%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU406+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 : n014.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 08:38:42 AM UTC 2026
% Result : Theorem 57.47s 12.46s
% Output : Refutation 53.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 469
% Syntax : Number of formulae : 940 ( 227 unt; 0 typ; 0 def)
% Number of atoms : 3045 ( 689 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 11073 ( 490 ~; 57 |; 783 &;8478 @)
% ( 93 <=>;1172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 16 con; 0-3 aty)
% Number of variables : 2673 ( 0 ^;2604 !; 69 ?;2673 :)
% Comments :
%------------------------------------------------------------------------------
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(v3_ordinal1_decl,type,
v3_ordinal1: $i > $o ).
thf(r1_ordinal1_decl,type,
r1_ordinal1: $i > $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(r2_pboole_decl,type,
r2_pboole: $i > $i > $i > $o ).
thf(k3_pboole_decl,type,
k3_pboole: $i > $i > $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k2_pboole_decl,type,
k2_pboole: $i > $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(r5_pboole_decl,type,
r5_pboole: $i > $i > $i > $o ).
thf(k4_pboole_decl,type,
k4_pboole: $i > $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k5_pboole_decl,type,
k5_pboole: $i > $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k1_pboole_decl,type,
k1_pboole: $i > $i ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(r4_pboole_decl,type,
r4_pboole: $i > $i > $i > $o ).
thf(v2_relat_2_decl,type,
v2_relat_2: $i > $o ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k11_pboole_decl,type,
k11_pboole: $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(r7_relat_2_decl,type,
r7_relat_2: $i > $i > $o ).
thf(m2_pboole_decl,type,
m2_pboole: $i > $i > $i > $o ).
thf(v3_relat_2_decl,type,
v3_relat_2: $i > $o ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(r2_relat_2_decl,type,
r2_relat_2: $i > $i > $o ).
thf(r6_relat_2_decl,type,
r6_relat_2: $i > $i > $o ).
thf(r5_relat_2_decl,type,
r5_relat_2: $i > $i > $o ).
thf(k5_xboole_0_decl,type,
k5_xboole_0: $i > $i > $i ).
thf(v1_card_1_decl,type,
v1_card_1: $i > $o ).
thf(f1_s1_pboole_decl,type,
f1_s1_pboole: $i ).
thf(f2_s1_pboole_decl,type,
f2_s1_pboole: $i > $i ).
thf(f1_s1_relset_1_decl,type,
f1_s1_relset_1: $i ).
thf(f2_s1_relset_1_decl,type,
f2_s1_relset_1: $i ).
thf(p1_s1_relset_1_decl,type,
p1_s1_relset_1: $i > $i > $o ).
thf(f1_s2_xboole_0_decl,type,
f1_s2_xboole_0: $i ).
thf(p1_s2_xboole_0_decl,type,
p1_s2_xboole_0: $i > $o ).
thf(f2_s2_xboole_0_decl,type,
f2_s2_xboole_0: $i ).
thf(p1_s2_card_1_decl,type,
p1_s2_card_1: $i > $o ).
thf(p1_s2_ordinal1_decl,type,
p1_s2_ordinal1: $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(f1_s4_subset_1_decl,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_decl,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_decl,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_decl,type,
f3_s4_subset_1: $i ).
thf(p1_s1_tarski_decl,type,
p1_s1_tarski: $i > $i > $o ).
thf(f1_s1_tarski_decl,type,
f1_s1_tarski: $i ).
thf(p1_s3_xboole_0_decl,type,
p1_s3_xboole_0: $i > $o ).
thf(f1_s1_relat_1_decl,type,
f1_s1_relat_1: $i ).
thf(f2_s1_relat_1_decl,type,
f2_s1_relat_1: $i ).
thf(p1_s1_relat_1_decl,type,
p1_s1_relat_1: $i > $i > $o ).
thf(f1_s1_xboole_0_decl,type,
f1_s1_xboole_0: $i ).
thf(p1_s1_xboole_0_decl,type,
p1_s1_xboole_0: $i > $o ).
thf(220,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(1322,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)],[220]) ).
thf(283,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(1633,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)],[283]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(1729,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(107,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_relat_1) ).
thf(846,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_orders_1) ).
thf(628,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(323,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(1850,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(136,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(941,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)],[136]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(1554,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(396,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(2250,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)],[396]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C @ p1_s3_xboole_0 ) )
& ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( C @ p1_s3_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_xboole_0) ).
thf(2612,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C @ p1_s3_xboole_0 )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C @ p1_s3_xboole_0 ) ) )
& ! [C: $i] :
( ( ( C @ p1_s3_xboole_0 )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( C @ p1_s3_xboole_0 ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(160,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(1024,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)],[160]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(189,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(1190,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)],[189]) ).
thf(414,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(2336,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)],[414]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(2131,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(87,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(777,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)],[87]) ).
thf(24,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(555,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(196,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(1211,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(212,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(1290,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)],[212]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(1068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( A = C ) )
=> ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(262,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(1522,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)],[262]) ).
