%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 06:46:23 AM UTC 2026
% Result : Theorem 83.40s 19.64s
% Output : Refutation 84.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 519
% Syntax : Number of formulae : 1040 ( 191 unt; 0 typ; 0 def)
% Number of atoms : 3743 ( 482 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 15240 ( 432 ~; 51 |; 810 &;12105 @)
% ( 78 <=>;1764 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 6 con; 0-4 aty)
% Number of variables : 2993 ( 0 ^;2939 !; 54 ?;2993 :)
% 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_closure3_decl,type,
k1_closure3: $i > $i > $i ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(r6_pboole_decl,type,
r6_pboole: $i > $i > $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k2_xboole_0_decl,type,
k2_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(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
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(k1_pboole_decl,type,
k1_pboole: $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k5_xboole_0_decl,type,
k5_xboole_0: $i > $i > $i ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
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(k2_pboole_decl,type,
k2_pboole: $i > $i > $i > $i ).
thf(r2_pboole_decl,type,
r2_pboole: $i > $i > $i > $o ).
thf(k3_pboole_decl,type,
k3_pboole: $i > $i > $i > $i ).
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(r1_pboole_decl,type,
r1_pboole: $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(k4_pboole_decl,type,
k4_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(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(r5_pboole_decl,type,
r5_pboole: $i > $i > $i > $o ).
thf(k5_pboole_decl,type,
k5_pboole: $i > $i > $i > $i ).
thf(r4_pboole_decl,type,
r4_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(k11_pboole_decl,type,
k11_pboole: $i > $i > $i > $i ).
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(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
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(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(1411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(1024,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)],[120]) ).
thf(158,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(1168,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',t126_pboole) ).
thf(2072,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)],[399]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',t58_pboole) ).
thf(1729,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)],[307]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(628,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(511,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_circ) ).
thf(2463,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',t22_pboole) ).
thf(1982,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)],[371]) ).
thf(160,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(1179,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(1295,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)],[194]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(1554,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)],[256]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(1586,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(809,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(205,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(1337,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',t50_pboole) ).
thf(1718,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)],[302]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).
thf(2336,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)],[468]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',t52_pboole) ).
thf(2031,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)],[387]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',t11_mssubfam) ).
thf(1956,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)],[365]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(1549,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',t23_mssubfam) ).
thf(2210,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)],[436]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',t15_pboole) ).
thf(1596,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)],[269]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(683,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',t16_mssubfam) ).
thf(2381,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)],[484]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',t41_pboole) ).
thf(2062,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)],[395]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',t18_pboole) ).
thf(2014,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)],[381]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',d21_pboole) ).
thf(2114,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)],[409]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(1305,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_xboole_1) ).
thf(1041,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(1486,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)],[241]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',t63_pboole) ).
thf(1855,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)],[338]) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',t140_pboole) ).
thf(2077,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)],[401]) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',t29_mssubfam) ).
thf(2099,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)],[407]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',t33_mboolean) ).
thf(1591,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)],[268]) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',t1_mboolean) ).
thf(1971,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)],[369]) ).
thf(322,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(1793,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(273,axiom,
k3_numbers != k2_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_numbers) ).
thf(1608,plain,
k3_numbers != k2_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(550,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)],[9]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',t104_pboole) ).
thf(1735,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)],[309]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',t20_mssubfam) ).
thf(2316,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)],[462]) ).
thf(506,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( A @ k1_pboole @ ( B @ ( A @ r3_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_pboole) ).
thf(2448,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)],[506]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(2141,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)],[416]) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',t124_pboole) ).
thf(1872,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)],[344]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(1327,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(747,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)],[45]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(945,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',t89_pboole) ).
thf(2042,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)],[390]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(538,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)],[5]) ).
thf(475,axiom,
~ ( k2_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_numbers) ).
thf(2360,plain,
~ ( k2_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',t8_pboole) ).
thf(1867,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)],[343]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',t108_pboole) ).
thf(2184,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)],[426]) ).
thf(517,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/sandbox2/benchmark/theBenchmark.p',t35_pboole) ).
thf(2476,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)],[517]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',t27_mssubfam) ).
thf(2168,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)],[423]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',t24_mboolean) ).
thf(698,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)],[34]) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',t75_pboole) ).
thf(1919,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)],[357]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_pboole) ).
thf(1988,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)],[374]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(1095,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(1196,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mboolean) ).
thf(898,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(329,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/sandbox2/benchmark/theBenchmark.p',t69_pboole) ).
thf(1835,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)],[329]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',t29_pboole) ).
thf(2046,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)],[392]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(1391,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1441,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(36,axiom,
! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mboolean) ).
thf(709,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)],[36]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
thf(973,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)],[102]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(565,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)],[13]) ).
thf(493,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/sandbox2/benchmark/theBenchmark.p',t45_pboole) ).
thf(2400,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)],[493]) ).
thf(184,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(1265,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(1482,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',dt_k2_pboole) ).
thf(1650,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)],[283]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',t38_pboole) ).
thf(1921,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)],[358]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',t60_pboole) ).
thf(2269,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)],[448]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1511,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 @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_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)],[248]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1455,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)],[233]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(1191,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(469,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_2) ).
