535]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
| ~ ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[536]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(560,plain,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(561,plain,
( ~ ? [A: $i] :
( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ? [A: $i] :
( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[560]) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( ~ ( B @ ( B @ r1_xboole_0 ) )
| ( B = k1_xboole_0 ) )
& ( ( A != k1_xboole_0 )
| ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[561]) ).
thf(564,plain,
! [A: $i] :
( ~ ( A @ ( A @ r1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[562]) ).
thf(567,plain,
! [A: $i] :
( ~ ( A @ ( A @ r1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[564]) ).
thf(568,plain,
! [A: $i] :
( ~ ( A @ ( A @ r1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[567]) ).
thf(8809,plain,
! [B: $i,A: $i] :
( ( B != sk86 )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1834]) ).
thf(8810,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk86 @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8809:[bind(A,$thf( A )),bind(B,$thf( sk86 ))]]) ).
thf(9188,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk86 @ r2_hidden ) ),
inference(simp,[status(thm)],[8810]) ).
thf(9595,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9188]) ).
thf(9596,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9595]) ).
thf(9616,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk86 ) ),
inference(simp,[status(thm)],[9596]) ).
thf(9625,plain,
( ( sk86 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[9616]) ).
thf(55869,plain,
! [A: $i] :
( ( A != sk86 )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,9625]) ).
thf(55870,plain,
! [A: $i] :
( ( A != sk86 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[55869]) ).
thf(55871,plain,
~ ( sk86 @ ( sk86 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[55870:[bind(A,$thf( sk86 ))]]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_pboole) ).
thf(1196,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_pboole) ).
thf(841,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(8729,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1802]) ).
thf(8730,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8729:[bind(A,$thf( sk1 ))]]) ).
thf(9159,plain,
~ ( sk1 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8730]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( B @ ( C @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_mssubfam) ).
thf(1650,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( B @ ( C @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_pboole) ).
thf(1359,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(363,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(1723,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1724,plain,
! [A: $i] : ( A @ ( A @ sk83 @ m1_pboole ) ),
inference(cnf,[status(esa)],[1723]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(1529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(651,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(202,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(1095,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(54,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_pboole) ).
thf(600,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(601,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[600]) ).
thf(602,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ ( A @ m1_pboole ) )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[601]) ).
thf(77890,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk83 @ m1_pboole ) )
!= ( k1_xboole_0 @ ( B @ m1_pboole ) ) )
| ~ $true
| ( B = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1724,602]) ).
thf(77891,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk83 @ m1_pboole ) )
!= ( k1_xboole_0 @ ( B @ m1_pboole ) ) )
| ( B = k1_xboole_0 ) ),
inference(simp,[status(thm)],[77890]) ).
thf(77892,plain,
( ( k1_xboole_0 @ sk83 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[77891:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 @ sk83 ))]]) ).
thf(7991,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k3_numbers )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1179]) ).
thf(7992,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( A @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7991:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(9284,plain,
~ ( k3_numbers @ k1_tarski @ ( k2_numbers @ r2_hidden ) ),
inference(simp,[status(thm)],[7992]) ).
thf(11939,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9284]) ).
thf(11940,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11939]) ).
thf(11957,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k3_numbers @ k1_tarski ) )
| ( A != k2_numbers ) ),
inference(simp,[status(thm)],[11940]) ).
thf(11979,plain,
( ( k2_numbers @ k1_tarski )
!= ( k3_numbers @ k1_tarski ) ),
inference(simp,[status(thm)],[11957]) ).
thf(14300,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A
!= ( k3_numbers @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,11979]) ).
thf(14301,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14300:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(14333,plain,
~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14301]) ).
thf(8821,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1807]) ).
thf(8822,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8821:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(9192,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ r2_hidden ) ),
inference(simp,[status(thm)],[8822]) ).
thf(9772,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9192]) ).
thf(9773,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ r2_hidden ) ) ),
inference(simp,[status(thm)],[9772]) ).
thf(9790,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != k2_numbers ) ),
inference(simp,[status(thm)],[9773]) ).
thf(9812,plain,
( ( k2_numbers @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[9790]) ).
thf(12797,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9812]) ).
thf(12798,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[12797:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(12833,plain,
k2_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[12798]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r1_subset_1 ) )
=> ( A @ ( B @ r1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_subset_1) ).
thf(1782,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r1_subset_1 ) )
=> ( A @ ( B @ r1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
| ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_pboole) ).
thf(782,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
| ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(285,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_2) ).
thf(1441,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(11079,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1807]) ).
thf(11080,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11079:[bind(A,$thf( k2_numbers ))]]) ).
thf(11568,plain,
k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11080]) ).
thf(23406,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,22680]) ).
thf(23407,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23406:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23443,plain,
k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23407]) ).
thf(55955,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,13083]) ).
thf(55956,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[55955]) ).
thf(55957,plain,
~ ( sk1 @ ( sk1 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[55956:[bind(A,$thf( sk1 ))]]) ).
thf(64794,plain,
! [A: $i] :
( ( A != sk86 )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[585,9625]) ).
thf(64795,plain,
! [A: $i] :
( ( A != sk86 )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[64794]) ).
thf(64796,plain,
~ ( sk86 @ ( sk86 @ k2_zfmisc_1 ) @ ( sk86 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[64795:[bind(A,$thf( sk86 ))]]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( A @ k1_pboole @ ( B @ ( A @ ( C @ m3_pboole ) ) ) )
=> ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_mssubfam) ).
thf(1703,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( A @ k1_pboole @ ( B @ ( A @ ( C @ m3_pboole ) ) ) )
=> ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ r1_pboole ) ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) )
& ( A @ ( B @ v1_pre_circ ) ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_mssubfam) ).
thf(1228,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ r1_pboole ) ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) )
& ( A @ ( B @ v1_pre_circ ) ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_pboole) ).
thf(1482,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(203,axiom,
k2_numbers @ ( k3_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_numbers) ).
thf(1098,plain,
k2_numbers @ ( k3_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(64962,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[585,12606]) ).
thf(64963,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(simp,[status(thm)],[64962]) ).
thf(64964,plain,
~ ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) @ ( k3_numbers @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[64963:[bind(A,$thf( k3_numbers ))]]) ).
thf(76909,plain,
( ( ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) @ ( k3_numbers @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,64964]) ).
thf(76910,plain,
( ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) @ ( k3_numbers @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[76909]) ).
thf(76947,plain,
( ( ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) )
!= k2_numbers )
| ( k3_numbers != k3_numbers ) ),
inference(simp,[status(thm)],[76910]) ).
thf(76966,plain,
( ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) )
!= k2_numbers ),
inference(simp,[status(thm)],[76947]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(569,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[569]) ).
thf(12741,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9625]) ).
thf(12742,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[12741:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski ))]]) ).
thf(12759,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[12742]) ).
thf(18400,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,12759]) ).
thf(18401,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[18400]) ).
thf(18425,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( sk86 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[18401]) ).
thf(18468,plain,
( ( sk86 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[18425]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( B @ ( D @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_pboole) ).
thf(719,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( B @ ( D @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(19289,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,3332]) ).
thf(19290,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19289:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(21370,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19290]) ).
thf(33940,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21370]) ).
thf(33941,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[33940]) ).
thf(34085,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[33941]) ).
thf(34109,plain,
( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[34085]) ).
thf(34192,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,34109]) ).
thf(34193,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[34192:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski @ k1_tarski ))]]) ).
thf(34228,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[34193]) ).
thf(24942,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,24878]) ).
thf(24943,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[24942:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(24971,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[24943]) ).
thf(23418,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,22680]) ).
thf(23419,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23418:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23447,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[23419]) ).
thf(23119,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,23076]) ).
thf(23120,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23119:[bind(A,$thf( sk1 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23172,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23120]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mboolean) ).
thf(751,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_pboole) ).
thf(802,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pboole) ).
thf(1462,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1047]) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1050]) ).
thf(1055,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1054]) ).
thf(95,axiom,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_funct_6) ).
thf(723,plain,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(724,plain,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[723]) ).
thf(10198,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3399]) ).
thf(10199,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10198:[bind(A,$thf( A )),bind(B,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) ))]]) ).
thf(11667,plain,
sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10199]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r3_pboole ) ) )
<=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_pboole) ).
thf(1792,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( B @ ( A @ r3_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r3_pboole ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(222,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1151,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1152,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[1151]) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk23 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1152]) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1153]) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1154]) ).
thf(1157,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[1156]) ).
thf(1857,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
| ~ $true
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[396,1157]) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(simp,[status(thm)],[1857]) ).
thf(1859,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) )
!= ( A @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[1858:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1860,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) )
!= ( A @ k1_tarski ) ),
inference(simp,[status(thm)],[1859]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_pboole) ).
thf(817,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(19367,plain,
! [B: $i,A: $i] :
( ( B != sk10 )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1803]) ).
thf(19368,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk10 @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19367:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(21394,plain,
~ ( sk10 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19368]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(545,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(546,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[545]) ).
thf(547,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[546]) ).
thf(258,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(1306,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1307,plain,
~ ! [A: $i] : ( A @ v2_setfam_1 ),
inference(miniscope,[status(thm)],[1306]) ).
thf(1308,plain,
~ ( sk39 @ v2_setfam_1 ),
inference(cnf,[status(esa)],[1307]) ).
thf(50791,plain,
! [A: $i] :
( ( A != sk39 )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[547,1308]) ).
thf(50792,plain,
( ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ ( sk39 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[50791:[bind(A,$thf( sk39 ))]]) ).
thf(55082,plain,
( ( ( sk39 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,50792]) ).
thf(55083,plain,
( ( ( sk39 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[55082]) ).
thf(55092,plain,
( ( sk39 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
inference(simp,[status(thm)],[55083]) ).
thf(20813,plain,
! [B: $i,A: $i] :
( ( A != sk82 )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1822]) ).
thf(20814,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20813:[bind(A,$thf( sk82 ))]]) ).
thf(21213,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20814]) ).
thf(23627,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,21213]) ).
thf(23628,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23627]) ).
thf(23740,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk82 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[23628]) ).
thf(23760,plain,
( ( sk82 @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[23740]) ).
thf(23811,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,23760]) ).
thf(23812,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23811:[bind(A,$thf( sk82 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23836,plain,
k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23812]) ).
thf(40330,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,23172]) ).
thf(40331,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[40330]) ).
thf(40504,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[40331]) ).
thf(40544,plain,
( ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[40504]) ).
thf(40654,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,40544]) ).
thf(40655,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[40654:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski @ k1_tarski @ k1_tarski ))]]) ).
thf(40710,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[40655]) ).
thf(20657,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,16643]) ).
thf(20658,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20657:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(21162,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20658]) ).
thf(24510,plain,
( ( ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21162]) ).
thf(24511,plain,
( ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[24510]) ).
thf(24536,plain,
( ( ( sk1 @ k1_tarski @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[24511]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ r1_pboole ) ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_mssubfam) ).
thf(1568,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ r1_pboole ) ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(47,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(571,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(572,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[571]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[572]) ).
thf(61393,plain,
! [B: $i,A: $i] :
( ( ( k2_numbers @ ( k3_numbers @ r1_tarski ) )
!= ( A @ ( B @ r1_tarski ) ) )
| ~ $true
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[1098,573]) ).
thf(61394,plain,
! [B: $i,A: $i] :
( ( ( k2_numbers @ ( k3_numbers @ r1_tarski ) )
!= ( A @ ( B @ r1_tarski ) ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[61393]) ).
thf(61395,plain,
~ ( k3_numbers @ ( k2_numbers @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[61394:[bind(A,$thf( k2_numbers )),bind(B,$thf( k3_numbers ))]]) ).
thf(61469,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ ( k2_numbers @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,61395]) ).
thf(61470,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ ( k2_numbers @ r2_hidden ) ) ),
inference(simp,[status(thm)],[61469]) ).
thf(61489,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= k3_numbers )
| ( A != k2_numbers ) ),
inference(simp,[status(thm)],[61470]) ).