thf(316,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(1808,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)],[316]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(994,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(405,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(2282,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)],[405]) ).
thf(421,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(2380,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)],[421]) ).
thf(264,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(1533,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)],[264]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r2_relat_2 ) )
<=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_2) ).
thf(1305,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r2_relat_2 ) ) )
& ( ( B @ ( A @ r2_relat_2 ) )
=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(171,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(1078,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)],[171]) ).
thf(360,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(2035,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(9,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(500,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)],[9]) ).
thf(209,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(1275,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)],[209]) ).
thf(336,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(1919,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)],[336]) ).
thf(137,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(945,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(227,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(1354,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)],[227]) ).
thf(200,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(1222,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)],[200]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
<=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(2575,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(169,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(1063,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)],[169]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(1954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(102,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(829,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)],[102]) ).
thf(391,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(2216,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)],[391]) ).
thf(418,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(2348,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)],[418]) ).
thf(246,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(1441,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)],[246]) ).
thf(70,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(709,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(105,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(841,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)],[105]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(354,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(2010,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)],[354]) ).
thf(279,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(1601,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)],[279]) ).
thf(253,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(1475,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)],[253]) ).
thf(346,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1967,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)],[346]) ).
thf(375,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(2136,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(444,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(2531,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)],[444]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(1650,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(1921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(465,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(2654,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)],[465]) ).
thf(30,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(570,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)],[30]) ).
thf(415,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(2339,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)],[415]) ).
thf(332,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(1907,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(326,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(1860,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(452,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(2562,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)],[452]) ).
thf(167,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(1059,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(468,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(2667,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)],[468]) ).
thf(73,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(719,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(2185,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_card_1) ).
thf(1577,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ~ ( A @ ( B @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(559,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ v3_relat_2 )
& ( A @ v3_relat_2 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ v3_relat_2 )
& ( B @ ( A @ k3_xboole_0 ) @ v3_relat_2 )
& ( B @ ( A @ k2_xboole_0 ) @ v3_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_relat_2) ).
thf(1800,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ v3_relat_2 )
& ( A @ v3_relat_2 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ v3_relat_2 )
& ( B @ ( A @ k3_xboole_0 ) @ v3_relat_2 )
& ( B @ ( A @ k2_xboole_0 ) @ v3_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(231,axiom,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(1379,plain,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(363,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(2049,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)],[363]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(1704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ v2_relat_2 )
=> ( B @ ( A @ k4_xboole_0 ) @ v2_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_2) ).
thf(606,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ v2_relat_2 )
=> ( B @ ( A @ k4_xboole_0 ) @ v2_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(84,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(770,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)],[84]) ).
thf(236,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(1398,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)],[236]) ).
thf(272,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(1568,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)],[272]) ).
thf(228,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( B @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(1362,plain,
! [A: $i] :
~ ! [B: $i] :
( ( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(175,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( C @ ( B @ k3_xboole_0 ) )
!= ( D @ k1_tarski ) )
& ( A @ ( C @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
| ( B = C ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_wellord2) ).
thf(1100,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( C @ ( B @ k3_xboole_0 ) )
!= ( D @ k1_tarski ) )
& ( A @ ( C @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
| ( B = C ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(393,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(2222,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)],[393]) ).
thf(128,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(924,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)],[128]) ).
thf(7,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_ordinal1) ).
thf(492,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(359,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(2027,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)],[359]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(230,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(1373,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)],[230]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(1040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(224,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(1334,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(320,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(1828,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)],[320]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(806,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(276,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(1581,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)],[276]) ).
thf(4,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(485,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)],[4]) ).
thf(181,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(1136,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)],[181]) ).
thf(184,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(1151,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)],[184]) ).
thf(134,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(937,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)],[134]) ).
thf(292,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(1677,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)],[292]) ).
thf(447,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(2540,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)],[447]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(905,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(3,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ~ ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ~ ( A @ ( B @ r2_hidden ) )
& ( B @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_ordinal1) ).
thf(480,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ~ ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ~ ( A @ ( B @ r2_hidden ) )
& ( B @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(431,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(2437,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)],[431]) ).
thf(113,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(866,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)],[113]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( A @ v3_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(1119,plain,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( A @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(234,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(1394,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)],[234]) ).
thf(51,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(660,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)],[51]) ).
thf(150,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(998,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)],[150]) ).
thf(243,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(1433,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)],[243]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(2205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(194,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(1206,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)],[194]) ).
thf(126,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(920,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)],[126]) ).
thf(58,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(678,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)],[58]) ).
thf(245,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(1438,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)],[245]) ).
thf(20,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(546,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)],[20]) ).
thf(462,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(2646,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)],[462]) ).
thf(96,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(810,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)],[96]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(1915,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(308,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(1768,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)],[308]) ).
thf(366,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(2061,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)],[366]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(529,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(295,axiom,
( ! [A: $i] :
~ ( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_pboole) ).
thf(1691,plain,
( ! [A: $i] :
~ ( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(91,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(798,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)],[91]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_tarski ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( C
= ( B @ ( A @ k2_tarski ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(399,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(2264,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)],[399]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(746,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(430,axiom,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relset_1) ).