thf(2339,plain,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_finseq_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_relat_1) ).
thf(785,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(1330,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)],[204]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(2444,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)],[504]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(1147,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)],[152]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(1319,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)],[200]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(1013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',t27_pboole) ).
thf(1741,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)],[312]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(1115,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)],[144]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',t34_mboolean) ).
thf(1931,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)],[361]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pboole) ).
thf(1963,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(173,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(1232,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',t94_pboole) ).
thf(1847,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)],[334]) ).
thf(252,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(1545,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v1_pboole ) )
<=> ( B @ v3_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v1_pboole) ).
thf(2420,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)],[499]) ).
thf(480,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(2373,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pboole) ).
thf(1572,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',t13_mboolean) ).
thf(2007,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)],[379]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(924,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',t16_pboole) ).
thf(2027,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)],[386]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
thf(1373,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(1418,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)],[223]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(937,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)],[91]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(966,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)],[101]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(756,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)],[47]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',t37_mboolean) ).
thf(1664,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)],[288]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(1383,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)],[213]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(602,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(332,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/sandbox2/benchmark/theBenchmark.p',t57_pboole) ).
thf(1843,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)],[332]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(687,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)],[33]) ).
thf(210,axiom,
k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_pboole) ).
thf(1377,plain,
k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',d8_pboole) ).
thf(2281,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)],[452]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(634,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)],[24]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',t61_pboole) ).
thf(2190,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)],[429]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(866,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',t115_pboole) ).
thf(1796,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)],[323]) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',t48_pboole) ).
thf(2424,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)],[500]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(1394,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',commutativity_k3_pboole) ).
thf(1600,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)],[271]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(1564,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)],[260]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',t86_pboole) ).
thf(2392,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)],[489]) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',t142_pboole) ).
thf(2154,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)],[419]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(1863,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)],[341]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mboolean) ).
thf(2204,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(297,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 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_pboole) ).
thf(1691,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_xboole_0 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k2_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k2_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(761,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',t111_pboole) ).
thf(1783,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)],[319]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(1067,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)],[132]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(714,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',d14_pboole) ).
thf(1636,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)],[279]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(167,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(1199,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',symmetry_r6_pboole) ).
thf(2364,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)],[477]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',t59_pboole) ).
thf(1915,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)],[355]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',t68_pboole) ).
thf(2093,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)],[405]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1311,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)],[199]) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',redefinition_r6_pboole) ).
thf(2307,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)],[460]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(1274,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(957,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(501,axiom,
~ ( k3_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_numbers) ).
thf(2428,plain,
~ ( k3_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(444,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/sandbox2/benchmark/theBenchmark.p',t36_pboole) ).
thf(2249,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)],[444]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(1580,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)],[264]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(1123,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)],[147]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',t22_mssubfam) ).
thf(1676,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)],[291]) ).
thf(65,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(820,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(12,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(561,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(788,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)],[55]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(815,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)],[63]) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',t12_mssubfam) ).
thf(2396,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)],[491]) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',t26_mboolean) ).
thf(1560,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)],[258]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',t62_pboole) ).
thf(1723,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)],[304]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(916,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(879,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(467,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2332,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',d4_pboole) ).
thf(1951,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)],[364]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',t139_pboole) ).
thf(1687,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)],[295]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',t17_mboolean) ).
thf(2068,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)],[397]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',t43_pboole) ).
thf(2200,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)],[433]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(1159,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',t138_pboole) ).
thf(1787,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)],[320]) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',fc2_pboole) ).
thf(2345,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)],[471]) ).
thf(520,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/sandbox2/benchmark/theBenchmark.p',t143_pboole) ).
thf(2492,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)],[520]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',t83_pboole) ).
thf(1634,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)],[278]) ).
thf(192,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(1291,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(1936,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)],[362]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(742,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(874,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)],[74]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',t10_mboolean) ).
thf(1375,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)],[209]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(980,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)],[104]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(1425,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(289,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/sandbox2/benchmark/theBenchmark.p',t120_pboole) ).
thf(1672,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)],[289]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(1138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(593,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)],[17]) ).
thf(72,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(869,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(783,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(1397,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)],[217]) ).
thf(174,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(1234,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(250,axiom,
k2_numbers @ ( k3_numbers @ r1_tarski ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_numbers) ).
thf(1541,plain,
k2_numbers @ ( k3_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(1270,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)],[186]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',t78_pboole) ).
thf(1851,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)],[336]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(1259,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',dt_k12_pboole) ).
thf(2377,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)],[482]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(948,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',t80_pboole) ).
thf(1659,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)],[286]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(554,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1739,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',t27_mboolean) ).
thf(1075,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)],[134]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(642,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',t99_pboole) ).
thf(1700,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)],[298]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',t105_pboole) ).
thf(1791,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)],[321]) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',t53_pboole) ).
thf(2038,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)],[389]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( A @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ~ ( A @ ( D @ r2_hidden ) ) )
& ( ~ ( A @ ( D @ r2_hidden ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(547,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)],[8]) ).
thf(510,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2460,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',t10_pboole) ).