thf(61502,plain,
( ( k2_numbers @ k1_tarski )
!= k3_numbers ),
inference(simp,[status(thm)],[61489]) ).
thf(61555,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B != k3_numbers )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,61502]) ).
thf(61556,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[61555:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(61587,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ r2_hidden ) ),
inference(simp,[status(thm)],[61556]) ).
thf(41310,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,41228]) ).
thf(41311,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk10 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[41310:[bind(A,$thf( sk10 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(41337,plain,
~ ( sk10 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[41311]) ).
thf(4717,plain,
! [A: $i] :
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( A @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) ) )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= ( A @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3364,1860]) ).
thf(4777,plain,
! [A: $i] :
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( A @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) ) )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[4717]) ).
thf(4809,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) ) ),
inference(simp,[status(thm)],[4777]) ).
thf(4976,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski ) ),
inference(rewrite,[status(thm)],[4809,3364]) ).
thf(5041,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( k1_xboole_0 @ k3_xboole_0 ) ) )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[716,4976]) ).
thf(5046,plain,
! [A: $i] :
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= k1_xboole_0 )
| ( A != k1_xboole_0 )
| ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[5041]) ).
thf(5076,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[5046]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_pboole) ).
thf(1778,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(22322,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,22271]) ).
thf(22323,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk86 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[22322:[bind(A,$thf( sk86 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(22348,plain,
~ ( sk86 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[22323]) ).
thf(23803,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,23760]) ).
thf(23804,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23803:[bind(A,$thf( sk82 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23853,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23804]) ).
thf(39307,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,23853]) ).
thf(39308,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[39307]) ).
thf(39451,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk82 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[39308]) ).
thf(39473,plain,
( ( sk82 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[39451]) ).
thf(39575,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,39473]) ).
thf(39576,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[39575:[bind(A,$thf( sk82 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(39600,plain,
~ ( sk82 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[39576]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_pboole) ).
thf(638,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(421,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11067,plain,
! [B: $i,A: $i] :
( ( A != sk86 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1834]) ).
thf(11068,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk86 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11067:[bind(A,$thf( sk86 ))]]) ).
thf(11564,plain,
k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11068]) ).
thf(56,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(605,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(606,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[605]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_pboole) ).
thf(1347,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( D @ ( C @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_mssubfam) ).
thf(1572,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( D @ ( C @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r1_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_pboole) ).
thf(1415,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(578,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[578]) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[579]) ).
thf(581,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[580]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk6 ) )
= A ),
inference(cnf,[status(esa)],[581]) ).
thf(63473,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk6 ) )
= A ),
inference(lifteq,[status(thm)],[582]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r3_pboole ) ) )
=> ~ ( B @ ( C @ ( A @ r3_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r3_pboole) ).
thf(1714,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r3_pboole ) ) )
=> ~ ( B @ ( C @ ( A @ r3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(23143,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,23076]) ).
thf(23144,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23143:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski @ k1_tarski ))]]) ).
thf(23180,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[23144]) ).
thf(26025,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,23180]) ).
thf(26026,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[26025]) ).
thf(26053,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) ) ),
inference(simp,[status(thm)],[26026]) ).
thf(26081,plain,
( ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[26053]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(442,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) ) ),
inference(simp,[status(thm)],[442]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(1109,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_pboole) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(128,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(821,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mboolean) ).
thf(905,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_pboole) ).
thf(924,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(8022,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != sk82 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3249]) ).
thf(8023,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8022:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(9298,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ r2_hidden ) ),
inference(simp,[status(thm)],[8023]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_pboole) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_relat_1) ).
thf(514,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(515,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[514]) ).
thf(516,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[515]) ).
thf(392,plain,
( sk2
!= ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) ),
inference(cnfConj,[status(thm)],[388]) ).
thf(393,plain,
( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 ),
inference(lifteq,[status(thm)],[392]) ).
thf(2009,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
!= ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) ) )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[516,393]) ).
thf(2010,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ k1_closure3 ) ) )
| ( sk2 != k1_xboole_0 )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[2009]) ).
thf(2012,plain,
( ( sk2 != k1_xboole_0 )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[2010]) ).
thf(2036,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) )
| ( sk2 != k1_xboole_0 )
| ( ( B @ k1_tarski )
!= sk2 )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[408,2012]) ).
thf(2037,plain,
! [A: $i] :
( ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 )
| ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
= k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[2036:[bind(A,$thf( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )),bind(B,$thf( B ))]]) ).
thf(2042,plain,
! [A: $i] :
( ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 )
| ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[2037]) ).
thf(2194,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) )
| ( sk2 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 )
| ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[2042,2012]) ).
thf(2195,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) ) )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 )
| ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) ) ),
inference(simp,[status(thm)],[2194]) ).
thf(2196,plain,
! [A: $i] :
( ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 )
| ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[2195:[]]) ).
thf(7426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( C @ v1_xboole_0 )
| ~ $true
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[2196,1601]) ).
thf(7427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( C @ v1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(simp,[status(thm)],[7426]) ).
thf(7428,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ v1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[7427:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( D @ sk3 ) )),bind(C,$thf( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) ))]]) ).
thf(7441,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ v1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(simp,[status(thm)],[7428]) ).
thf(34204,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,34109]) ).
thf(34205,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[34204:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(34232,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[34205]) ).
thf(14237,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,11779]) ).
thf(14238,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk82 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14237:[bind(A,$thf( sk82 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14267,plain,
~ ( sk82 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14238]) ).
thf(19,axiom,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mboolean) ).
thf(484,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(485,plain,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(cnf,[status(esa)],[484]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k4_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_pboole) ).
thf(1136,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k4_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(390,plain,
sk2 @ v2_relat_1,
inference(cnfConj,[status(thm)],[388]) ).
thf(50776,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v2_relat_1 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[547,390]) ).
thf(50777,plain,
( ( k1_xboole_0 @ v2_relat_1 )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[50776:[bind(A,$thf( sk2 ))]]) ).
thf(52512,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,50777]) ).
thf(52513,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( k1_xboole_0 @ v2_relat_1 ) ),
inference(simp,[status(thm)],[52512]) ).
thf(52522,plain,
( ( sk2 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_relat_1 ) ),
inference(simp,[status(thm)],[52513]) ).
thf(57392,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( k1_xboole_0 @ v2_relat_1 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,52522]) ).
thf(57393,plain,
! [A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ v2_relat_1 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[57392]) ).
thf(57394,plain,
( ( k1_xboole_0 @ v2_relat_1 )
| ~ ( sk2 @ ( sk2 @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[57393:[bind(A,$thf( sk2 ))]]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_pboole) ).
thf(806,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(23131,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,23076]) ).
thf(23132,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23131:[bind(A,$thf( sk1 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23176,plain,
k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23132]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_pboole) ).
thf(966,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(23819,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,23760]) ).
thf(23820,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23819:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski ))]]) ).
thf(23839,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[23820]) ).
thf(1840,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,454]) ).
thf(1841,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1843,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[1841]) ).
thf(30754,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,14264]) ).
thf(30755,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30754]) ).
thf(30780,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( sk82 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[30755]) ).
thf(30806,plain,
( ( sk82 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[30780]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_pboole) ).
thf(1351,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(422,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ~ ? [B: $i] :
( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ~ ? [B: $i] :
( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[421]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( C @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) )
& ( ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[422]) ).
thf(425,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[423]) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[425]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[427]) ).
thf(12801,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9812]) ).
thf(12802,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[12801:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(12817,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[12802]) ).
thf(30342,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,12817]) ).
thf(30343,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30342]) ).
thf(30366,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( k2_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[30343]) ).
thf(30388,plain,
( ( k2_numbers @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[30366]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pboole) ).
thf(1521,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_pboole) ).
thf(506,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[506]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) )
= ( B @ ( C @ ( A @ k2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_pboole) ).
thf(527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) )
= ( B @ ( C @ ( A @ k2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(351,axiom,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pboole) ).
thf(1695,plain,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1696,plain,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
inference(cnf,[status(esa)],[1695]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
<=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_pboole) ).
thf(1564,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) )
& ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(56039,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,12606]) ).
thf(56040,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[56039]) ).
thf(56041,plain,
~ ( k3_numbers @ ( k3_numbers @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[56040:[bind(A,$thf( k3_numbers ))]]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_pboole) ).
thf(766,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) )
= ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_pboole) ).
thf(1169,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) )
= ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(397,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(877,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_pboole) ).
thf(692,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(386,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_circ) ).
thf(1796,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mboolean) ).
thf(1072,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_pboole) ).
thf(1622,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_mboolean) ).
thf(774,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_pboole) ).
thf(660,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( C @ v1_pre_circ ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ ( B @ v1_pre_circ ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_mssubfam) ).
thf(1345,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( C @ v1_pre_circ ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ ( B @ v1_pre_circ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r7_pboole ) ) )
& ( C @ ( B @ ( A @ r7_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r7_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_pboole) ).
thf(1697,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r7_pboole ) ) )
& ( C @ ( B @ ( A @ r7_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r7_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ( A @ ( B @ v1_pre_circ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_mssubfam) ).
thf(1242,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ( A @ ( B @ v1_pre_circ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(135,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(848,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(849,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[848]) ).
thf(10112,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3332]) ).
thf(10113,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10112:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(11597,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10113]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( A @ k1_pboole @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_pboole) ).
thf(920,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( A @ k1_pboole @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(14229,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,11779]) ).
thf(14230,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk82 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14229:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski ))]]) ).
thf(14263,plain,
sk82 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14230]) ).
thf(16755,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,16643]) ).
thf(16756,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[16755:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(16780,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[16756]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_pboole) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(23125,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,23076]) ).
thf(23126,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23125:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski @ k1_tarski ))]]) ).
thf(23175,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23126]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k2_pboole ) ) )
= ( B @ ( C @ ( A @ k2_pboole ) ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[527]) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) )
| ( ( C @ ( B @ ( A @ k2_pboole ) ) )
= ( B @ ( C @ ( A @ k2_pboole ) ) ) ) ),
inference(lifteq,[status(thm)],[528]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v2_pboole ) )
<=> ( B @ v2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v2_pboole) ).
thf(1691,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ( B @ v2_relat_1 )
=> ( A @ ( B @ v2_pboole ) ) )
& ( ( A @ ( B @ v2_pboole ) )
=> ( B @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[533]) ).
thf(9486,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( sk1 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[396,9159]) ).
thf(9487,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( sk1 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ) )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(simp,[status(thm)],[9486]) ).
thf(9488,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[9487:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(14304,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B
!= ( k3_numbers @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,11979]) ).
thf(14305,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14304:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14317,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14305]) ).
thf(31866,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,14317]) ).
thf(31867,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[31866]) ).
thf(31890,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k2_numbers @ k1_tarski @ k1_tarski ) )
| ( A
!= ( k3_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[31867]) ).
thf(31906,plain,
( ( k2_numbers @ k1_tarski @ k1_tarski )
!= ( k3_numbers @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[31890]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r5_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_pboole) ).
thf(1519,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r5_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_pboole) ).
thf(1355,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_pboole) ).
thf(1255,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) )
=> ( B @ v3_relat_1 ) )
& ( ( B @ v3_relat_1 )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(139,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(862,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(344,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
& ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_pboole) ).
thf(1676,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
& ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mboolean) ).
thf(598,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(7911,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3332]) ).
thf(7912,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7911:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(9245,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[7912]) ).
thf(14925,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,9245]) ).
thf(14926,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[14925]) ).
thf(14946,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[14926]) ).
thf(14978,plain,
( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[14946]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( A @ k1_pboole @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_pboole) ).
thf(1487,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( A @ k1_pboole @ ( A @ k1_pboole @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_pboole) ).
thf(630,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(240,axiom,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(1238,plain,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_pboole) ).
thf(910,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(170,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(957,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(894,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(746,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(12733,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9625]) ).