thf(2428,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(451,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(2560,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)],[451]) ).
thf(159,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(1021,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(164,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(1042,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)],[164]) ).
thf(261,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(1519,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)],[261]) ).
thf(39,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(598,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(561,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(98,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(815,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)],[98]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v3_relat_2 )
<=> ( A @ k3_relat_1 @ ( A @ r3_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_2) ).
thf(729,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k3_relat_1 @ ( A @ r3_relat_2 ) )
=> ( A @ v3_relat_2 ) )
& ( ( A @ v3_relat_2 )
=> ( A @ k3_relat_1 @ ( A @ r3_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(306,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(1751,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)],[306]) ).
thf(99,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(820,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)],[99]) ).
thf(63,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(693,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)],[63]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(630,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(469,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(2670,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)],[469]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(2565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(852,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)],[110]) ).
thf(343,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(1951,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(214,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(1296,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)],[214]) ).
thf(289,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(1656,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)],[289]) ).
thf(413,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(2327,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)],[413]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2345,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(682,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(211,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(1281,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)],[211]) ).
thf(233,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(1392,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)],[233]) ).
thf(340,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(1938,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)],[340]) ).
thf(28,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(566,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)],[28]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(583,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,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(522,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)],[14]) ).
thf(22,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(551,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)],[22]) ).
thf(439,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(2492,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)],[439]) ).
thf(237,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(1402,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)],[237]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(1936,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(874,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(1017,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(177,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(1121,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)],[177]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(1856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(443,axiom,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(2509,plain,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(267,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(1540,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(459,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(2631,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)],[459]) ).
thf(446,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(2537,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_ordinal1) ).
thf(869,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(519,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(578,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(173,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(1089,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)],[173]) ).
thf(202,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(1234,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)],[202]) ).
thf(420,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(2377,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)],[420]) ).
thf(138,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(948,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)],[138]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_latsum_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(471,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(1329,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(187,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(1160,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)],[187]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r5_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_2) ).
thf(1028,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r5_relat_2 ) ) )
& ( ( B @ ( A @ r5_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(1659,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(132,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(933,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)],[132]) ).
thf(303,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(1739,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)],[303]) ).
thf(55,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(669,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_1) ).
thf(686,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(526,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_relat_1) ).
thf(1700,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(317,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(1810,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)],[317]) ).
thf(463,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(2649,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)],[463]) ).
thf(240,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(1419,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)],[240]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_card_1) ).
thf(1263,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(145,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(985,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)],[145]) ).
thf(66,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(701,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(179,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(1131,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)],[179]) ).
thf(394,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(2243,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)],[394]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(152,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(1002,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)],[152]) ).
thf(364,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(2052,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)],[364]) ).
thf(298,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(1715,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)],[298]) ).
thf(348,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(1979,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(376,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(2140,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(622,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v2_relat_2 )
<=> ( A @ k3_relat_1 @ ( A @ r2_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_2) ).
thf(837,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k3_relat_1 @ ( A @ r2_relat_2 ) )
=> ( A @ v2_relat_2 ) )
& ( ( A @ v2_relat_2 )
=> ( A @ k3_relat_1 @ ( A @ r2_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(319,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(1825,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(79,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(738,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1530,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(249,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(1456,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(378,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(2153,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)],[378]) ).
thf(201,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(1231,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(144,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(984,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(123,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(911,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)],[123]) ).
thf(10,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(503,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)],[10]) ).
thf(307,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(1759,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)],[307]) ).
thf(460,axiom,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1) ).
thf(2634,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) ) )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(89,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(792,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)],[89]) ).
thf(50,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(633,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)],[50]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(1466,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(1616,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(90,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(794,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)],[90]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(662,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(204,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(1241,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)],[204]) ).
thf(449,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(2546,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)],[449]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(1026,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(1895,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(210,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_pboole) ).
thf(1278,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(300,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(1727,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)],[300]) ).
thf(206,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(1251,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)],[206]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(513,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(424,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(2391,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)],[424]) ).
thf(397,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(2253,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)],[397]) ).
thf(457,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(2585,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)],[457]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(1483,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(216,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(1301,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( A @ ( A @ r1_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(733,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( A @ ( A @ r1_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(40,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(601,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)],[40]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(1219,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(100,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(824,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)],[100]) ).
thf(185,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(1154,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)],[185]) ).
thf(154,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(1007,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)],[154]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relset_1) ).
thf(843,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(466,axiom,
? [A: $i] :
! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0) ).
thf(2657,plain,
? [A: $i] :
! [B: $i] :
( ( ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(743,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(265,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(1535,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)],[265]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(958,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(385,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ v3_ordinal1 ) ) )
=> ( A @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(2188,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ v3_ordinal1 ) ) )
=> ( A @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(85,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(772,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)],[85]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(454,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(2568,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)],[454]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(1503,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(31,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(572,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,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(713,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)],[71]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(1332,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(432,axiom,
( ( ! [A: $i] :
( ( f2_s2_xboole_0 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s2_xboole_0 ) )
& ! [A: $i] :
( ( f1_s2_xboole_0 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s2_xboole_0 ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_xboole_0) ).