thf(1683,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)],[293]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',t20_mboolean) ).
thf(2196,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)],[431]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',t40_pboole) ).
thf(1889,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)],[348]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',t54_pboole) ).
thf(1644,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)],[281]) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',t34_pboole) ).
thf(2472,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)],[515]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(679,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mboolean) ).
thf(1039,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(837,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 @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_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)],[69]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(1324,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(1451,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)],[232]) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',d13_pboole) ).
thf(2487,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)],[519]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',t19_mboolean) ).
thf(1131,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)],[148]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',t71_pboole) ).
thf(1947,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)],[363]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',t151_pboole) ).
thf(1984,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)],[372]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',t29_mboolean) ).
thf(1002,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)],[111]) ).
thf(179,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1246,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
& ( B
!= ( A @ k1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_pboole) ).
thf(1720,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)],[303]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(605,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( A @ r1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r1_subset_1) ).
thf(2370,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)],[479]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(1776,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)],[317]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(997,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)],[109]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',redefinition_r3_pboole) ).
thf(2450,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)],[507]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',t18_mboolean) ).
thf(2125,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)],[411]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(1478,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)],[239]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(1249,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)],[180]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',t1_closure3) ).
thf(2387,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)],[487]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',t130_pboole) ).
thf(1831,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)],[327]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).
thf(2465,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)],[512]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(1060,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',redefinition_r2_subset_1) ).
thf(1050,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)],[128]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',t42_pboole) ).
thf(1857,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)],[339]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(1202,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(1241,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k2_pboole ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_pboole) ).
thf(1779,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)],[318]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(921,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(541,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(1170,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)],[159]) ).
thf(190,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(1286,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(495,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t6_closure3) ).
thf(2408,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)],[495]) ).
thf(121,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(1026,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(1185,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(57,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(794,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(394,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/sandbox2/benchmark/theBenchmark.p',t150_pboole) ).
thf(2057,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)],[394]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',t7_mboolean) ).
thf(1466,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)],[234]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(558,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(1071,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',t26_pboole) ).
thf(1727,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)],[306]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(1251,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ v2_setfam_1 )
<=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_setfam_1) ).
thf(2176,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)],[425]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',dt_k4_pboole) ).
thf(2292,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)],[454]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',d17_pboole) ).
thf(2033,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)],[388]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',t7_pboole) ).
thf(1927,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)],[360]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(745,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)],[44]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',t28_pboole) ).
thf(2235,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)],[441]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k3_pboole ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_pboole) ).
thf(2144,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)],[417]) ).
thf(81,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(906,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(1135,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)],[149]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',t85_pboole) ).
thf(1648,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)],[282]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(975,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',t18_mssubfam) ).
thf(1833,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)],[328]) ).
thf(113,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(1007,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',dt_k5_pboole) ).
thf(2188,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)],[428]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(1620,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)],[276]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',t36_mboolean) ).
thf(1752,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)],[314]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',d3_pre_circ) ).
thf(1652,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)],[284]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',d12_pboole) ).
thf(2016,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)],[382]) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',antisymmetry_r3_pboole) ).
thf(2398,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)],[492]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(1226,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(826,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)],[67]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(711,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ~ ( ( B @ ( A @ r2_hidden ) )
<=> ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
=> ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(1503,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(572,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)],[14]) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',t103_pboole) ).
thf(1865,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)],[342]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',t112_pboole) ).
thf(1733,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)],[308]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(1239,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)],[176]) ).
thf(516,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/sandbox2/benchmark/theBenchmark.p',symmetry_r4_pboole) ).
thf(2474,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)],[516]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',t6_pboole) ).
thf(2148,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)],[418]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',t88_pboole) ).
thf(2055,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)],[393]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(1092,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',t97_pboole) ).
thf(2166,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)],[422]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(1090,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)],[138]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(764,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_setfam_1) ).
thf(1194,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(900,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
thf(2478,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)],[518]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',t25_pboole) ).
thf(2229,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)],[439]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r7_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r7_pboole) ).
thf(2415,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)],[497]) ).
thf(145,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(1117,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)],[145]) ).
thf(41,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(736,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',t81_pboole) ).
thf(1589,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)],[267]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(1542,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',t51_pboole) ).
thf(1853,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)],[337]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',t72_pboole) ).
thf(2214,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)],[437]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',t98_pboole) ).
thf(2383,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)],[485]) ).
thf(443,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(2246,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(1492,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)],[243]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',d5_pboole) ).
thf(1603,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)],[272]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',t39_pboole) ).
thf(2299,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)],[457]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(599,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(228,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(1439,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(1471,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(631,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(758,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',t44_pboole) ).
thf(1630,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)],[277]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',t79_pboole) ).
thf(2267,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)],[447]) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',t135_pboole) ).
thf(2446,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)],[505]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(700,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(193,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(1293,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',dt_k3_pboole) ).
thf(2025,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)],[385]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',existence_m2_finseq_2) ).
thf(1080,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)],[136]) ).
thf(461,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/sandbox2/benchmark/theBenchmark.p',t19_mssubfam) ).
thf(2314,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)],[461]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',t3_pboole) ).
thf(2129,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)],[413]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(535,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',t84_pboole) ).