thf(12734,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[12733:[bind(A,$thf( sk86 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(12773,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[12734]) ).
thf(10264,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk82 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3249]) ).
thf(10265,plain,
! [A: $i] :
( ( A != sk82 )
| ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10264:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(11238,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10265]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( B @ ( A @ r7_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_pboole) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( B @ ( A @ r7_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pboole) ).
thf(1502,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_pboole) ).
thf(1751,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(10064,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9450]) ).
thf(10065,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[10064:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(10102,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[10065]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(429,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11069,plain,
! [B: $i,A: $i] :
( ( B != sk86 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1834]) ).
thf(11070,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk86 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11069:[bind(A,$thf( A )),bind(B,$thf( sk86 ))]]) ).
thf(11565,plain,
sk86 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11070]) ).
thf(271,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(1370,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(22314,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,22271]) ).
thf(22315,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk86 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[22314:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski ))]]) ).
thf(22346,plain,
sk86 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[22315]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_pboole) ).
thf(729,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_mboolean) ).
thf(916,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
<=> ( ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pboole) ).
thf(1365,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) )
& ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(24930,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,24878]) ).
thf(24931,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[24930:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(24967,plain,
~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[24931]) ).
thf(21784,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[893,21164]) ).
thf(21785,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21784]) ).
thf(21911,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( B @ ( A @ k3_xboole_0 ) )
!= ( sk1 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[21785]) ).
thf(21922,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_tarski @ k3_xboole_0 ) )
!= ( sk1 @ k1_tarski ) ),
inference(simp,[status(thm)],[21911]) ).
thf(77936,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,13083]) ).
thf(77937,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[77936]) ).
thf(77938,plain,
~ ( k1_xboole_0 @ ( sk1 @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[77937:[bind(A,$thf( sk1 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(458,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(459,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_setfam_1 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ k1_tarski @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[458]) ).
thf(461,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_setfam_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[459]) ).
thf(337,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
=> ~ ( B @ v3_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_pboole) ).
thf(1656,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
=> ~ ( B @ v3_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(79982,plain,
! [A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,16643]) ).
thf(79983,plain,
! [A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[79982]) ).
thf(79984,plain,
~ ( k1_xboole_0 @ ( sk1 @ k1_tarski @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[79983:[bind(A,$thf( sk1 @ k1_tarski ))]]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_pboole) ).
thf(1128,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(10284,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1803]) ).
thf(10285,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk10 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10284:[bind(A,$thf( sk10 ))]]) ).
thf(11244,plain,
k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10285]) ).
thf(14363,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,12181]) ).
thf(14364,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk10 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14363:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski ))]]) ).
thf(14401,plain,
sk10 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14364]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
thf(1602,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(10977,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1802]) ).
thf(10978,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk1 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10977:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(11532,plain,
sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10978]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pboole) ).
thf(1624,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_mboolean) ).
thf(710,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(12745,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9625]) ).
thf(12746,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk86 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[12745:[bind(A,$thf( sk86 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(12760,plain,
~ ( sk86 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[12746]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ( A @ ( C @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_pboole) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ( A @ ( C @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(948,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_pboole) ).
thf(615,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_pboole) ).
thf(1064,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
thf(1111,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(342,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_2) ).
thf(1670,plain,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1671,plain,
! [A: $i] :
( ~ ( A @ sk79 @ v1_xboole_0 )
& ( A @ ( A @ sk79 @ m1_finseq_2 ) ) ),
inference(cnf,[status(esa)],[1670]) ).
thf(1672,plain,
! [A: $i] : ( A @ ( A @ sk79 @ m1_finseq_2 ) ),
inference(cnfConj,[status(thm)],[1671]) ).
thf(10751,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9450]) ).
thf(10752,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10751:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(11435,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10752]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(495,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(496,plain,
~ ? [A: $i,B: $i] :
( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[495]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[496]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[497]) ).
thf(499,plain,
! [A: $i] :
~ ( A @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[498]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
<=> ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pboole) ).
thf(1592,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(1089,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(8831,plain,
! [B: $i,A: $i] :
( ( A != sk82 )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1822]) ).
thf(8832,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8831:[bind(A,$thf( sk82 ))]]) ).
thf(9196,plain,
~ ( sk82 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8832]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(1270,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(177,axiom,
k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_pboole) ).
thf(1007,plain,
k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(78408,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k1_pboole @ m1_pboole ) )
!= ( k1_xboole_0 @ ( B @ m1_pboole ) ) )
| ~ $true
| ( B = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1696,602]) ).
thf(78409,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k1_pboole @ m1_pboole ) )
!= ( k1_xboole_0 @ ( B @ m1_pboole ) ) )
| ( B = k1_xboole_0 ) ),
inference(simp,[status(thm)],[78408]) ).
thf(78410,plain,
( ( k1_xboole_0 @ k1_pboole )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[78409:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 @ k1_pboole ))]]) ).
thf(81751,plain,
k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ r1_pboole ) ),
inference(rewrite,[status(thm)],[1007,78410]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_pboole) ).
thf(1587,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(1138,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v1_pre_circ ) )
<=> ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_mssubfam) ).
thf(607,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
=> ( A @ ( B @ v1_pre_circ ) ) )
& ( ( A @ ( B @ v1_pre_circ ) )
=> ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ v1_pre_circ ) )
| ~ ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
| ~ ( A @ ( B @ m1_pboole ) ) )
& ( ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
| ~ ( A @ ( B @ v1_pre_circ ) )
| ~ ( A @ ( B @ m1_pboole ) ) ) ),
inference(cnf,[status(esa)],[607]) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v1_pre_circ ) )
| ~ ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[608]) ).
thf(8104,plain,
! [B: $i,A: $i] :
( ( A != k3_numbers )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1828]) ).
thf(8105,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k3_numbers @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8104:[bind(A,$thf( k3_numbers ))]]) ).
thf(9333,plain,
~ ( k3_numbers @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8105]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_mboolean) ).
thf(1118,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_pboole) ).
thf(884,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( D @ ( A @ r1_pboole ) ) )
=> ( B @ ( D @ ( A @ r2_pboole ) ) ) ) )
=> ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_mboolean) ).
thf(1160,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( D @ ( A @ r1_pboole ) ) )
=> ( B @ ( D @ ( A @ r2_pboole ) ) ) ) )
=> ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(22306,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,22271]) ).
thf(22307,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk86 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[22306:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski ))]]) ).
thf(22343,plain,
~ ( sk86 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[22307]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_pre_circ ) @ ( B @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_mboolean) ).
thf(476,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_pre_circ ) @ ( B @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20667,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1802]) ).
thf(20668,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20667:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(21165,plain,
~ ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20668]) ).
thf(22054,plain,
( ( ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21165]) ).
thf(22055,plain,
( ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22054]) ).
thf(22072,plain,
( ( ( sk1 @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[22055]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(489,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77893,plain,
! [A: $i] :
( ( A != sk10 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,1803]) ).
thf(77894,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[77893]) ).
thf(77895,plain,
~ ( k1_xboole_0 @ ( sk10 @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[77894:[bind(A,$thf( sk10 ))]]) ).
thf(27181,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,23839]) ).
thf(27182,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[27181]) ).
thf(27203,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( sk82 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[27182]) ).
thf(27223,plain,
( ( sk82 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[27203]) ).
thf(391,plain,
sk1 @ ( sk2 @ m1_pboole ),
inference(cnfConj,[status(thm)],[388]) ).
thf(49944,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[547,391]) ).
thf(49945,plain,
( ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
| ~ ( sk2 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[49944:[bind(A,$thf( sk2 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(465,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(466,plain,
( ! [A: $i,B: $i] :
( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[465]) ).
thf(467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ k1_tarski @ ( C @ r1_tarski ) )
| ( C
!= ( D @ k1_tarski ) ) )
& ( ( D @ k1_tarski @ ( C @ r1_tarski ) )
| ( C != k1_xboole_0 ) )
& ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ r1_tarski ) ) ) ),
inference(cnf,[status(esa)],[466]) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ r1_tarski ) ) ),
inference(cnfConj,[status(thm)],[467]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_tarski @ ( A @ r1_tarski ) )
| ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[468]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_pboole) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[553]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_pboole) ).
thf(753,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
<=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_pboole) ).
thf(1739,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ v2_relat_1 ) )
& ( ( B @ v2_relat_1 )
=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) )
| ~ ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[536]) ).
thf(12805,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,9812]) ).
thf(12806,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[12805:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(12818,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[12806]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
thf(669,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(520,plain,
( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[519]) ).
thf(521,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ k3_xboole_0 ) @ ( F @ k2_zfmisc_1 ) )
= ( E @ ( F @ k2_zfmisc_1 ) @ ( D @ ( F @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[520]) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(cnfConj,[status(thm)],[521]) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[523]) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(simp,[status(thm)],[525]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_pboole) ).
thf(1612,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( E @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_pboole) ).
thf(1039,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( E @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r5_pboole) ).
thf(1776,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_pboole) ).
thf(1099,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_mboolean) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(14367,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,12181]) ).
thf(14368,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14367:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski ))]]) ).
thf(14383,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14368]) ).
thf(32278,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,14383]) ).
thf(32279,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[32278]) ).
thf(32302,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( sk10 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[32279]) ).
thf(32327,plain,
( ( sk10 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[32302]) ).
thf(39569,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,39473]) ).
thf(39570,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[39569:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski @ k1_tarski ))]]) ).
thf(39597,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[39570]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r7_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r7_pboole) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r7_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(12793,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9812]) ).
thf(12794,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[12793:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(12831,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[12794]) ).
thf(2283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( C @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true
| ~ ( C @ v1_setfam_1 )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[396,759]) ).
thf(2284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ r2_hidden ) )
!= ( C @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ ( C @ v1_setfam_1 )
| ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( B @ k1_tarski ) ) ),
inference(simp,[status(thm)],[2283]) ).
thf(2285,plain,
! [A: $i] :
( ~ ( A @ v1_setfam_1 )
| ( ( k1_xboole_0 @ k1_tarski @ ( A @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[2284:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_pboole) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k2_mboolean ) @ ( A @ k1_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_mboolean) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k2_mboolean ) @ ( A @ k1_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(25182,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,25115]) ).
thf(25183,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[25182:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski ))]]) ).
thf(25210,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[25183]) ).
thf(28439,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,25210]) ).
thf(28440,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[28439]) ).
thf(28461,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( sk10 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[28440]) ).
thf(28476,plain,
( ( sk10 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[28461]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r6_pboole) ).
thf(1393,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(503,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61551,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A != k3_numbers )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,61502]) ).
thf(61552,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[61551:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(61586,plain,
~ ( k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[61552]) ).
thf(10108,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3332]) ).
thf(10109,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10108:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(11593,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10109]) ).
thf(20815,plain,
! [B: $i,A: $i] :
( ( B != sk82 )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1822]) ).
thf(20816,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20815:[bind(A,$thf( A )),bind(B,$thf( sk82 ))]]) ).
thf(21214,plain,
~ ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20816]) ).
thf(23960,plain,
( ( ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21214]) ).
thf(23961,plain,
( ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23960]) ).
thf(23980,plain,
( ( ( sk82 @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[23961]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(508,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19369,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != sk82 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,3249]) ).
thf(19370,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19369:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(21395,plain,
~ ( sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19370]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ( C @ ( A @ ( B @ m2_pboole ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_mssubfam) ).
thf(1712,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ( C @ ( A @ ( B @ m2_pboole ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(22302,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,22271]) ).
thf(22303,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[22302:[bind(A,$thf( sk86 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(22341,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[22303]) ).
thf(35771,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,22341]) ).
thf(35772,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[35771]) ).
thf(35915,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( sk86 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[35772]) ).
thf(35947,plain,
( ( sk86 @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[35915]) ).
thf(36017,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,35947]) ).
thf(36018,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[36017:[bind(A,$thf( sk86 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(36077,plain,
k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[36018]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_pboole) ).
thf(1515,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_pboole) ).