thf(2442,plain,
( ( ! [A: $i] :
( ( ( A @ p1_s2_xboole_0 )
=> ( f2_s2_xboole_0 @ ( A @ r2_hidden ) ) )
& ( ( f2_s2_xboole_0 @ ( A @ r2_hidden ) )
=> ( A @ p1_s2_xboole_0 ) ) )
& ! [A: $i] :
( ( ( A @ p1_s2_xboole_0 )
=> ( f1_s2_xboole_0 @ ( A @ r2_hidden ) ) )
& ( ( f1_s2_xboole_0 @ ( A @ r2_hidden ) )
=> ( A @ p1_s2_xboole_0 ) ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(365,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(2055,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)],[365]) ).
thf(382,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(2166,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)],[382]) ).
thf(93,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(804,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(429,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(2425,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)],[429]) ).
thf(208,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(1271,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)],[208]) ).
thf(409,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(2308,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)],[409]) ).
thf(191,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(1194,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)],[191]) ).
thf(195,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1209,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(324,axiom,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(1853,plain,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(436,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(2478,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)],[436]) ).
thf(156,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(1011,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)],[156]) ).
thf(78,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(736,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)],[78]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k3_tarski @ r1_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal2) ).
thf(990,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k3_tarski @ r1_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(268,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(1542,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)],[268]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(371,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(2116,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)],[371]) ).
thf(309,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(1771,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)],[309]) ).
thf(45,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(616,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)],[45]) ).
thf(273,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(1571,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)],[273]) ).
thf(390,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(2214,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)],[390]) ).
thf(422,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(2383,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)],[422]) ).
thf(271,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(1557,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)],[271]) ).
thf(410,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(2314,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)],[410]) ).
thf(400,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(2267,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)],[400]) ).
thf(333,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1909,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(108,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(848,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(1325,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(117,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(895,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)],[117]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(915,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(250,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(1460,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)],[250]) ).
thf(467,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(2664,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)],[467]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(433,axiom,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_card_1) ).
thf(2461,plain,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(168,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1061,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(294,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(1688,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(2261,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(302,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(1731,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)],[302]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v2_relat_2 )
<=> ( A @ ( A @ k3_relat_1 @ k6_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_2) ).
thf(594,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ ( A @ k3_relat_1 @ k6_relat_1 @ r1_xboole_0 ) )
=> ( A @ v2_relat_2 ) )
& ( ( A @ v2_relat_2 )
=> ( A @ ( A @ k3_relat_1 @ k6_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(428,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(2418,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)],[428]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(1396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(419,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(2350,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)],[419]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(2212,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(285,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(1643,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)],[285]) ).
thf(157,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(1015,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)],[157]) ).
thf(43,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(608,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)],[43]) ).
thf(27,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(563,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)],[27]) ).
thf(151,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(1000,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)],[151]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(1477,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(127,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(922,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)],[127]) ).
thf(315,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(1805,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)],[315]) ).
thf(442,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(2506,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)],[442]) ).
thf(197,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1213,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(768,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(101,axiom,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_1) ).
thf(827,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ~ ( ! [D: $i] :
( ( D @ v3_ordinal1 )
=> ( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_ordinal1 ) ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ( A != k1_xboole_0 )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(1044,plain,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ~ ( ! [D: $i] :
( ( D @ v3_ordinal1 )
=> ( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_ordinal1 ) ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ( A != k1_xboole_0 )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(437,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(2481,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)],[437]) ).
thf(352,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(2005,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)],[352]) ).
thf(342,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(1948,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)],[342]) ).
thf(291,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(1662,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)],[291]) ).
thf(369,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(2107,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)],[369]) ).
thf(331,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(1905,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(361,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(2037,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)],[361]) ).
thf(441,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(2503,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)],[441]) ).
thf(97,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(812,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(172,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(1081,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)],[172]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r6_relat_2 ) ) )
=> ( C @ ( A @ r6_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_orders_1) ).
thf(939,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r6_relat_2 ) ) )
=> ( C @ ( A @ r6_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) )
=> ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(23,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(553,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(490,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(675,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(589,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2652,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(435,axiom,
( ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_ordinal1 ) ) )
=> ( A @ p1_s2_ordinal1 ) ) )
=> ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ p1_s2_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_ordinal1) ).
thf(2471,plain,
( ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_ordinal1 ) ) )
=> ( A @ p1_s2_ordinal1 ) ) )
=> ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ p1_s2_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_1) ).
thf(548,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(180,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(1134,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(5,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(487,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)],[5]) ).
thf(350,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_ordinal1) ).
thf(1990,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(2202,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(260,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(1516,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_orders_1) ).
thf(705,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(69,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(707,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(2192,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v1_relat_1 ) )
& ( ( A @ v1_relat_1 )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(355,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(2012,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)],[355]) ).
thf(140,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(954,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(470,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(2678,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)],[470]) ).
thf(427,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(2407,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)],[427]) ).
thf(423,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(2386,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)],[423]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(1790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r3_relat_2 ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).