thf(2343,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)],[470]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(1162,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(943,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)],[92]) ).
thf(119,axiom,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_funct_6) ).
thf(1022,plain,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',t66_pboole) ).
thf(1841,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)],[331]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
<=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(1044,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)],[127]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_xboole_1) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(2390,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)],[488]) ).
thf(458,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/sandbox2/benchmark/theBenchmark.p',t113_pboole) ).
thf(2303,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)],[458]) ).
thf(420,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/sandbox2/benchmark/theBenchmark.p',t37_pboole) ).
thf(2156,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)],[420]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(912,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)],[83]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
= ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ k1_closure3 ) )
= ( C @ ( A @ k1_closure3 ) ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_closure3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
= ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ k1_closure3 ) )
= ( C @ ( A @ k1_closure3 ) ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(521,plain,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( C @ v2_relat_1 ) )
=> ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
= ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ k1_closure3 ) )
= ( C @ ( A @ k1_closure3 ) ) ) )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(983,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(498,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(2418,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(415,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/sandbox2/benchmark/theBenchmark.p',t19_pboole) ).
thf(2139,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)],[415]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',t106_pboole) ).
thf(2064,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)],[396]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',t116_pboole) ).
thf(2244,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)],[442]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(2005,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(1583,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(927,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)],[89]) ).
thf(189,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1277,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)],[189]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(812,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)],[62]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
<=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(749,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
<=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_pboole) ).
thf(1990,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)],[375]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(1340,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)],[206]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k2_mboolean ) @ ( A @ k1_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_mboolean) ).
thf(1018,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)],[117]) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',t11_pboole) ).
thf(1958,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)],[366]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(463,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(2318,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',t23_mboolean) ).
thf(2271,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)],[449]) ).
thf(352,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/sandbox2/benchmark/theBenchmark.p',commutativity_k5_pboole) ).
thf(1905,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)],[352]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(1420,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)],[224]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',redefinition_r1_subset_1) ).
thf(1181,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)],[161]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(823,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',t16_mboolean) ).
thf(1845,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)],[333]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',t76_pboole) ).
thf(1798,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)],[324]) ).
thf(270,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(1598,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',t35_mboolean) ).
thf(1743,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)],[313]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',t67_pboole) ).
thf(2192,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)],[430]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( A @ k1_pboole @ ( B @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_pboole) ).
thf(2012,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)],[380]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(739,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',t28_mboolean) ).
thf(993,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)],[107]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',commutativity_k2_pboole) ).
thf(1611,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)],[274]) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',t132_pboole) ).
thf(2375,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)],[481]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',t149_pboole) ).
thf(1711,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)],[300]) ).
thf(29,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(673,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(508,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/sandbox2/benchmark/theBenchmark.p',t46_pboole) ).
thf(2454,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)],[508]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(791,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(1188,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(585,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)],[16]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1262,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(370,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_finseq_2) ).
thf(1980,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(465,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/sandbox2/benchmark/theBenchmark.p',t148_pboole) ).
thf(2322,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)],[465]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1538,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(391,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/sandbox2/benchmark/theBenchmark.p',t96_pboole) ).
thf(2044,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)],[391]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',t145_pboole) ).
thf(2468,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)],[513]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(544,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)],[7]) ).
thf(496,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(2411,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_closure3) ).
thf(1766,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)],[316]) ).
thf(335,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/sandbox2/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(1849,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)],[335]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(1141,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)],[151]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(1802,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)],[325]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',t23_pboole) ).
thf(2279,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)],[451]) ).
thf(464,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
=> ~ ( B @ v3_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pboole) ).
thf(2320,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)],[464]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(864,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)],[70]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',d22_pboole) ).
thf(1702,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)],[299]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).
thf(2379,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)],[483]) ).
thf(346,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(1881,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)],[346]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(1272,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',t74_pboole) ).
thf(1839,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)],[330]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ( A @ ( C @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pboole) ).
thf(2458,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)],[509]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(1966,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)],[368]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(1685,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)],[294]) ).
thf(80,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_pboole) ).
thf(903,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',t47_pboole) ).
thf(2347,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)],[472]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(1448,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(154,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(1157,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(1321,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(354,axiom,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pboole) ).
thf(1913,plain,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',t17_pboole) ).
thf(2110,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)],[408]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(1010,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)],[114]) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',symmetry_r5_pboole) ).
thf(2305,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)],[459]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(1575,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)],[262]) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',t95_pboole) ).
thf(1674,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)],[290]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',t12_pboole) ).
thf(2290,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)],[453]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',t73_pboole) ).
thf(2135,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)],[414]) ).
thf(247,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(1508,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)],[247]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(652,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)],[28]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',t9_mboolean) ).
thf(1244,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)],[178]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_mboolean) ).
thf(995,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)],[108]) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',symmetry_r1_subset_1) ).
thf(2394,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)],[490]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(963,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(450,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/sandbox2/benchmark/theBenchmark.p',d10_pboole) ).
thf(2273,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)],[450]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pboole) ).
thf(2174,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',t6_mboolean) ).
thf(1476,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)],[238]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(1030,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)],[122]) ).