thf(926,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(118,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(792,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(40662,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,40544]) ).
thf(40663,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[40662:[bind(A,$thf( sk1 @ k1_tarski @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(40711,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[40663]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pboole) ).
thf(1466,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(558,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(340,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(1663,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(1026,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(14795,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,12606]) ).
thf(14796,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14795:[bind(A,$thf( k3_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14826,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14796]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
<=> ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_pboole) ).
thf(1616,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r4_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(24938,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,24878]) ).
thf(24939,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k3_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[24938:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(24970,plain,
k3_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[24939]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(530,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pboole) ).
thf(794,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(662,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_pboole) ).
thf(888,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(23823,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,23760]) ).
thf(23824,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23823:[bind(A,$thf( sk82 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23840,plain,
~ ( sk82 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[23824]) ).
thf(345,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ~ ( B @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_pboole) ).
thf(1680,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ~ ( B @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(824,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(25174,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,25115]) ).
thf(25175,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[25174:[bind(A,$thf( sk10 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(25207,plain,
k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[25175]) ).
thf(20807,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1807]) ).
thf(20808,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k2_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20807:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(21211,plain,
~ ( k2_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20808]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_pboole) ).
thf(1374,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_pboole) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k12_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_mboolean) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k12_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(410,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
!= ( A @ k1_tarski ) ) ),
inference(cnf,[status(esa)],[410]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[411]) ).
thf(20775,plain,
! [B: $i,A: $i] :
( ( B != sk86 )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1834]) ).
thf(20776,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk86 @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20775:[bind(A,$thf( A )),bind(B,$thf( sk86 ))]]) ).
thf(21201,plain,
~ ( sk86 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20776]) ).
thf(22459,plain,
( ( ( sk86 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21201]) ).
thf(22460,plain,
( ( sk86 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22459]) ).
thf(22479,plain,
( ( ( sk86 @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[22460]) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[512]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[429]) ).
thf(369,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_pboole) ).
thf(1747,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[598]) ).
thf(76678,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m1_pboole ) )
!= ( A @ ( B @ m1_pboole ) ) )
| ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,599]) ).
thf(76679,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ m1_pboole ) )
!= ( A @ ( B @ m1_pboole ) ) )
| ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
inference(simp,[status(thm)],[76678]) ).
thf(76680,plain,
sk1 @ ( sk2 @ ( sk1 @ k2_mboolean ) @ m1_pboole ),
inference(pattern_uni,[status(thm)],[76679:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(819,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(76823,plain,
! [A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,64964]) ).
thf(76824,plain,
! [A: $i] :
( ( A @ ( A @ r1_tarski ) )
!= ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[76823]) ).
thf(76957,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) ) )
| ( A != k3_numbers ) ),
inference(simp,[status(thm)],[76824]) ).
thf(76974,plain,
( ( k3_numbers @ ( k3_numbers @ k2_zfmisc_1 ) )
!= k3_numbers ),
inference(simp,[status(thm)],[76957]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r1_pboole ) ) )
& ( A @ ( C @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_pboole) ).
thf(1784,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r1_pboole ) ) )
& ( A @ ( C @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(843,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 )
| ~ ( C @ v1_finset_1 )
| ~ ( B @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[558]) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(cnf,[status(esa)],[550]) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(lifteq,[status(thm)],[551]) ).
thf(54285,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ v1_finset_1 )
| ~ ( C @ v1_finset_1 )
| ~ ( B @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(rewrite,[status(thm)],[559,552]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_mssubfam) ).
thf(1652,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( A @ ( C @ v1_pre_circ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
=> ( A @ ( B @ r2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).
thf(1701,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
=> ( A @ ( B @ r2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_mboolean) ).
thf(694,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_pboole) ).
thf(772,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(25178,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,25115]) ).
thf(25179,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk10 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[25178:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski ))]]) ).
thf(25209,plain,
sk10 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[25179]) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[415]) ).
thf(418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[416]) ).
thf(2798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( B != k1_xboole_0 )
| ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[418,1802]) ).
thf(2799,plain,
! [C: $i,B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( sk1 ))]]) ).
thf(3047,plain,
! [B: $i,A: $i] : ( B @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[2799]) ).
thf(3418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) ) )
| ( C @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1055,3047]) ).
thf(3419,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[3418:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(3472,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[3419]) ).
thf(19539,plain,
! [B: $i,A: $i] :
( ( A != k3_numbers )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1828]) ).
thf(19540,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19539:[bind(A,$thf( k3_numbers ))]]) ).
thf(21455,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19540]) ).
thf(25488,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21455]) ).
thf(25489,plain,
( ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25488]) ).
thf(25506,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( k3_numbers @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[25489]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_pboole) ).
thf(1388,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) )
=> ( C @ ( B @ ( A @ r5_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(24843,plain,
( ( ( k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21335]) ).
thf(24844,plain,
( ( k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[24843]) ).
thf(24865,plain,
( ( ( k2_numbers @ k1_tarski )
!= k2_numbers )
| ( ( k3_numbers @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[24844]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_pboole) ).
thf(576,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[576]) ).
thf(36029,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,35947]) ).
thf(36030,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[36029:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski @ k1_tarski ))]]) ).
thf(36081,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[36030]) ).
thf(8811,plain,
! [B: $i,A: $i] :
( ( A != sk86 )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1834]) ).
thf(8812,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk86 @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8811:[bind(A,$thf( sk86 ))]]) ).
thf(9189,plain,
~ ( sk86 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8812]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_pboole) ).
thf(1226,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(32690,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,14829]) ).
thf(32691,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[32690]) ).
thf(32714,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( k3_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[32691]) ).
thf(32744,plain,
( ( k3_numbers @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[32714]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_pboole) ).
thf(1058,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(10232,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k3_numbers )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1179]) ).
thf(10233,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10232:[bind(A,$thf( k2_numbers ))]]) ).
thf(11678,plain,
k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10233]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(1092,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k1_mboolean ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_mboolean) ).
thf(804,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k1_mboolean ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(16759,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,16643]) ).
thf(16760,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[16759:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(16782,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[16760]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_pboole) ).
thf(1464,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(7915,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3332]) ).
thf(7916,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7915:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(9248,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[7916]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(lifteq,[status(thm)],[435]) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[444]) ).
thf(7993,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k3_numbers )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1179]) ).
thf(7994,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( k2_numbers @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7993:[bind(A,$thf( k2_numbers ))]]) ).
thf(9285,plain,
~ ( k2_numbers @ k1_tarski @ ( k3_numbers @ r2_hidden ) ),
inference(simp,[status(thm)],[7994]) ).
thf(357,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure3) ).
thf(1707,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(2291,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( B @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ $true
| ~ ( B @ v1_setfam_1 ) ),
inference(paramod_ordered,[status(thm)],[441,759]) ).
thf(2292,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( B @ ( k1_xboole_0 @ r2_hidden ) ) )
| ~ ( B @ v1_setfam_1 ) ),
inference(simp,[status(thm)],[2291]) ).
thf(2293,plain,
~ ( k1_xboole_0 @ k1_tarski @ v1_setfam_1 ),
inference(pattern_uni,[status(thm)],[2292:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(16751,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,16643]) ).
thf(16752,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk1 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[16751:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(16779,plain,
sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[16752]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_pboole) ).
thf(539,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[539]) ).
thf(23720,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21213]) ).
thf(23721,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23720]) ).
thf(23741,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( sk82 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[23721]) ).
thf(23815,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,23760]) ).
thf(23816,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk82 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23815:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski ))]]) ).
thf(23838,plain,
sk82 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23816]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_pboole) ).
thf(1282,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(77572,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,24878]) ).
thf(77573,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[77572]) ).
thf(77574,plain,
~ ( k1_xboole_0 @ ( k3_numbers @ k1_tarski @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[77573:[bind(A,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).
thf(1589,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(10975,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1802]) ).
thf(10976,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk1 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10975:[bind(A,$thf( sk1 ))]]) ).
thf(11531,plain,
k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10976]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_pboole) ).
thf(764,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_pboole) ).
thf(603,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
| ~ ( A @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[603]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(681,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(56344,plain,
! [A: $i] :
( ( A != sk82 )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,30806]) ).
thf(56345,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[56344]) ).
thf(56346,plain,
~ ( sk82 @ ( sk82 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[56345:[bind(A,$thf( sk82 ))]]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ v3_relat_1 ) )
=> ( C @ v3_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_pboole) ).
thf(1542,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ v3_relat_1 ) )
=> ( C @ v3_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(61402,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( A @ ( B @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3356,573]) ).
thf(61403,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( A @ ( B @ r1_tarski ) ) ),
inference(simp,[status(thm)],[61402]) ).
thf(61404,plain,
~ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ ( sk82 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[61403:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) )),bind(B,$thf( sk82 ))]]) ).
thf(63592,plain,
! [A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ ( sk82 @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,61404]) ).
thf(63593,plain,
! [A: $i] :
( ( A @ ( A @ r1_tarski ) )
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) @ ( sk82 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[63592]) ).
thf(63717,plain,
! [A: $i] :
( ( A
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( A != sk82 ) ),
inference(simp,[status(thm)],[63593]) ).
thf(63742,plain,
( ( sk82 @ ( k1_xboole_0 @ sk3 ) )
!= sk82 ),
inference(simp,[status(thm)],[63717]) ).
thf(377,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( ( D @ ( C @ ( A @ k3_pboole ) ) )
= ( A @ k1_pboole ) )
& ( D @ ( B @ ( A @ r3_pboole ) ) )
& ( C @ ( B @ ( A @ r3_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_pboole) ).
thf(1771,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( ( D @ ( C @ ( A @ k3_pboole ) ) )
= ( A @ k1_pboole ) )
& ( D @ ( B @ ( A @ r3_pboole ) ) )
& ( C @ ( B @ ( A @ r3_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( C @ ( E @ ( A @ r5_pboole ) ) )
& ( B @ ( D @ ( A @ r5_pboole ) ) )
& ( E @ ( D @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) )
=> ( ( B @ ( E @ ( A @ r6_pboole ) ) )
& ( C @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_pboole) ).
thf(737,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( C @ ( E @ ( A @ r5_pboole ) ) )
& ( B @ ( D @ ( A @ r5_pboole ) ) )
& ( E @ ( D @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) )
=> ( ( B @ ( E @ ( A @ r6_pboole ) ) )
& ( C @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[508]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( A @ k1_pboole @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_pboole) ).
thf(880,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( A @ k1_pboole @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C
= ( B @ ( A @ k2_mboolean ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mboolean) ).
thf(1376,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) )
=> ( C
= ( B @ ( A @ k2_mboolean ) ) ) )
& ( ( C
= ( B @ ( A @ k2_mboolean ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(20373,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,9450]) ).
thf(20374,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20373:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(21746,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20374]) ).
thf(17487,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,16780]) ).
thf(17488,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[17487]) ).
thf(17511,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( sk1 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[17488]) ).
thf(17541,plain,
( ( sk1 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[17511]) ).
thf(17914,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,17541]) ).
thf(17915,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[17914:[bind(A,$thf( sk1 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(17957,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[17915]) ).
thf(490,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[489]) ).
thf(491,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[490]) ).
thf(493,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[491]) ).
thf(494,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(simp,[status(thm)],[493]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[480]) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(11081,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1807]) ).
thf(11082,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k2_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11081:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(11569,plain,
k2_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11082]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_pboole) ).
thf(1149,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(24934,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,24878]) ).
thf(24935,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[24934:[bind(A,$thf( k3_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(24968,plain,
k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[24935]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(1460,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(890,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r2_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).
thf(1667,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(477,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_pre_circ ) @ ( B @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(cnf,[status(esa)],[476]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(811,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_pboole) ).
thf(858,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(19541,plain,
! [B: $i,A: $i] :
( ( B != k3_numbers )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1828]) ).
thf(19542,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k3_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19541:[bind(A,$thf( A )),bind(B,$thf( k3_numbers ))]]) ).