thf(1813,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r3_relat_2 ) ) )
& ( ( B @ ( A @ r3_relat_2 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(717,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(312,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(1785,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)],[312]) ).
thf(321,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(1830,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)],[321]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_1) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(362,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(2044,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r6_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
thf(1336,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r6_relat_2 ) ) )
& ( ( B @ ( A @ r6_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(434,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(2468,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)],[434]) ).
thf(403,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(2276,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)],[403]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(373,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(2128,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)],[373]) ).
thf(32,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(576,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(411,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(2322,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(266,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(1538,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)],[266]) ).
thf(95,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(808,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)],[95]) ).
thf(19,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(544,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)],[19]) ).
thf(122,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(907,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(440,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(2500,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)],[440]) ).
thf(67,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(703,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)],[67]) ).
thf(349,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(1981,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)],[349]) ).
thf(448,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(2543,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)],[448]) ).
thf(404,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(2279,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(112,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(864,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)],[112]) ).
thf(75,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(727,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)],[75]) ).
thf(299,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(1717,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)],[299]) ).
thf(44,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(612,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)],[44]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r7_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_2) ).
thf(1404,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r7_relat_2 ) ) )
& ( ( B @ ( A @ r7_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(395,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(2247,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)],[395]) ).
thf(329,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(1898,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(322,axiom,
k1_xboole_0 @ v3_ordinal1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_ordinal1) ).
thf(1849,plain,
k1_xboole_0 @ v3_ordinal1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(166,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(1052,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)],[166]) ).
thf(258,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(1506,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)],[258]) ).
thf(341,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(1940,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)],[341]) ).
thf(367,axiom,
? [A: $i] : ( A @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_card_1) ).
thf(2088,plain,
? [A: $i] : ( A @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(56,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(671,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)],[56]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(1157,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(2325,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(198,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(1216,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(247,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(1448,plain,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(931,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(293,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(1685,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)],[293]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(688,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( A @ ( B @ r1_ordinal1 ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(903,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( A @ ( B @ r1_ordinal1 ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(15,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(524,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)],[15]) ).
thf(34,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_1) ).
thf(581,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(370,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(2110,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)],[370]) ).
thf(416,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(2342,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(274,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(1575,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)],[274]) ).
thf(248,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(1453,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)],[248]) ).
thf(461,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(2643,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)],[461]) ).
thf(286,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ v2_relat_2 )
& ( A @ v2_relat_2 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_relat_2 )
& ( B @ ( A @ k2_xboole_0 ) @ v2_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_2) ).
thf(1646,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ v2_relat_2 )
& ( A @ v2_relat_2 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_relat_2 )
& ( B @ ( A @ k2_xboole_0 ) @ v2_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(65,axiom,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pboole) ).
thf(699,plain,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(383,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(2174,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)],[383]) ).
thf(284,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(1639,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)],[284]) ).
thf(255,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(1481,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(305,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(1745,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)],[305]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(1244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).
thf(781,plain,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(425,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(2394,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)],[425]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(963,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(12,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(517,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)],[12]) ).
thf(402,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(2273,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(29,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(568,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)],[29]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(1777,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(381,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(2162,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)],[381]) ).
thf(259,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(1513,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)],[259]) ).
thf(119,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(899,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)],[119]) ).
thf(372,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(2120,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)],[372]) ).
thf(60,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(684,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)],[60]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(800,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(54,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(667,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(1294,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(377,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(2142,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)],[377]) ).
thf(46,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(620,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)],[46]) ).
thf(310,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(1774,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(407,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(2302,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)],[407]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(833,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(183,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(1148,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)],[183]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(603,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(379,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(2155,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)],[379]) ).
thf(445,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(2534,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)],[445]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( B @ ( A @ r1_ordinal1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(950,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_ordinal1 ) ) )
& ( ( B @ ( A @ r1_ordinal1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(1097,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(353,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(2008,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)],[353]) ).
thf(217,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(1303,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(1436,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(125,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(918,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(455,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(2572,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)],[455]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_ordinal1) ).
thf(897,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(53,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(664,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(192,axiom,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_4) ).
thf(1197,plain,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(426,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(2404,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)],[426]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(532,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(64,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(696,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)],[64]) ).
thf(358,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(2021,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)],[358]) ).
thf(142,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(960,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1473,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(304,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(1742,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)],[304]) ).
thf(450,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski) ).
thf(2549,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(130,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(928,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)],[130]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(740,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(111,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(860,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)],[111]) ).
thf(347,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(1976,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(148,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(992,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)],[148]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(109,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(850,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)],[109]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(438,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(2484,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)],[438]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(871,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(401,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(2270,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(203,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(1236,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)],[203]) ).
thf(146,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(987,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(380,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(2159,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)],[380]) ).
thf(226,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(1352,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(242,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(1431,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)],[242]) ).
thf(153,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(1004,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(1606,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(288,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(1653,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)],[288]) ).
thf(357,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(2018,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)],[357]) ).
thf(86,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(775,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(1416,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(37,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(592,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)],[37]) ).