thf(84,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(914,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',t144_pboole) ).
thf(2330,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)],[466]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(1661,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)],[287]) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',t55_pboole) ).
thf(2095,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)],[406]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',t26_mssubfam) ).
thf(1994,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)],[376]) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',t109_pboole) ).
thf(2019,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)],[383]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',t10_pre_circ) ).
thf(1614,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)],[275]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ( A @ ( B @ v1_pre_circ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_mssubfam) ).
thf(1689,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)],[296]) ).
thf(402,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/sandbox2/benchmark/theBenchmark.p',redefinition_m2_finseq_2) ).
thf(2081,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)],[402]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',t102_pboole) ).
thf(2198,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)],[432]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(1077,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(476,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/sandbox2/benchmark/theBenchmark.p',t6_pre_circ) ).
thf(2362,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)],[476]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',t24_pboole) ).
thf(2162,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)],[421]) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',d2_mboolean) ).
thf(1893,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)],[350]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',t137_pboole) ).
thf(2294,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)],[455]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(620,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',t118_pboole) ).
thf(1642,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)],[280]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(1725,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)],[305]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(1578,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)],[263]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pboole) ).
thf(2385,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
thf(2255,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)],[445]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(64,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(818,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',t11_mboolean) ).
thf(1876,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)],[345]) ).
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 @ ( B @ ( A @ k4_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k4_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pboole) ).
thf(1757,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 ) @ k4_xboole_0 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k4_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k4_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k4_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',d11_pboole) ).
thf(1908,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)],[353]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',t121_pboole) ).
thf(2003,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)],[377]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',t123_pboole) ).
thf(2123,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)],[410]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',t28_mssubfam) ).
thf(2218,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)],[438]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(950,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)],[95]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',t21_mboolean) ).
thf(1097,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)],[141]) ).
thf(172,axiom,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(1229,plain,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',t56_pboole) ).
thf(2233,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)],[440]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(1303,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',t12_mboolean) ).
thf(1986,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)],[373]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',t21_pboole) ).
thf(1859,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)],[340]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(285,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/sandbox2/benchmark/theBenchmark.p',t101_pboole) ).
thf(1657,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)],[285]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',t119_pboole) ).
thf(2186,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)],[427]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',t128_pboole) ).
thf(2070,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)],[398]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(767,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)],[51]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( A @ ( B @ v2_pboole ) )
<=> ( B @ v2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v2_pboole) ).
thf(2366,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)],[478]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',t100_pboole) ).
thf(1891,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)],[349]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(828,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)],[68]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(955,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(796,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(886,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)],[77]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(918,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)],[86]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(801,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(1288,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',t127_pboole) ).
thf(2091,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)],[404]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',t146_pboole) ).
thf(2404,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)],[494]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(960,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(1473,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)],[237]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(720,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',t20_pboole) ).
thf(2021,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)],[384]) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(1346,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)],[207]) ).
thf(474,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/sandbox2/benchmark/theBenchmark.p',t147_pboole) ).
thf(2353,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)],[474]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(728,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',t129_pboole) ).
thf(1829,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)],[326]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',t21_finset_1) ).
thf(1378,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)],[211]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',t110_pboole) ).
thf(2265,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)],[446]) ).
thf(26,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(644,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',t21_mssubfam) ).
thf(908,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)],[82]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',t15_mboolean) ).
thf(1923,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)],[359]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',d15_pboole) ).
thf(1713,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)],[301]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(1004,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(1299,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_pboole) ).
thf(1902,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)],[351]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',t82_pboole) ).
thf(1885,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)],[347]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(1505,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)],[246]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(1236,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)],[175]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(987,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)],[106]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',t114_pboole) ).
thf(2127,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)],[412]) ).
thf(502,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/sandbox2/benchmark/theBenchmark.p',s2_pboole) ).
thf(2430,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)],[502]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',t32_mboolean) ).
thf(1268,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)],[185]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(575,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(90,axiom,
! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_mboolean) ).
thf(935,plain,
! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(1416,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)],[222]) ).
thf(473,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ~ ( B @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_pboole) ).
thf(2351,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)],[473]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(1204,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',t91_pboole) ).
thf(2087,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)],[403]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',t77_pboole) ).
thf(2206,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)],[435]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',t9_pboole) ).
thf(1737,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)],[310]) ).
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 @ 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/sandbox2/benchmark/theBenchmark.p',t87_pboole) ).
thf(1681,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)],[292]) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(2074,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)],[400]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',d16_pboole) ).
thf(2438,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)],[503]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_pboole) ).
thf(2297,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)],[456]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(775,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(356,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/sandbox2/benchmark/theBenchmark.p',t70_pboole) ).
thf(1917,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)],[356]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(676,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(1468,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(514,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/sandbox2/benchmark/theBenchmark.p',dt_k11_pboole) ).
thf(2470,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)],[514]) ).