thf(21456,plain,
~ ( k3_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19542]) ).
thf(26362,plain,
( ( ( k3_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21456]) ).
thf(26363,plain,
( ( k3_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26362]) ).
thf(26383,plain,
( ( ( k3_numbers @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[26363]) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
| ~ ( A @ ( B @ v1_pre_circ ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnfConj,[status(thm)],[608]) ).
thf(366,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_pboole) ).
thf(1731,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ! [C: $i] :
( ( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_pboole) ).
thf(1022,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(462,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34186,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,34109]) ).
thf(34187,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[34186:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(34225,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[34187]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_pboole) ).
thf(932,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_pboole) ).
thf(912,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k12_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_pboole) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k12_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(958,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[957]) ).
thf(959,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[958]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
<=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_pboole) ).
thf(1445,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) )
=> ( B @ v3_relat_1 ) )
& ( ( B @ v3_relat_1 )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_pboole) ).
thf(780,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(26525,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,22347]) ).
thf(26526,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[26525]) ).
thf(26548,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( sk86 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[26526]) ).
thf(26564,plain,
( ( sk86 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[26548]) ).
thf(296,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_pboole) ).
thf(1477,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(34198,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,34109]) ).
thf(34199,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[34198:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski @ k1_tarski ))]]) ).
thf(34229,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[34199]) ).
thf(45506,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,34229]) ).
thf(45507,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[45506]) ).
thf(45534,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ) ),
inference(simp,[status(thm)],[45507]) ).
thf(45567,plain,
( ( k1_xboole_0 @ k1_tarski @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[45534]) ).
thf(23149,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,23076]) ).
thf(23150,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23149:[bind(A,$thf( sk1 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(23183,plain,
~ ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[23150]) ).
thf(652,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[651]) ).
thf(653,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[652]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_pboole) ).
thf(1562,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v1_pre_circ ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_finset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_circ) ).
thf(1213,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_finset_1 ) )
=> ( A @ ( B @ v1_pre_circ ) ) )
& ( ( A @ ( B @ v1_pre_circ ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_finset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_subset_1 ) )
<=> ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_subset_1) ).
thf(768,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( A @ r2_subset_1 ) ) )
& ( ( B @ ( A @ r2_subset_1 ) )
=> ( B @ ( A @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(10286,plain,
! [B: $i,A: $i] :
( ( B != sk10 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1803]) ).
thf(10287,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk10 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10286:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(11245,plain,
sk10 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10287]) ).
thf(25083,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21393]) ).
thf(25084,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk10 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25083]) ).
thf(25104,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( sk10 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[25084]) ).
thf(25170,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk10 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,25115]) ).
thf(25171,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk10 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[25170:[bind(A,$thf( A )),bind(B,$thf( sk10 @ k1_tarski ))]]) ).
thf(25206,plain,
~ ( sk10 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[25171]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_pboole) ).
thf(1583,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[423]) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[424]) ).
thf(167,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(944,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_pboole) ).
thf(548,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( A @ ( B @ m2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_mssubfam) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( A @ ( B @ m2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pre_circ) ).
thf(1684,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_pboole) ).
thf(749,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_pboole) ).
thf(1145,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
<=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_mboolean) ).
thf(836,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
& ( ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pboole) ).
thf(1134,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(23410,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,22680]) ).
thf(23411,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[23410:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(23445,plain,
k2_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[23411]) ).
thf(2800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != sk1 )
| ( A != k1_xboole_0 )
| ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[418,1802]) ).
thf(2801,plain,
! [C: $i,B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( C @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[2800:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(3048,plain,
! [B: $i,A: $i] : ( B @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[2801]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(617,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(10234,plain,
! [B: $i,A: $i] :
( ( B != k2_numbers )
| ( A != k3_numbers )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1179]) ).
thf(10235,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( k2_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10234:[bind(A,$thf( A )),bind(B,$thf( k2_numbers ))]]) ).
thf(11679,plain,
k2_numbers @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10235]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_mboolean) ).
thf(690,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( E @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( A @ r1_pboole ) ) ) )
=> ( ( A @ k1_pboole @ ( E @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
| ( D = E ) ) ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ v2_relat_1 ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_mboolean) ).
thf(640,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( E @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( A @ r1_pboole ) ) ) )
=> ( ( A @ k1_pboole @ ( E @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
| ( D = E ) ) ) ) )
& ( C @ ( B @ ( A @ k2_pboole ) ) @ v2_relat_1 ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(24926,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,24878]) ).
thf(24927,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[24926:[bind(A,$thf( k3_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(24965,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[24927]) ).
thf(39642,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[542,24965]) ).
thf(39643,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[39642]) ).
thf(39787,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( k3_numbers @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[39643]) ).
thf(39827,plain,
( ( k3_numbers @ k1_tarski @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[39787]) ).
thf(39904,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,39827]) ).
thf(39905,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[39904:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski @ k1_tarski ))]]) ).
thf(39938,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[39905]) ).
thf(140,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(871,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(872,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[871]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(10360,plain,
! [B: $i,A: $i] :
( ( A != k3_numbers )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1828]) ).
thf(10361,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10360:[bind(A,$thf( k3_numbers ))]]) ).
thf(11275,plain,
k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10361]) ).
thf(61547,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A != k3_numbers )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,61502]) ).
thf(61548,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[61547:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(61585,plain,
k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[61548]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_pboole) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(372,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( C
= ( B @ ( A @ k1_closure3 ) ) )
<=> ( C
= ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
thf(1753,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( C
= ( B @ ( A @ a_2_0_closure3 ) ) )
=> ( C
= ( B @ ( A @ k1_closure3 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_closure3 ) ) )
=> ( C
= ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(22310,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,22271]) ).
thf(22311,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[22310:[bind(A,$thf( sk86 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(22344,plain,
k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[22311]) ).
thf(501,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[500]) ).
thf(502,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
| ~ ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[501]) ).
thf(23309,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ $true
| ~ ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[3356,502]) ).
thf(23310,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[23309]) ).
thf(23311,plain,
~ ( sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[23310:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) )),bind(B,$thf( sk82 ))]]) ).
thf(5569,plain,
! [B: $i,A: $i] :
( ( ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( sk82 @ k3_xboole_0 ) )
!= ( B @ ( A @ k3_xboole_0 ) ) )
| ( A @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[3364,893]) ).
thf(5570,plain,
sk82 @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ r1_tarski ),
inference(pattern_uni,[status(thm)],[5569:[bind(A,$thf( sk82 )),bind(B,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski ))]]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(776,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_pboole) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(556,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[555]) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ r1_xboole_0 ) )
| ~ ( D @ ( B @ r1_xboole_0 ) )
| ~ ( D @ ( C @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[556]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_pboole) ).
thf(1003,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1829,plain,
( ( ( sk86 @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1690,1766]) ).
thf(1830,plain,
( ( sk86 @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1829]) ).
thf(1833,plain,
sk86 != sk80,
inference(simp,[status(thm)],[1830]) ).
thf(2606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != sk86 )
| ( A != sk80 )
| ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[418,1833]) ).
thf(2607,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk80 )
| ( C @ ( sk86 @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[2606:[bind(A,$thf( A )),bind(B,$thf( sk86 ))]]) ).
thf(2952,plain,
! [B: $i,A: $i] : ( B @ ( sk86 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk80 @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[2607]) ).
thf(6800,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( sk80 @ k1_tarski @ k2_zfmisc_1 ) ) )
| ( C @ ( sk86 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1055,2952]) ).
thf(6801,plain,
! [A: $i] : ( A @ ( sk86 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6800:[bind(A,$thf( sk80 @ k1_tarski )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(6885,plain,
! [A: $i] : ( A @ ( sk86 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[6801]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(1400,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= B )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[405]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= B )
| ( A = k1_xboole_0 )
| ( A
= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[407]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_pboole) ).
thf(673,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
<=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mboolean) ).
thf(1432,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
=> ( B @ ( D @ ( A @ r1_pboole ) ) ) )
& ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
=> ( B @ ( D @ ( A @ r1_pboole ) ) ) )
& ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(1186,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( D @ ( E @ ( A @ r1_pboole ) ) )
<=> ( ( C @ ( E @ ( A @ r1_pboole ) ) )
& ( B @ ( E @ ( A @ r1_pboole ) ) ) ) ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_pboole) ).
thf(1262,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( ( C @ ( E @ ( A @ r1_pboole ) ) )
& ( B @ ( E @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( E @ ( A @ r1_pboole ) ) ) )
& ( ( D @ ( E @ ( A @ r1_pboole ) ) )
=> ( ( C @ ( E @ ( A @ r1_pboole ) ) )
& ( B @ ( E @ ( A @ r1_pboole ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(808,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(14807,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,12606]) ).
thf(14808,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14807:[bind(A,$thf( k3_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14832,plain,
~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14808]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1128]) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1129]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) )
=> ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_mboolean) ).
thf(1218,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) )
=> ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(23555,plain,
( ( ( k2_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21211]) ).
thf(23556,plain,
( ( k2_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23555]) ).
thf(23575,plain,
( ( ( k2_numbers @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[23556]) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ k1_closure3 ) ) )
| ( ( B @ k1_tarski @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 )
| ( A @ ( A @ ( B @ sk3 ) @ r2_hidden ) )
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[408,393]) ).
thf(1878,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 )
| ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ ( sk1 @ k1_closure3 ) @ ( A @ sk3 ) @ r2_hidden ) )
| ( ( sk2 @ ( sk1 @ k1_closure3 ) )
= k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[1877:[bind(A,$thf( sk2 @ ( sk1 @ k1_closure3 ) )),bind(B,$thf( B ))]]) ).
thf(1987,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( sk2 @ k7_relat_1 ) @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= sk2 )
| ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ ( sk1 @ k1_closure3 ) @ ( A @ sk3 ) @ r2_hidden ) )
| ( ( sk2 @ ( sk1 @ k1_closure3 ) )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[1878]) ).
thf(61543,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B != k3_numbers )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,61502]) ).
thf(61544,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[61543:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(61583,plain,
k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[61544]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_pboole) ).
thf(717,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
& ( B
!= ( A @ k1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_pboole) ).
thf(1658,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
& ( B
!= ( A @ k1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(10192,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3399]) ).
thf(10193,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10192:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) )),bind(B,$thf( B ))]]) ).
thf(11661,plain,
k1_xboole_0 @ k1_tarski @ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10193]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k2_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pboole) ).
thf(543,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k2_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ k2_pboole ) ) @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[543]) ).
thf(154,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(907,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_pboole) ).
thf(703,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) )
=> ( B
= ( A @ k1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pboole) ).
thf(1536,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) )
=> ( B
= ( A @ k1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_pboole) ).
thf(1506,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(19373,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != sk82 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,3249]) ).
thf(19374,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19373:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(21397,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19374]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_pboole) ).
thf(1140,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(23402,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,22680]) ).
thf(23403,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23402:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(23442,plain,
~ ( k2_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23403]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k2_pboole ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_pboole) ).
thf(656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k2_pboole ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_pboole) ).
thf(613,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(56375,plain,
! [A: $i] :
( ( A != k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,30388]) ).
thf(56376,plain,
! [A: $i] :
( ( A != k2_numbers )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[56375]) ).
thf(56377,plain,
~ ( k2_numbers @ ( k2_numbers @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[56376:[bind(A,$thf( k2_numbers ))]]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( D @ ( E @ ( A @ r1_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( E @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
& ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( B @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_mboolean) ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( A @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( D @ ( E @ ( A @ r1_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( E @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
& ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( B @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(370,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( A @ k1_pboole @ ( B @ ( A @ r3_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_pboole) ).
thf(1749,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( A @ k1_pboole @ ( B @ ( A @ r3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(283,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(1427,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1797,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
inference(cnf,[status(esa)],[1796]) ).
thf(54215,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,49945]) ).
thf(54216,plain,
( ( ( sk2 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
inference(simp,[status(thm)],[54215]) ).