thf(8,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(496,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)],[8]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_1) ).
thf(935,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(155,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(1009,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)],[155]) ).
thf(13064,plain,
$false,
inference(e,[status(thm)],[1322,1633,1729,846,628,1850,941,1554,2250,2612,1024,1369,1190,2336,2131,777,555,1211,1290,1068,1522,1808,994,1544,2282,2380,1533,1305,1078,2035,500,1275,1919,945,1354,1222,2575,1063,1954,829,2216,2348,1441,709,841,1613,2010,1601,1475,1967,2136,2531,1650,1921,2654,570,2339,1907,1860,1313,2562,1059,2667,719,2185,1577,559,1800,1379,2049,1704,606,770,1398,1568,1362,1100,2222,924,492,2027,2090,1373,1040,1334,1828,806,1581,485,1136,1151,937,1677,2540,905,480,2437,866,1119,1394,660,998,1433,2205,1206,920,678,1438,546,2646,810,1915,1768,2061,529,1691,798,1163,2264,746,2428,2560,1021,1042,1519,598,561,815,729,1751,820,693,630,2670,2565,852,1951,1296,1656,2327,2345,682,1281,1392,1938,566,583,522,551,2492,1402,1936,874,1017,1121,1856,2509,1540,2631,2537,869,519,1592,578,1089,1234,2377,948,471,1329,1160,1028,1659,933,1739,669,686,526,1584,1700,1810,2649,1419,1263,985,701,1131,2243,1192,721,1002,2052,1715,1979,2140,622,837,1825,2285,738,2304,1530,1456,2153,1231,984,911,503,1759,2634,792,633,1466,1616,794,662,926,1241,2546,1026,1895,1278,1727,1251,513,2391,2253,2585,1483,1301,733,601,1219,824,1154,1007,843,2657,743,1535,958,1124,2188,772,2016,2568,1428,1503,572,713,1997,1332,2442,2055,2166,804,2425,1271,2308,1194,1209,1853,2478,1011,736,990,1542,1144,2116,1771,616,1571,2214,2383,1557,2314,2267,1909,1862,848,1325,895,915,1460,2664,1381,2461,1061,1688,2261,1731,594,2418,1396,2350,2212,1643,1015,608,563,1000,1477,922,1805,2506,1213,768,827,1044,2481,2005,1948,1662,2107,1905,2037,2503,812,1081,939,1958,553,490,675,1203,589,2652,2471,548,1134,487,1990,2202,1516,705,707,2192,2012,954,2678,2407,2386,1790,1813,717,1785,1830,1901,2044,1336,2468,2276,2219,2128,576,2322,1538,808,544,907,2500,703,1981,2543,2279,864,727,1717,612,1404,2247,1898,1849,1052,1506,1940,2088,671,1157,2325,1216,1448,931,1685,688,903,524,581,2110,2342,1575,1453,2643,1646,699,2174,1639,1481,1745,1244,781,2394,963,517,2273,568,1777,2162,1513,899,2120,684,800,667,1294,2142,620,1774,2302,833,1148,603,2155,2534,950,1097,2008,1303,1436,918,2572,897,664,1197,2404,532,696,2021,960,1473,1742,2549,928,740,860,1976,992,1923,850,1299,2484,871,2270,1236,987,2159,1352,1431,1004,1606,1653,2018,775,1416,592,496,1912,935,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 09:28:05 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.70/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.82/1.24 % [INFO] Parsing done (522ms).
% 2.82/1.25 % [INFO] Running in sequential loop mode.
% 3.68/1.44 % [INFO] eprover registered as external prover.
% 3.68/1.45 % [INFO] Scanning for conjecture ...
% 5.38/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 4433 axioms. Running axiom selection ...
% 7.45/2.39 % [INFO] Axiom selection finished. Selected 468 axioms (removed 3965 axioms).
% 8.71/2.73 % [INFO] Problem is first-order (TPTP FOF).
% 8.71/2.76 % [INFO] Type checking passed.
% 8.71/2.77 % [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 ...
% 57.47/12.45 % External prover 'e' found a proof!
% 57.47/12.45 % [INFO] Killing All external provers ...