thf(33178,plain,
$false,
inference(e,[status(thm)],[1411,1024,1168,2072,1729,628,2463,1982,1179,1295,1554,1586,809,1337,1718,2336,2031,1956,1549,2210,1596,683,2381,2062,2014,2114,1305,1041,1486,1855,2077,2099,1591,1971,1793,1608,533,550,1735,2316,2448,2141,1872,1327,747,945,2042,538,2360,1867,2184,2476,2168,698,1919,1988,1095,1196,898,1835,2046,1391,1441,709,973,565,2400,1265,1482,1650,1921,2269,1511,1455,1191,2339,785,1330,2444,1147,1319,1013,1741,1115,1931,1963,1232,1847,1545,2420,2373,1572,2007,1489,924,2027,1373,1418,937,966,756,1664,1383,1020,602,1843,687,1377,2281,634,2190,866,1796,2424,1394,1405,1600,1564,2392,2154,1863,2204,1691,761,1783,1067,714,1636,1057,1199,2364,1915,2093,1311,2307,1274,957,2428,2249,952,1580,1123,1676,820,561,788,815,2396,1560,1387,1723,1423,916,879,2332,1951,1687,2068,2200,1159,1787,2345,2492,1634,1291,1936,742,874,1375,980,1425,1672,1138,593,869,783,1397,1234,1541,1270,1851,1259,2377,948,1082,1659,554,1739,1075,642,1700,1791,2038,1207,547,2460,1683,1414,2196,1889,1644,2472,679,1039,837,1324,1451,2487,1131,1947,1984,1002,1246,1720,605,2370,1776,997,2450,2125,1478,1249,2387,1831,2465,1060,1050,1857,1202,1241,1779,921,541,1170,1286,2408,1026,1185,794,2057,1054,1466,558,1071,1727,1251,2176,2292,1103,2033,1927,745,2235,2144,906,1135,1648,975,1833,1007,2188,1620,1752,1652,2016,2398,1226,826,711,1428,1503,572,1865,1733,1239,2474,2148,2055,1092,2166,1090,764,1194,900,2478,2229,2415,1117,736,1589,1542,649,1853,1408,2214,2383,2246,1492,1603,2299,599,1439,1471,631,758,1557,1630,2267,2446,700,1149,1293,2025,1080,2314,2129,535,2343,799,1162,943,1022,1841,1044,1445,1113,2390,2303,2156,1562,912,521,983,2418,2139,883,2064,1015,2244,1000,2005,1583,927,1277,812,749,1990,1340,1018,1958,1551,2318,2271,1905,1420,1181,823,1845,1798,1598,872,1743,2192,2012,739,993,1611,2375,1711,673,2454,791,1188,585,1262,1980,2322,1538,2044,2468,544,2411,1766,1849,1141,1802,2279,2320,864,1702,2379,1881,1272,1839,2458,1966,1685,903,2347,1448,1157,1321,1913,2110,1010,2305,1575,1674,2290,2135,1508,652,1244,995,2394,963,2273,2174,1476,1030,914,2330,1661,2095,1994,2019,1614,1689,2081,1308,2198,1077,2362,2162,1893,2294,620,1642,1725,1578,2385,2255,1546,818,1380,1876,1757,1908,2003,2123,2218,950,1097,1229,2233,1303,1986,1859,1495,1657,2186,2070,767,2366,1891,828,955,796,886,918,801,1033,1288,2091,2404,960,1473,720,1165,2021,1346,2353,728,1829,1378,2265,644,908,1923,1713,1004,1299,1902,1885,1505,1120,1236,987,2127,2430,1268,575,935,1416,2351,1204,2087,2206,1737,1681,2074,2438,1037,2297,775,1917,676,1468,2470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n010.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 21:36:31 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.98/1.87 % [INFO] Parsing done (875ms).
% 3.98/1.88 % [INFO] Running in sequential loop mode.
% 4.69/2.24 % [INFO] eprover registered as external prover.
% 4.69/2.25 % [INFO] Scanning for conjecture ...
% 6.08/2.65 % [INFO] Found a conjecture (or negated_conjecture) and 4730 axioms. Running axiom selection ...
% 7.53/3.11 % [INFO] Axiom selection finished. Selected 518 axioms (removed 4212 axioms).
% 8.46/3.32 % [INFO] Problem is first-order (TPTP FOF).
% 8.46/3.35 % [INFO] Type checking passed.
% 8.46/3.35 % [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 ...
% 83.40/19.63 % External prover 'e' found a proof!
% 83.40/19.63 % [INFO] Killing All external provers ...