thf(54241,plain,
( ( sk2 != k1_xboole_0 )
| ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
inference(simp,[status(thm)],[54216]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
thf(1008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
<=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_pboole) ).
thf(1272,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) )
& ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 )
| ~ ( D @ v1_finset_1 )
| ~ ( C @ v1_finset_1 )
| ~ ( B @ v1_finset_1 )
| ~ ( A @ v1_finset_1 ) ),
inference(cnf,[status(esa)],[611]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r4_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_pboole) ).
thf(1240,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r4_pboole ) ) )
& ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(39910,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,39827]) ).
thf(39911,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k3_numbers @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[39910:[bind(A,$thf( k3_numbers @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(39941,plain,
~ ( k3_numbers @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[39911]) ).
thf(17908,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,17541]) ).
thf(17909,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[17908:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski @ k1_tarski ))]]) ).
thf(17956,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[17909]) ).
thf(33350,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,17956]) ).
thf(33351,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[33350]) ).
thf(33382,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ( A
!= ( sk1 @ k1_tarski @ k1_tarski ) ) ),
inference(simp,[status(thm)],[33351]) ).
thf(33430,plain,
( ( sk1 @ k1_tarski @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) ),
inference(simp,[status(thm)],[33382]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_pboole) ).
thf(845,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(7981,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,3399]) ).
thf(7982,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[7981:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) )),bind(B,$thf( B ))]]) ).
thf(9279,plain,
~ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[7982]) ).
thf(229,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k2_pre_circ ) @ ( A @ ( D @ m3_pboole ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ? [F: $i] :
( ( C @ ( F @ ( A @ r3_pboole ) ) )
& ( F
= ( E @ ( D @ k10_funct_6 @ k1_funct_1 ) ) )
& ( A @ ( F @ m1_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_pre_circ) ).
thf(1180,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k2_pre_circ ) @ ( A @ ( D @ m3_pboole ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ? [F: $i] :
( ( C @ ( F @ ( A @ r3_pboole ) ) )
& ( F
= ( E @ ( D @ k10_funct_6 @ k1_funct_1 ) ) )
& ( A @ ( F @ m1_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(21889,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21164]) ).
thf(21890,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21889]) ).
thf(21910,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( sk1 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[21890]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_pboole) ).
thf(671,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_mboolean) ).
thf(903,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(cnfConj,[status(thm)],[521]) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[522]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_pboole) ).
thf(1517,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(5226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) ) )
| ( C @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1055,3048]) ).
thf(5227,plain,
! [A: $i] : ( A @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[5226:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(5308,plain,
! [A: $i] : ( A @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[5227]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_closure3) ).
thf(1289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(206,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(1108,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(1316,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(336,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(1654,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(1010,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1673,plain,
! [A: $i] :
~ ( A @ sk79 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1671]) ).
thf(1863,plain,
! [A: $i] :
( ( ( A @ sk79 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,1673]) ).
thf(1864,plain,
! [A: $i] :
( ( A @ sk79 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1863]) ).
thf(1866,plain,
! [A: $i] :
( ( A @ sk79 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[1864]) ).
thf(11089,plain,
! [B: $i,A: $i] :
( ( B != sk82 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1822]) ).
thf(11090,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk82 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[11089:[bind(A,$thf( A )),bind(B,$thf( sk82 ))]]) ).
thf(11572,plain,
sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[11090]) ).
thf(1732,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ( ! [C: $i] :
( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
inference(miniscope,[status(thm)],[1731]) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk84 @ k1_funct_1 ) @ ( C @ r2_hidden ) )
| ~ ( C @ ( A @ p1_s2_pboole ) )
| ~ ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ p1_s2_pboole ) )
| ~ ( A @ ( sk84 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( A @ ( sk84 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( f1_s2_pboole @ ( sk84 @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[1732]) ).
thf(1734,plain,
f1_s2_pboole @ ( sk84 @ m1_pboole ),
inference(cnfConj,[status(thm)],[1733]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_pboole) ).
thf(1385,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(1745,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(25323,plain,
( ( ( sk10 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21394]) ).
thf(25324,plain,
( ( sk10 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25323]) ).
thf(25342,plain,
( ( ( sk10 @ k1_tarski )
!= k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[25324]) ).
thf(12737,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk86 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9625]) ).
thf(12738,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk86 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[12737:[bind(A,$thf( A )),bind(B,$thf( sk86 @ k1_tarski ))]]) ).
thf(12758,plain,
sk86 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[12738]) ).
thf(78390,plain,
! [A: $i] :
( ( A != k2_numbers )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,30388]) ).
thf(78391,plain,
! [A: $i] :
( ( A != k2_numbers )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[78390]) ).
thf(78392,plain,
~ ( k1_xboole_0 @ ( k2_numbers @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[78391:[bind(A,$thf( k2_numbers ))]]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_pboole) ).
thf(1276,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_pboole) ).
thf(1253,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_pboole) ).
thf(699,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mboolean) ).
thf(1062,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(36035,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk86 @ k1_tarski @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,35947]) ).
thf(36036,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk86 @ k1_tarski @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[36035:[bind(A,$thf( sk86 @ k1_tarski @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(36054,plain,
~ ( sk86 @ k1_tarski @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[36036]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k12_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d22_pboole) ).
thf(1244,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k12_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k12_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_pboole) ).
thf(786,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(48500,plain,
! [A: $i] :
( ( A
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[547,3399]) ).
thf(48501,plain,
! [A: $i] :
( ( A
!= ( sk82 @ ( k1_xboole_0 @ sk3 ) ) )
| ~ ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[48500]) ).
thf(48502,plain,
~ ( sk82 @ ( k1_xboole_0 @ sk3 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[48501:[bind(A,$thf( sk82 @ ( k1_xboole_0 @ sk3 ) ))]]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( D @ ( A @ r1_pboole ) ) )
<=> ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_pboole) ).
thf(1309,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r1_pboole ) ) ) )
& ( ( C @ ( D @ ( A @ r1_pboole ) ) )
=> ( B @ ( D @ ( A @ r1_pboole ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(22219,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21200]) ).
thf(22220,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk86 @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[22219]) ).
thf(22239,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( sk86 @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[22220]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(1030,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_mssubfam) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( A @ ( B @ v1_pre_circ ) )
& ( B @ v2_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( B @ ( D @ ( A @ r1_pboole ) ) )
=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
& ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ ( D @ ( A @ r1_pboole ) ) )
& ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(63979,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,61586]) ).
thf(63980,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[63979]) ).
thf(64011,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k3_numbers @ k1_tarski ) )
| ( A
!= ( k2_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[63980]) ).
thf(64017,plain,
( ( k2_numbers @ k1_tarski @ k1_tarski )
!= ( k3_numbers @ k1_tarski ) ),
inference(simp,[status(thm)],[64011]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
<=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( E @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( D @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_pboole) ).
thf(1077,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( E @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( D @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( E @ ( C @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
& ( B @ ( D @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(78359,plain,
! [A: $i] :
( ( A != sk82 )
| ( ( k1_xboole_0 @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,30806]) ).
thf(78360,plain,
! [A: $i] :
( ( A != sk82 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[78359]) ).
thf(78361,plain,
~ ( k1_xboole_0 @ ( sk82 @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[78360:[bind(A,$thf( sk82 ))]]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
| ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_pboole) ).
thf(899,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
| ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_pboole) ).
thf(1661,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
<=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_mboolean) ).
thf(832,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(14225,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk82 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,11779]) ).
thf(14226,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14225:[bind(A,$thf( sk82 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14261,plain,
k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk82 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14226]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(684,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[548]) ).
thf(1442,plain,
! [A: $i] : ( A @ ( A @ sk57 @ m1_finseq_2 ) ),
inference(cnf,[status(esa)],[1441]) ).
thf(327,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_mboolean) ).
thf(1614,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( B @ ( D @ ( A @ k4_pboole ) ) @ ( C @ ( D @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_pboole) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( B @ ( D @ ( A @ k4_pboole ) ) @ ( C @ ( D @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_finseq_2) ).
thf(1642,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_finseq_2 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_pboole) ).
thf(1774,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(434,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A ) ),
inference(lifteq,[status(thm)],[434]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk4 ) @ r2_hidden ) )
| ( B
= ( A @ k1_tarski ) )
| ( ( A @ ( B @ sk5 ) )
= A ) ),
inference(simp,[status(thm)],[446]) ).
thf(14371,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk10 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,12181]) ).
thf(14372,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( sk10 @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[14371:[bind(A,$thf( sk10 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14386,plain,
~ ( sk10 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[14372]) ).
thf(55916,plain,
! [A: $i] :
( ( A != sk10 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[568,1803]) ).
thf(55917,plain,
! [A: $i] :
( ( A != sk10 )
| ~ ( A @ ( A @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[55916]) ).
thf(55918,plain,
~ ( sk10 @ ( sk10 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[55917:[bind(A,$thf( sk10 ))]]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( D @ ( A @ r1_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_mboolean) ).
thf(1395,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( D @ ( A @ r1_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
=> ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(10755,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,9450]) ).
thf(10756,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk1 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10755:[bind(A,$thf( A )),bind(B,$thf( sk1 @ k1_tarski ))]]) ).
thf(11437,plain,
sk1 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10756]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_pboole) ).
thf(735,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( B @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_pboole) ).
thf(999,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(620,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v1_pboole ) )
<=> ( B @ v3_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v1_pboole) ).
thf(1725,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ( B @ v3_relat_1 )
=> ( A @ ( B @ v1_pboole ) ) )
& ( ( A @ ( B @ v1_pboole ) )
=> ( B @ v3_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1280,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(81267,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ sk83 )
!= ( A @ sk83 ) )
| ( A @ ( k1_xboole_0 @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[77892,1724]) ).
thf(81268,plain,
k1_xboole_0 @ ( k1_xboole_0 @ m1_pboole ),
inference(pattern_uni,[status(thm)],[81267:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(19193,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k3_numbers )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,1179]) ).
thf(19194,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19193:[bind(A,$thf( k2_numbers ))]]) ).
thf(21334,plain,
~ ( k3_numbers @ k1_tarski @ ( k2_numbers @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19194]) ).
thf(14296,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,11979]) ).
thf(14297,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( k2_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14296:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(14332,plain,
k2_numbers @ k1_tarski @ k1_tarski @ ( k3_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14297]) ).
thf(23807,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk82 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,23760]) ).
thf(23808,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk82 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[23807:[bind(A,$thf( A )),bind(B,$thf( sk82 @ k1_tarski ))]]) ).
thf(23835,plain,
~ ( sk82 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[23808]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r1_subset_1 ) )
<=> ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_subset_1) ).
thf(854,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_subset_1 ) ) )
& ( ( B @ ( A @ r1_subset_1 ) )
=> ( B @ ( A @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_pboole) ).
thf(1527,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_2) ).
thf(790,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_finseq_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_finseq_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(2047,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,959]) ).
thf(2048,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2047]) ).
thf(2050,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[2048]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(1363,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[2196,1157]) ).
thf(2326,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(simp,[status(thm)],[2325]) ).
thf(2328,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= k1_xboole_0 )
| ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) @ ( A @ sk3 ) )
!= B )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(simp,[status(thm)],[2326]) ).
thf(2334,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ ( sk1 @ k1_pboole @ k1_funct_4 ) )
!= k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( A @ k1_tarski )
!= sk2 ) ),
inference(simp,[status(thm)],[2328]) ).
thf(77845,plain,
! [A: $i] :
( ( A != sk86 )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,9625]) ).
thf(77846,plain,
! [A: $i] :
( ( A != sk86 )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[77845]) ).
thf(77847,plain,
~ ( k1_xboole_0 @ ( sk86 @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[77846:[bind(A,$thf( sk86 ))]]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_pboole) ).
thf(1056,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(696,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pboole) ).
thf(1165,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(955,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
thf(918,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_pboole) ).
thf(1172,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(897,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_pboole) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(1710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(960,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pboole) ).