% 57.47/12.46 % Time passed: 11942ms (effective reasoning time: 11202ms)
% 57.47/12.46 % 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)>
% 57.47/12.46 % Axioms used in derivation (468): t106_xboole_1, t72_xboole_1, existence_m2_pboole, t42_xboole_1, t21_zfmisc_1, t44_xboole_1, t5_boole, t13_zfmisc_1, redefinition_r1_ordinal1, dt_k11_pboole, t19_xboole_1, t62_pboole, t109_pboole, t20_zfmisc_1, fc1_zfmisc_1, d1_tarski, t25_relset_1, t30_relat_1, t17_xboole_1, t112_xboole_1, t135_zfmisc_1, t17_zfmisc_1, d5_relat_1, t140_zfmisc_1, t1_funct_4, t110_xboole_1, t92_xboole_1, d12_pboole, t73_xboole_1, reflexivity_r2_pboole, t105_zfmisc_1, d6_relat_2, t109_xboole_1, idempotence_k3_xboole_0, t1_boole, t7_subset_1, t66_xboole_1, t23_xboole_1, t3_xboole_1, t180_orders_1, t97_xboole_1, fc1_xboole_0, t113_zfmisc_1, t34_xboole_1, t113_xboole_1, t111_zfmisc_1, t44_pboole, t8_subset_1, d5_tarski, d11_pboole, fc4_relat_1, t101_xboole_1, t4_ordinal1, t1_subset, t10_partfun1, t39_ordinal1, d5_xboole_0, t52_zfmisc_1, fc4_subset_1, t17_pboole, t43_xboole_1, t81_zfmisc_1, t5_ordinal2, t18_xboole_1, d5_relat_2, t42_zfmisc_1, d5_pboole, t6_xboole_1, t19_zfmisc_1, t70_xboole_1, fc3_relat_1, t96_zfmisc_1, t68_xboole_1, t25_xboole_1, t2_boole, t117_zfmisc_1, t32_relat_1, t59_pboole, t14_card_1, t122_zfmisc_1, t38_ordinal1, t110_zfmisc_1, t35_zfmisc_1, t27_wellord2, t71_xboole_1, t108_pboole, t27_xboole_1, t32_ordinal1, t43_zfmisc_1, t30_ordinal1, t95_zfmisc_1, t15_relset_1, t140_pboole, t99_zfmisc_1, t81_xboole_1, dt_k4_pboole, t45_zfmisc_1, t70_zfmisc_1, t69_zfmisc_1, t43_pboole, t19_pboole, t103_zfmisc_1, s2_pboole, d8_pboole, t56_relat_1, t37_xboole_1, t9_xboole_1, t41_zfmisc_1, dt_m2_relset_1, t131_zfmisc_1, t95_xboole_1, t50_zfmisc_1, t112_pboole, commutativity_k3_xboole_0, t21_pboole, t27_zfmisc_1, d9_pboole, cc1_relat_1, d7_pboole, t16_pboole, t49_zfmisc_1, commutativity_k3_pboole, t137_zfmisc_1, t129_zfmisc_1, t86_xboole_1, t89_xboole_1, s2_card_1, t31_relat_1, t150_pboole, t18_pboole, symmetry_r5_pboole, t115_zfmisc_1, t135_pboole, d2_tarski, fc2_xboole_0, dt_k2_pboole, t27_relat_1, d1_xboole_0, t108_xboole_1, t129_pboole, t138_zfmisc_1, t130_zfmisc_1, t51_xboole_1, t108_zfmisc_1, t27_relset_1, t122_pboole, t14_relset_1, t16_relset_1, t119_pboole, t46_zfmisc_1, t6_boole, rc2_subset_1, t50_xboole_1, t10_relat_1, d1_relat_1, t118_zfmisc_1, s4_subset_1, s2_xboole_0, t56_zfmisc_1, t1_xboole_1, t26_relset_1, t20_pboole, t4_relat_1, t52_xboole_1, t75_xboole_1, commutativity_k2_xboole_0, t5_subset, t31_ordinal1, t73_relat_1, t22_pboole, t34_relat_1, fc3_subset_1, t128_zfmisc_1, d10_pboole, t25_zfmisc_1, t75_zfmisc_1, t94_zfmisc_1, t48_zfmisc_1, t65_xboole_1, s1_xboole_0, t1_zfmisc_1, t4_pboole, t6_pboole, t19_relset_1, t113_pboole, t79_zfmisc_1, t4_xboole_0, idempotence_k2_pboole, t123_zfmisc_1, fc2_subset_1, t60_zfmisc_1, t102_zfmisc_1, t102_xboole_1, t28_relset_1, t2_tarski, t33_xboole_1, t5_pboole, s1_pboole, t114_xboole_1, t8_zfmisc_1, t67_zfmisc_1, t23_pboole, t97_zfmisc_1, t106_pboole, t9_relat_1, t28_zfmisc_1, t72_zfmisc_1, t33_relat_1, t18_relat_2, t2_zfmisc_1, t84_xboole_1, t23_zfmisc_1, t57_zfmisc_1, t21_xboole_1, t98_zfmisc_1, t4_subset, t76_xboole_1, fc3_xboole_0, d2_xboole_0, t30_xboole_1, t74_zfmisc_1, d17_pboole, t32_relat_2, t32_xboole_1, d4_tarski, t5_ordinal1, t4_boole, t53_xboole_1, t80_xboole_1, t67_xboole_1, t12_zfmisc_1, s1_tarski, t56_subset_1, s1_relset_1, t29_xboole_1, t96_xboole_1, commutativity_k5_xboole_0, t88_pboole, t141_zfmisc_1, t9_zfmisc_1, t