% 83.40/19.64 % Time passed: 19093ms (effective reasoning time: 17744ms)
% 83.40/19.64 % 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)>
% 83.40/19.64 % Axioms used in derivation (518): rc2_setfam_1, t106_xboole_1, t72_xboole_1, t15_finset_1, existence_m2_pboole, t42_xboole_1, t24_mboolean, t34_mboolean, t1_mboolean, t21_zfmisc_1, t92_pboole, t44_xboole_1, t13_zfmisc_1, t143_pboole, t102_pboole, t5_boole, t6_mboolean, dt_k11_pboole, antisymmetry_r3_pboole, t19_xboole_1, t62_pboole, t109_pboole, t20_zfmisc_1, d1_tarski, t27_mboolean, t14_finset_1, t17_xboole_1, t112_xboole_1, t135_zfmisc_1, t17_zfmisc_1, d9_setfam_1, t1_boole, t92_xboole_1, d12_pboole, dt_k2_pre_circ, d3_closure3, irreflexivity_r1_subset_1, t58_pboole, t73_xboole_1, reflexivity_r2_pboole, t140_zfmisc_1, t24_pboole, t1_closure3, t109_xboole_1, cc1_mssubfam, idempotence_k3_xboole_0, t110_xboole_1, t136_pboole, t66_xboole_1, t23_xboole_1, redefinition_m2_finseq_2, t3_xboole_1, t97_xboole_1, t113_zfmisc_1, t34_xboole_1, t113_xboole_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, fc4_setfam_1, t101_xboole_1, d5_xboole_0, t52_zfmisc_1, fc4_subset_1, t17_pboole, t36_pboole, t43_xboole_1, t16_fraenkel, t18_xboole_1, t33_mboolean, t6_xboole_1, t70_xboole_1, d4_zfmisc_1, t22_mboolean, t73_pboole, t39_pboole, t96_zfmisc_1, t13_numbers, t17_mboolean, d5_pboole, t68_xboole_1, t19_finset_1, t25_xboole_1, t2_boole, t117_zfmisc_1, t59_pboole, t122_zfmisc_1, t37_pboole, t66_pboole, t43_zfmisc_1, t71_xboole_1, t108_pboole, t27_xboole_1, t95_zfmisc_1, t140_pboole, t28_pboole, t12_mssubfam, t81_xboole_1, existence_m2_finseq_2, dt_k4_pboole, t141_pboole, dt_m3_pboole, t45_zfmisc_1, t69_zfmisc_1, t43_pboole, t19_pboole, s2_pboole, d8_pboole, t21_pboole, t37_xboole_1, t9_xboole_1, t41_zfmisc_1, t131_zfmisc_1, t95_xboole_1, t112_pboole, t16_mboolean, fc2_pboole, t84_pboole, t103_pboole, d9_pboole, t128_pboole, t9_pboole, d7_pboole, t16_pboole, t142_pboole, t49_zfmisc_1, commutativity_k3_pboole, commutativity_k3_xboole_0, t23_mboolean, fraenkel_a_2_0_closure3, fc11_finset_1, t86_pboole, t135_pboole, t86_xboole_1, t89_xboole_1, t27_mssubfam, t150_pboole, t18_pboole, t52_pboole, t63_pboole, symmetry_r5_pboole, t115_zfmisc_1, t123_pboole, t35_pboole, t137_zfmisc_1, fc2_xboole_0, dt_k2_pboole, fc2_numbers, d1_xboole_0, d15_pboole, t108_xboole_1, t130_pboole, t129_pboole, t138_zfmisc_1, t130_zfmisc_1, t51_xboole_1, t118_zfmisc_1, t122_pboole, fc2_setfam_1, t119_pboole, cc1_pboole, t46_zfmisc_1, t94_pboole, fc2_funct_2, t56_zfmisc_1, t6_boole, fc9_finset_1, t50_xboole_1, t132_pboole, fc10_finset_1, t1_xboole_1, t7_mboolean, t20_pboole, t97_pboole, t29_mboolean, t52_xboole_1, t75_xboole_1, fc17_finset_1, t22_pboole, t37_mboolean, commutativity_k2_xboole_0, 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, t6_pboole, t32_mboolean, t113_pboole, t4_xboole_0, idempotence_k2_pboole, t40_pboole, t4_pboole, rc3_setfam_1, t127_pboole, t123_zfmisc_1, fc2_subset_1, fraenkel_a_2_1_closure3, t15_mboolean, d3_zfmisc_1, t102_xboole_1, t2_tarski, fc6_subset_1, t5_pboole, redefinition_v1_pboole, t114_xboole_1, t67_zfmisc_1, t23_pboole, t97_zfmisc_1, t106_pboole, t144_pboole, t33_xboole_1, t27_pboole, t2_zfmisc_1, t148_pboole, t87_pboole, t84_xboole_1, t98_zfmisc_1, t76_xboole_1, fc3_xboole_0, fc3_numbers, d2_xboole_0, t30_xboole_1, d17_pboole, t124_pboole, t34_pboole, t32_xboole_1, t5_ordinal1, t4_boole, t53_xboole_1, t21_xboole_1, dt_k2_mboolean, d4_tarski, dt_k1_mboolean, t80_xboole_1, t25_finset_1, t79_xboole_1, t67_xboole_1, t29_xboole_1, t96_xboole_1, commutativity_k5_xboole_0, t88_pboole, t141_zfmisc_1, commutativity_k2_pboole, t58_zfmisc_1, t99_pboole, t1_xboole_0, t139_zfmisc_1, t7_boole, symmetry_r1_subset_1, t13_finset_1, t48_xboole_1, t3_ordinal1, d2_subset_1, t54_pboole, t66_zfmisc_1, t137_pboole, t101_pboole, t7_ordinal1, t67_pboole, dt_k3_pboole, d16_pboole, t31_xboole_1, t88_xboole_1, t12_pboole, t85_xboole_1, t22_finset_1, d3_pre_circ, t50_pboole, t60_pboole, t89_pboole, t21_mboolean, cc2_setfam_1, reflexivity_r6_pboole, t61_pboole, t24_xboole_1, t69_xboole_1, t6_closure3, existence_m3_pboole, t116_zfmisc_1, t64_zfmisc_1, d7_xboole_0, t83_xboole_1, redefinition_r1_subset_1, t47_pboole, t20_xboole_1, t20_mssubfam, dt_m2_pboole, t82_xboole_1, existence_m1_pboole, t54_xboole_1, t16_mssubfam, t14_funct_2, t16_zfmisc_1, t101_zfmisc_1, t134_pboole, t124_zfmisc_1, t120_zfmisc_1, d14_pboole, t55_xboole_1, t5_realset1, fc5_subset_1, existence_m1_subset_1, t35_xboole_1, d6_xboole_0, t115_pboole, t14_xboole_1, t44_zfmisc_1, t110_pboole, t47_xboole_1, fc1_finset_1, idempotence_k3_pboole, t23_mssubfam, d4_pboole, t92_zfmisc_1, t121_pboole, t114_pboole, t125_zfmisc_1, t69_pboole, t31_mboolean, redefinition_r6_pboole, t16_xboole_1, t42_pboole, t15_xboole_1, t57_setfam_1, redefinition_r2_subset_1, t98_xboole_1, t138_pboole, t114_zfmisc_1, t31_zfmisc_1, t26_xboole_1, t63_xboole_1, t64_pboole, t12_mboolean, t111_xboole_1, t26_mssubfam, t22_xboole_1, t79_pboole, t71_pboole, commutativity_k5_pboole, t81_pboole, cc2_pboole, t139_pboole, t70_pboole, t100_xboole_1, t23_numbers, t8_xboole_1, d3_tarski, t151_pboole, t39_zfmisc_1, t104_pboole, t10_pre_circ, t13_xboole_1, t54_zfmisc_1, reflexivity_r1_tarski, symmetry_r2_subset_1, t103_xboole_1, t8_pboole, t78_xboole_1, t28_xboole_1, t5_xboole_0, t119_zfmisc_1, t6_zfmisc_1, t77_pboole, t121_zfmisc_1, t56_setfam_1, t75_pboole, t20_finset_1, t2_xboole_1, t38_pboole, t18_mssubfam, t56_pboole, t53_pboole, t4_xboole_1, t10_pboole, t76_pboole, t1_partfun1, t41_xboole_1, t90_xboole_1, t11_mboolean, t96_pboole, t26_mboolean, dt_k1_pboole, t94_xboole_1, t133_pboole, d4_xboole_0, t18_zfmisc_1, t126_pboole, t41_pboole, t36_xboole_1, t51_zfmisc_1, rc1_finset_1, t64_xboole_1, t18_mboolean, t127_zfmisc_1, t15_pboole, t49_xboole_1, cc1_finset_1, t93_xboole_1, t57_pboole, t29_mssubfam, t77_xboole_1, t100_pboole, t105_pboole, t111_pboole, t68_zfmisc_1, t11_pboole, t78_pboole, fc12_finset_1, t21_mssubfam, t8_boole, rc1_xboole_0, t11_xboole_1, t23_finset_1, t24_zfmisc_1, t49_pboole, t12_xboole_1, t16_finset_1, t111_relat_1, t26_pboole, t5_mboolean, t37_zfmisc_1, t72_pboole, t149_pboole, symmetry_r1_xboole_0, t126_zfmisc_1, t2_subset, existence_m1_finseq_2, reflexivity_r7_pboole, t3_pboole, t51_pboole, t116_pboole, t65_pboole, t134_zfmisc_1, t28_finset_1, idempotence_k2_xboole_0, t80_pboole, d13_pboole, t36_mboolean, d10_xboole_0, d11_setfam_1, t7_xboole_1, d21_pboole, t46_xboole_1, t107_xboole_1, t22_mssubfam, t147_pboole, t120_pboole, t74_xboole_1, t5_xboole_1, t35_mboolean, t7_tarski, dt_k5_pboole, t83_pboole, t88_funct_6, t3_xboole_0, t91_xboole_1, t3_boole, t6_ordinal1, t28_mssubfam, t82_pboole, t30_mboolean, t99_xboole_1, fc16_finset_1, fc14_finset_1, redefinition_r3_pboole, rc1_setfam_1, t29_pboole, t9_mboolean, symmetry_r6_pboole, t145_pboole, t40_zfmisc_1, rc2_xboole_0, t45_xboole_1, dt_k12_pboole, t2_xboole_0, symmetry_r4_pboole, t87_xboole_1, t74_pboole, t118_pboole, t10_mboolean, t40_xboole_1, t46_pboole, t10_xboole_1, t2_mboolean, t11_mssubfam, t65_zfmisc_1, d3_xboole_0, t38_xboole_1, t39_xboole_1, 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
% 83.40/19.64 % No. of inferences in proof: 1040
% 83.40/19.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19093 ms resp. 17744 ms w/o parsing
% 84.72/19.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 84.72/19.99 % [INFO] Killing All external provers ...
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