thf(1473,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(14799,plain,
! [B: $i,A: $i] :
( ( B
!= ( k3_numbers @ k1_tarski ) )
| ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,12606]) ).
thf(14800,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k3_numbers @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14799:[bind(A,$thf( A )),bind(B,$thf( k3_numbers @ k1_tarski ))]]) ).
thf(14828,plain,
k3_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14800]) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[530]) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[531]) ).
thf(24946,plain,
! [B: $i,A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,24878]) ).
thf(24947,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[24946:[bind(A,$thf( k3_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(24972,plain,
~ ( k3_numbers @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[24947]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( A @ r1_pboole ) ) )
& ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( A @ ( D @ m1_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_mboolean) ).
thf(796,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( A @ r1_pboole ) ) )
& ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( A @ ( D @ m1_pboole ) ) )
=> ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) )
& ( ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
=> ? [D: $i] :
( ( C @ ( D @ ( A @ r1_pboole ) ) )
& ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( A @ ( D @ m1_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(23414,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,22680]) ).
thf(23415,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[23414:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski ))]]) ).
thf(23446,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[23415]) ).
thf(26853,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,23446]) ).
thf(26854,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[26853]) ).
thf(26877,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( k2_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[26854]) ).
thf(26913,plain,
( ( k2_numbers @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[26877]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_pboole) ).
thf(886,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(928,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_pboole) ).
thf(1236,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
& ( C @ ( B @ ( A @ r1_pboole ) ) ) )
=> ( D @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(463,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(cnf,[status(esa)],[462]) ).
thf(464,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(lifteq,[status(thm)],[463]) ).
thf(575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
| ~ ( A @ ( D @ m1_pboole ) )
| ~ ( A @ ( C @ m1_pboole ) )
| ~ ( A @ ( B @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[574]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k3_pboole ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_pboole) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k3_pboole ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pboole) ).
thf(1550,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_pboole) ).
thf(1357,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(78046,plain,
! [A: $i] :
( ( A != k3_numbers )
| ( ( k1_xboole_0 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(paramod_ordered,[status(thm)],[602,12606]) ).
thf(78047,plain,
! [A: $i] :
( ( A != k3_numbers )
| ~ ( k1_xboole_0 @ ( A @ m1_pboole ) ) ),
inference(simp,[status(thm)],[78046]) ).
thf(78048,plain,
~ ( k1_xboole_0 @ ( k3_numbers @ m1_pboole ) ),
inference(pattern_uni,[status(thm)],[78047:[bind(A,$thf( k3_numbers ))]]) ).
thf(28111,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[441,24971]) ).
thf(28112,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ k1_tarski @ ( k3_numbers @ k1_tarski @ r2_hidden ) ) ),
inference(simp,[status(thm)],[28111]) ).
thf(28133,plain,
! [A: $i] :
( ( ( A @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A
!= ( k3_numbers @ k1_tarski ) ) ),
inference(simp,[status(thm)],[28112]) ).
thf(28167,plain,
( ( k3_numbers @ k1_tarski @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[28133]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ r2_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_pboole) ).
thf(1597,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ r2_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(728,plain,
sk10 @ v1_finset_1,
inference(cnfConj,[status(thm)],[726]) ).
thf(10260,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( B != sk82 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,3249]) ).
thf(10261,plain,
! [A: $i] :
( ( A != sk82 )
| ( A @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10260:[bind(A,$thf( k1_xboole_0 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(11236,plain,
sk82 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10261]) ).
thf(21949,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[893,21165]) ).
thf(21950,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
!= ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21949]) ).
thf(22074,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( ( B @ ( A @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(simp,[status(thm)],[21950]) ).
thf(22094,plain,
! [A: $i] :
( ( A @ ( sk1 @ k1_tarski @ k3_xboole_0 ) )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[22074]) ).
thf(8823,plain,
! [B: $i,A: $i] :
( ( A != k2_numbers )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1807]) ).
thf(8824,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k2_numbers @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8823:[bind(A,$thf( k2_numbers ))]]) ).
thf(9193,plain,
~ ( k2_numbers @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8824]) ).
thf(1817,plain,
( ( ( sk82 @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1690,1718]) ).
thf(1818,plain,
( ( sk82 @ v1_xboole_0 )
!= ( sk80 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1817]) ).
thf(1821,plain,
sk82 != sk80,
inference(simp,[status(thm)],[1818]) ).
thf(2654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != sk82 )
| ( A != sk80 )
| ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[418,1821]) ).
thf(2655,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk80 )
| ( C @ ( sk82 @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[2654:[bind(A,$thf( A )),bind(B,$thf( sk82 ))]]) ).
thf(2976,plain,
! [B: $i,A: $i] : ( B @ ( sk82 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk80 @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[2655]) ).
thf(7297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( sk80 @ k1_tarski @ k2_zfmisc_1 ) ) )
| ( C @ ( sk82 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1055,2976]) ).
thf(7298,plain,
! [A: $i] : ( A @ ( sk82 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7297:[bind(A,$thf( sk80 @ k1_tarski )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(7370,plain,
! [A: $i] : ( A @ ( sk82 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[7298]) ).
thf(14292,plain,
! [B: $i,A: $i] :
( ( A
!= ( k2_numbers @ k1_tarski ) )
| ( B
!= ( k3_numbers @ k1_tarski ) )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,11979]) ).
thf(14293,plain,
! [A: $i] :
( ( A
!= ( k3_numbers @ k1_tarski ) )
| ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14292:[bind(A,$thf( k2_numbers @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(14330,plain,
k3_numbers @ k1_tarski @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14293]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( D @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_pboole) ).
thf(850,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( D @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(23006,plain,
( ( ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1098,21160]) ).
thf(23007,plain,
( ( k1_xboole_0 @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) )
!= ( k2_numbers @ ( k3_numbers @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23006]) ).
thf(23032,plain,
( ( ( k1_xboole_0 @ k1_tarski )
!= k2_numbers )
| ( ( sk1 @ k1_tarski @ k1_tarski )
!= k3_numbers ) ),
inference(simp,[status(thm)],[23007]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(10362,plain,
! [B: $i,A: $i] :
( ( B != k3_numbers )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[457,1828]) ).
thf(10363,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( k3_numbers @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[10362:[bind(A,$thf( A )),bind(B,$thf( k3_numbers ))]]) ).
thf(11276,plain,
k3_numbers @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[10363]) ).
thf(20369,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ k1_tarski ) )
| ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,9450]) ).
thf(20370,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[20369:[bind(A,$thf( sk1 @ k1_tarski )),bind(B,$thf( B ))]]) ).
thf(21744,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( sk1 @ k1_tarski @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[20370]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ~ ( ( F @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( D @ ( F @ ( A @ r2_pboole ) ) )
& ( A @ ( F @ v1_pre_circ ) )
& ( C @ ( E @ ( A @ r2_pboole ) ) )
& ( A @ ( E @ v1_pre_circ ) ) ) ) )
& ( D @ ( C @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_mssubfam) ).
thf(1449,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ~ ( ( F @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( D @ ( F @ ( A @ r2_pboole ) ) )
& ( A @ ( F @ v1_pre_circ ) )
& ( C @ ( E @ ( A @ r2_pboole ) ) )
& ( A @ ( E @ v1_pre_circ ) ) ) ) )
& ( D @ ( C @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
& ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_pboole) ).
thf(708,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(8032,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,1803]) ).
thf(8033,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( sk10 @ k1_tarski @ ( A @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[8032:[bind(A,$thf( sk10 ))]]) ).
thf(9303,plain,
~ ( sk10 @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[8033]) ).
thf(37747,plain,
! [B: $i,A: $i] :
( ( B
!= ( k2_numbers @ k1_tarski @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[451,37682]) ).
thf(37748,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( A @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r2_hidden ) ) ),
inference(pattern_uni,[status(thm)],[37747:[bind(A,$thf( A )),bind(B,$thf( k2_numbers @ k1_tarski @ k1_tarski ))]]) ).
thf(37795,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k2_numbers @ k1_tarski @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[37748]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_pboole) ).
thf(1769,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(19293,plain,
! [B: $i,A: $i] :
( ( B
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A != k1_xboole_0 )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[488,3332]) ).
thf(19294,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(pattern_uni,[status(thm)],[19293:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(21372,plain,
~ ( k1_xboole_0 @ k1_tarski @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[19294]) ).
thf(75570,plain,
! [A: $i] :
( ( ( A @ ( A @ r1_tarski ) )
!= ( sk86 @ ( sk86 @ k2_zfmisc_1 ) @ ( sk86 @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,64796]) ).
thf(75571,plain,
! [A: $i] :
( ( A @ ( A @ r1_tarski ) )
!= ( sk86 @ ( sk86 @ k2_zfmisc_1 ) @ ( sk86 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[75570]) ).
thf(75696,plain,
! [A: $i] :
( ( A
!= ( sk86 @ ( sk86 @ k2_zfmisc_1 ) ) )
| ( A != sk86 ) ),
inference(simp,[status(thm)],[75571]) ).
thf(75724,plain,
( ( sk86 @ ( sk86 @ k2_zfmisc_1 ) )
!= sk86 ),
inference(simp,[status(thm)],[75696]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( A @ ( C @ m2_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_pboole) ).
thf(1468,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_pboole ) ) ) )
& ( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(1014,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(972,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(89529,plain,
$false,
inference(e,[status(thm)],[892,24878,1718,1411,1024,1168,1633,1767,1105,1729,628,8283,893,1179,555,1554,3399,21164,76079,518,1686,481,1200,1005,1068,11571,1443,1422,741,1142,511,677,597,14399,408,7886,762,1544,25211,873,449,15239,1041,1705,1788,25204,14264,16777,3332,550,37798,14829,1233,1260,68589,930,1458,23179,533,500,22347,41334,9278,538,55871,1196,841,9159,9195,1650,1359,1724,1529,1803,651,9625,1095,77892,14333,12833,1782,3249,782,1441,11568,23443,13083,1601,55957,64796,1703,1228,1482,389,76966,570,18468,21210,719,34228,9332,24971,23447,23172,751,802,12606,1462,542,1055,724,11667,1792,21160,1860,817,21394,55092,23836,40710,24536,1568,61587,41337,5076,1778,22348,39600,638,421,11564,606,1347,1572,1415,63473,1714,26081,443,1109,1828,574,821,905,924,9298,1302,756,21335,4820,7441,34232,14267,1682,485,1136,57394,514,1151,21213,806,23176,966,23839,1843,30806,396,1351,428,30388,1521,507,527,1696,1564,602,56041,766,1169,397,877,692,1796,1072,1622,774,22271,660,1345,21200,1697,1242,849,11597,1074,920,1306,14263,16780,714,1730,1206,452,23175,512,7782,529,1691,534,23180,9488,31906,1519,1355,1255,862,1676,598,14978,1487,630,1238,9158,1723,910,957,894,746,12773,11238,1343,1502,1751,10102,429,11565,1370,22346,729,916,1365,24967,14317,21922,583,77938,461,50792,1656,79984,1128,11244,484,14401,1602,11532,1624,61502,710,12760,1762,948,615,9245,1064,1111,725,1672,11435,593,499,519,1592,578,1089,9196,1270,81751,403,1587,1138,1719,610,9333,420,1118,1683,884,1160,1028,488,64964,22343,476,22072,489,21370,77895,27223,547,49945,23853,471,554,753,1739,537,12818,669,2196,526,1612,1039,1776,1099,701,32327,21162,457,39597,569,1599,1720,3364,12831,2285,393,1114,1131,654,41228,721,28476,1393,503,605,61586,64876,11593,23980,508,1695,21395,541,1712,1035,36077,1515,926,792,40711,1086,3225,1466,558,40544,9284,1663,1026,14826,1167,1616,21214,24970,530,794,586,662,888,21165,23840,1680,824,25207,573,21211,1374,733,37682,1278,1648,412,1764,22479,513,430,1747,76680,819,402,76974,1784,843,54285,1652,1701,413,1007,694,772,25209,3472,25506,1388,24865,577,36081,10100,21201,9189,1226,545,32744,391,1058,11678,12759,1092,78410,804,16782,1464,9248,445,9285,936,1707,2293,611,16779,540,23741,23838,52522,1282,23760,77574,1589,451,11531,764,604,681,56346,1542,63742,1771,737,509,880,649,599,11979,1376,21746,17957,494,535,483,848,11569,1149,24968,1460,1177,64841,890,1667,477,9302,811,387,858,552,26383,609,21456,1731,21393,943,1022,462,34225,932,912,399,1699,959,9450,1445,780,26564,1477,45567,23183,431,653,1562,1213,768,455,11245,394,2288,25104,25206,1583,426,944,548,1420,1684,749,1145,553,458,836,1134,23445,3048,617,516,11679,12817,580,690,640,39938,872,705,11275,2012,61585,1780,1753,22344,1098,23311,5570,776,712,557,1003,6885,1400,61395,409,1484,673,1432,1186,441,585,502,1262,22680,808,14832,1130,1218,1053,16643,17541,23440,23575,1987,1716,61583,717,576,1658,11661,544,907,1766,21455,703,1536,3356,1506,21397,727,1140,14383,571,23442,656,1802,613,4976,56377,1284,1353,600,1749,1427,1670,1797,54241,1008,1272,612,1240,39941,33430,845,465,9279,9192,1180,539,21910,671,903,524,1517,759,39827,5308,1289,1108,1316,24965,1157,1834,495,1654,1010,34229,1866,11572,1734,50777,1807,1385,517,1674,390,1745,632,25342,12758,78392,1276,1253,699,1062,36054,1244,1822,418,786,25210,48502,1689,914,510,1308,1309,22239,1045,1030,1491,568,12181,64017,34109,1077,478,78361,899,1661,832,14261,684,549,1442,716,1614,23076,1116,9812,1642,1774,447,14386,55918,410,1395,11437,17956,603,735,999,620,1725,1280,39473,81268,21334,14332,23835,854,1527,1673,790,2050,1363,2334,77847,506,1056,696,1165,955,25115,918,1172,897,1033,1710,400,960,11779,1473,14828,532,24972,796,26913,886,928,1236,464,575,1532,1550,1357,78048,28167,61404,1597,871,1120,23446,728,11236,22094,723,9193,7370,14330,850,23032,1299,11276,607,9188,486,9399,22341,543,7602,560,21744,1449,708,9303,9297,37795,1769,21372,75724,1468,3047,454,35947,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG225+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n001.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 21:40:32 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.91/1.81 % [INFO] Parsing done (815ms).