79_xboole_1, commutativity_k2_pboole, t58_zfmisc_1, t99_pboole, t1_xboole_0, t35_relat_2, t139_zfmisc_1, t7_boole, t23_ordinal1, t104_zfmisc_1, d3_relat_2, t33_relat_2, t48_xboole_1, t3_ordinal1, d10_relat_1, t55_zfmisc_1, d2_subset_1, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, t60_pboole, t7_ordinal1, rc1_subset_1, dt_k3_pboole, t85_xboole_1, connectedness_r1_ordinal1, t26_zfmisc_1, t89_pboole, t31_xboole_1, t63_zfmisc_1, t4_subset_1, t88_xboole_1, t14_zfmisc_1, t91_orders_1, t61_pboole, t24_xboole_1, t69_xboole_1, t116_zfmisc_1, t64_zfmisc_1, d7_xboole_0, t83_xboole_1, t20_xboole_1, dt_m2_pboole, t82_xboole_1, existence_m1_pboole, t16_zfmisc_1, t101_zfmisc_1, t134_pboole, t124_zfmisc_1, t32_zfmisc_1, t54_xboole_1, t120_zfmisc_1, t55_xboole_1, t4_relset_1, t3_subset, cc1_relset_1, t24_ordinal1, t55_subset_1, d2_zfmisc_1, existence_m1_subset_1, t8_relset_1, commutativity_k2_tarski, t3_relat_1, t35_xboole_1, d6_xboole_0, t125_zfmisc_1, t115_pboole, t14_xboole_1, t44_zfmisc_1, t110_pboole, t47_xboole_1, idempotence_k3_pboole, t17_relset_1, t132_zfmisc_1, t29_zfmisc_1, t92_zfmisc_1, t107_zfmisc_1, t106_zfmisc_1, t114_pboole, t26_ordinal1, s2_ordinal1, t100_zfmisc_1, t22_zfmisc_1, t15_xboole_1, t138_pboole, t38_zfmisc_1, t114_zfmisc_1, t31_zfmisc_1, d1_zfmisc_1, t16_xboole_1, t26_xboole_1, t63_xboole_1, t86_zfmisc_1, rc2_relat_1, existence_m2_relset_1, t98_xboole_1, d2_relat_2, t37_ordinal1, t36_ordinal1, t111_xboole_1, t22_xboole_1, t84_zfmisc_1, t36_zfmisc_1, commutativity_k5_pboole, t100_xboole_1, t8_xboole_1, t103_xboole_1, d3_tarski, d7_relat_2, t151_pboole, t39_zfmisc_1, rc1_relat_1, t13_xboole_1, t83_zfmisc_1, t54_zfmisc_1, reflexivity_r1_tarski, t6_relset_1, t78_xboole_1, t28_xboole_1, t5_xboole_0, t119_zfmisc_1, t6_zfmisc_1, t96_orders_1, t2_xboole_1, t4_xboole_1, t47_zfmisc_1, dt_k6_relat_1, d11_relat_2, reflexivity_r1_ordinal1, t121_zfmisc_1, t10_subset_1, t59_zfmisc_1, fc6_relat_1, t1_partfun1, t41_xboole_1, t90_xboole_1, d4_xboole_0, t35_funct_1, t18_zfmisc_1, t29_relset_1, dt_k1_pboole, t73_zfmisc_1, t46_relset_1, t36_xboole_1, t51_zfmisc_1, d10_relat_2, t94_xboole_1, t35_ordinal1, t64_xboole_1, s3_xboole_0, t127_zfmisc_1, t15_pboole, t49_xboole_1, t93_xboole_1, fc1_relat_1, t77_xboole_1, t11_xboole_1, t111_pboole, t68_zfmisc_1, t8_boole, rc1_xboole_0, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t49_pboole, t12_xboole_1, d3_relat_1, t26_pboole, t3_pboole, t53_zfmisc_1, t116_pboole, t109_zfmisc_1, symmetry_r1_xboole_0, t134_zfmisc_1, t126_zfmisc_1, fc8_relat_1, t10_zfmisc_1, t2_subset, t37_zfmisc_1, fc2_relat_1, idempotence_k2_xboole_0, t48_subset_1, t28_relat_1, t7_xboole_1, d21_pboole, t46_xboole_1, t107_xboole_1, d10_xboole_0, t186_orders_1, t120_pboole, t74_xboole_1, t5_xboole_1, dt_k5_pboole, s1_relat_1, t3_xboole_0, t91_xboole_1, t3_boole, t6_ordinal1, t93_zfmisc_1, t82_pboole, t99_xboole_1, t49_subset_1, rc1_card_1, t7_tarski, t30_zfmisc_1, t81_relat_1, t40_zfmisc_1, rc2_xboole_0, t118_pboole, t45_xboole_1, t112_zfmisc_1, t40_xboole_1, t2_xboole_0, symmetry_r4_pboole, t87_xboole_1, t10_xboole_1, t6_relat_1, t65_zfmisc_1, t63_subset_1, d3_xboole_0, t38_xboole_1, d2_relat_1, t39_xboole_1, t13_card_1, antisymmetry_r2_hidden, t26_relat_1, t27_ordinal1
% 57.47/12.46 % No. of inferences in proof: 940
% 57.47/12.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11942 ms resp. 11202 ms w/o parsing
% 53.21/12.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.21/12.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------