% 3.91/1.83 % [INFO] Running in sequential loop mode.
% 4.46/2.19 % [INFO] eprover registered as external prover.
% 4.46/2.20 % [INFO] Scanning for conjecture ...
% 6.15/2.62 % [INFO] Found a conjecture (or negated_conjecture) and 4729 axioms. Running axiom selection ...
% 7.51/3.13 % [INFO] Axiom selection finished. Selected 384 axioms (removed 4345 axioms).
% 8.50/3.45 % [INFO] Problem is first-order (TPTP FOF).
% 8.50/3.49 % [INFO] Type checking passed.
% 8.50/3.49 % [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 ...
% 138.83/38.17 % External prover 'e' found a proof!
% 138.83/38.17 % [INFO] Killing All external provers ...
% 138.83/38.17 % Time passed: 37629ms (effective reasoning time: 36340ms)
% 138.83/38.17 % 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)>
% 138.83/38.18 % Axioms used in derivation (384): rc2_setfam_1, t15_finset_1, existence_m2_pboole, t24_mboolean, t34_mboolean, t1_mboolean, t92_pboole, t6_mboolean, t143_pboole, t102_pboole, dt_k11_pboole, antisymmetry_r3_pboole, t19_xboole_1, t17_xboole_1, t62_pboole, t109_pboole, d1_tarski, t27_mboolean, t135_zfmisc_1, t17_zfmisc_1, t24_pboole, d9_setfam_1, t136_pboole, d12_pboole, t66_xboole_1, dt_k2_pre_circ, d3_closure3, irreflexivity_r1_subset_1, t58_pboole, reflexivity_r2_pboole, t1_closure3, cc1_mssubfam, idempotence_k3_xboole_0, redefinition_m2_finseq_2, t3_xboole_1, t113_zfmisc_1, t44_pboole, t25_pboole, t28_mboolean, t19_mboolean, d11_pboole, t4_ordinal1, t1_subset, t10_partfun1, cc1_setfam_1, fc1_xboole_0, t85_pboole, t20_mboolean, d5_xboole_0, t52_zfmisc_1, fc4_subset_1, t17_pboole, t36_pboole, t16_fraenkel, t18_xboole_1, t39_pboole, t33_mboolean, d4_zfmisc_1, t22_mboolean, t73_pboole, t13_numbers, t17_mboolean, d5_pboole, t68_xboole_1, t19_finset_1, t2_boole, t117_zfmisc_1, t59_pboole, t122_zfmisc_1, t37_pboole, t66_pboole, t108_pboole, t27_xboole_1, t95_zfmisc_1, t140_pboole, t28_pboole, t12_mssubfam, existence_m2_finseq_2, dt_k4_pboole, t141_pboole, dt_m3_pboole, t43_pboole, t19_pboole, s2_pboole, d8_pboole, t21_pboole, t41_zfmisc_1, t131_zfmisc_1, t112_pboole, t16_mboolean, fc2_pboole, t84_pboole, t103_pboole, t128_pboole, t9_pboole, t16_pboole, t142_pboole, commutativity_k3_pboole, commutativity_k3_xboole_0, t23_mboolean, fraenkel_a_2_0_closure3, fc11_finset_1, t86_pboole, t135_pboole, t27_mssubfam, dt_k2_pboole, t150_pboole, t18_pboole, t52_pboole, t63_pboole, symmetry_r5_pboole, t115_zfmisc_1, t123_pboole, t35_pboole, t137_zfmisc_1, fc2_numbers, d1_xboole_0, d15_pboole, t108_xboole_1, t130_pboole, t129_pboole, t138_zfmisc_1, t130_zfmisc_1, t118_zfmisc_1, t122_pboole, fc2_setfam_1, t119_pboole, cc1_pboole, t94_pboole, fc2_funct_2, t56_zfmisc_1, t6_boole, t132_pboole, fc10_finset_1, t1_xboole_1, t7_mboolean, t20_pboole, t97_pboole, t29_mboolean, t75_xboole_1, t22_pboole, t37_mboolean, d10_pboole, t98_pboole, t13_mboolean, t68_pboole, t48_pboole, t21_finset_1, t19_mssubfam, t94_zfmisc_1, d2_mboolean, t65_xboole_1, d22_pboole, t40_pboole, t6_pboole, t32_mboolean, t113_pboole, t4_xboole_0, idempotence_k2_pboole, rc3_setfam_1, t127_pboole, t123_zfmisc_1, fc2_subset_1, fraenkel_a_2_1_closure3, t15_mboolean, d3_zfmisc_1, t2_tarski, fc6_subset_1, t27_pboole, t5_pboole, redefinition_v1_pboole, t23_pboole, t97_zfmisc_1, t106_pboole, t144_pboole, t2_zfmisc_1, t148_pboole, t87_pboole, t5_ordinal1, dt_k2_mboolean, t98_zfmisc_1, t76_xboole_1, fc3_numbers, d17_pboole, t124_pboole, t34_pboole, d4_tarski, dt_k1_mboolean, t88_pboole, t25_finset_1, t67_xboole_1, t99_pboole, commutativity_k2_pboole, t58_zfmisc_1, t139_zfmisc_1, t7_boole, symmetry_r1_subset_1, t13_finset_1, t3_ordinal1, d2_subset_1, t54_pboole, t137_pboole, t101_pboole, t7_ordinal1, t67_pboole, dt_k3_pboole, d16_pboole, t12_pboole, t22_finset_1, d3_pre_circ, t61_pboole, t50_pboole, t60_pboole, t89_pboole, t21_mboolean, cc2_setfam_1, reflexivity_r6_pboole, t69_xboole_1, existence_m3_pboole, t116_zfmisc_1, d7_xboole_0, redefinition_r1_subset_1, t47_pboole, t20_xboole_1, t20_mssubfam, t16_zfmisc_1, dt_m2_pboole, existence_m1_pboole, t16_mssubfam, t14_funct_2, t134_pboole, t124_zfmisc_1, d14_pboole, fc5_subset_1, existence_m1_subset_1, t69_pboole, t115_pboole, t110_pboole, fc1_finset_1, idempotence_k3_pboole, t23_mssubfam, d4_pboole, t92_zfmisc_1, t121_pboole, t114_pboole, t31_mboolean, redefinition_r6_pboole, t16_xboole_1, t42_pboole, redefinition_r2_subset_1, t138_pboole, t114_zfmisc_1, t31_zfmisc_1, t26_xboole_1, t63_xboole_1, t64_pboole, t12_mboolean, t26_mssubfam, t79_pboole, t71_pboole, commutativity_k5_pboole, t81_pboole, cc2_pboole, t139_pboole, t70_pboole, t23_numbers, t8_pboole, t28_xboole_1, d3_tarski, t151_pboole, t39_zfmisc_1, t119_zfmisc_1, t104_pboole, t10_pre_circ, t54_zfmisc_1, reflexivity_r1_tarski, symmetry_r2_subset_1, t6_zfmisc_1, t77_pboole, t56_setfam_1, t75_pboole, t20_finset_1, t2_xboole_1, t53_pboole, t38_pboole, t18_mssubfam, t56_pboole, t10_pboole, t76_pboole, t133_pboole, t11_mboolean, t96_pboole, t26_mboolean, dt_k1_pboole, t18_zfmisc_1, t126_pboole, t41_pboole, t51_zfmisc_1, rc1_finset_1, t64_xboole_1, t18_mboolean, t127_zfmisc_1, t15_pboole, cc1_finset_1, t57_pboole, t29_mssubfam, t77_xboole_1, t23_finset_1, t100_pboole, t105_pboole, t111_pboole, t11_pboole, t78_pboole, t21_mssubfam, t8_boole, rc1_xboole_0, t24_zfmisc_1, t49_pboole, t111_relat_1, t26_pboole, t5_mboolean, t37_zfmisc_1, t72_pboole, t149_pboole, symmetry_r1_xboole_0, t134_zfmisc_1, t2_subset, existence_m1_finseq_2, reflexivity_r7_pboole, t3_pboole, t51_pboole, t116_pboole, t65_pboole, t80_pboole, d13_pboole, t36_mboolean, d10_xboole_0, d11_setfam_1, d21_pboole, t22_mssubfam, t147_pboole, t120_pboole, t74_xboole_1, t35_mboolean, t7_tarski, dt_k5_pboole, t83_pboole, t88_funct_6, t3_xboole_0, t6_ordinal1, t28_mssubfam, t82_pboole, t30_mboolean, fc16_finset_1, fc14_finset_1, redefinition_r3_pboole, rc1_setfam_1, t29_pboole, t9_mboolean, symmetry_r6_pboole, symmetry_r4_pboole, t145_pboole, rc2_xboole_0, dt_k12_pboole, t46_pboole, t74_pboole, t118_pboole, t10_mboolean, t2_mboolean, t11_mssubfam, d3_xboole_0, t55_pboole, antisymmetry_r2_hidden, fc15_finset_1, fc1_funct_2, t6_pre_circ, redefinition_v2_pboole, rc1_finseq_2, t91_pboole, t95_pboole, irreflexivity_r2_subset_1, t7_pboole, t45_pboole, t146_pboole
% 138.83/38.18 % No. of inferences in proof: 1937
% 138.83/38.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 37629 ms resp. 36340 ms w/o parsing
% 140.35/38.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 140.35/38.69 % [INFO] Killing All external provers ...
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