%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU444+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:38:59 AM UTC 2026
% Result : Theorem 38.05s 9.73s
% Output : Refutation 40.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 519
% Syntax : Number of formulae : 1100 ( 199 unt; 0 typ; 16 def)
% Number of atoms : 4479 (1045 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 16596 ( 653 ~; 153 |;1487 &;12604 @)
% ( 93 <=>;1606 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 39 con; 0-8 aty)
% Number of variables : 3419 ( 1 ^;3294 !; 108 ?;3419 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k1_funct_5_decl,type,
k1_funct_5: $i > $i ).
thf(k10_relset_1_decl,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k6_relset_1_decl,type,
k6_relset_1: $i > $i > $i > $i ).
thf(k2_funct_5_decl,type,
k2_funct_5: $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k8_relset_2_decl,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k5_relset_2_decl,type,
k5_relset_2: $i > $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k4_relset_1_decl,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k6_enumset1_decl,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k3_relset_2_decl,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k11_relset_1_decl,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k3_enumset1_decl,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(k5_xboole_0_decl,type,
k5_xboole_0: $i > $i > $i ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_subset_1_decl,type,
k7_subset_1: $i > $i > $i > $i ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k1_eqrel_1_decl,type,
k1_eqrel_1: $i > $i ).
thf(k2_relset_2_decl,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k1_enumset1_decl,type,
k1_enumset1: $i > $i > $i > $i ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(k5_relset_1_decl,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_decl,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(k5_enumset1_decl,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_relset_1_decl,type,
k8_relset_1: $i > $i > $i > $i > $i ).
thf(k9_relset_1_decl,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(f1_s14_funct_2_decl,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_decl,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_decl,type,
p1_s14_funct_2: $i > $i > $o ).
thf(f1_s12_funct_2_decl,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_decl,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_decl,type,
f2_s12_funct_2: $i ).
thf(f1_s13_funct_2_decl,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_decl,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_decl,type,
f2_s13_funct_2: $i ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk34_decl,type,
sk34: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk92_decl,type,
sk92: $i ).
thf(sk155_decl,type,
sk155: $i ).
thf(sk168_decl,type,
sk168: $i > $i ).
thf(sk172_decl,type,
sk172: $o ).
thf(sk173_decl,type,
sk173: $i ).
thf(sk174_decl,type,
sk174: $i ).
thf(sk176_decl,type,
sk176: $o ).
thf(sk177_decl,type,
sk177: $i ).
thf(sk178_decl,type,
sk178: $i ).
thf(sk182_decl,type,
sk182: $o ).
thf(sk183_decl,type,
sk183: $i ).
thf(sk184_decl,type,
sk184: $i ).
thf(sk197_decl,type,
sk197: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ k2_funct_5 @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( A @ ( B @ ( sk1 @ ( A @ k10_relset_1 ) ) ) @ ( B @ ( sk1 @ ( A @ k6_relset_1 ) ) @ ( A @ ( sk1 @ k10_relset_1 ) ) ) )
= ( B @ k2_funct_5 @ ( B @ ( sk1 @ ( A @ k6_relset_1 ) ) @ ( A @ ( sk1 @ k10_relset_1 ) ) ) ) )
& ( ( B @ k1_funct_5 )
= ( sk1 @ ( B @ ( sk1 @ ( A @ k6_relset_1 ) ) @ ( A @ ( sk1 @ k10_relset_1 ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
=> ( ( ( sk2 @ ( A @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) @ ( A @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
= ( A @ k2_funct_5 @ ( A @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) )
& ( ( A @ k1_funct_5 )
= ( sk1 @ ( A @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk92_def,definition,
( sk92
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk155_def,definition,
( sk155
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk168_def,definition,
( sk168
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk173_def,definition,
( sk173
= ( @+[A: $i] :
~ ( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk174_def,definition,
( sk174
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk177_def,definition,
( sk177
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk178_def,definition,
( sk178
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk183_def,definition,
( sk183
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk184_def,definition,
( sk184
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk197_def,definition,
( sk197
= ( @+[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 ) ) )
& ! [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 ) ) ) ) ) ) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_partfun1) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(2452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(181,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(1411,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(444,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(2778,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_partfun1) ).
thf(893,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(394,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(2499,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)],[394]) ).
thf(214,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(1549,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(2295,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)],[354]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_subset_1) ).
thf(2306,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(164,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(1237,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(846,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)],[94]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_2) ).
thf(777,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_2) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).
thf(2309,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k6_relset_1 ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ ( B @ ( C @ ( B @ ( A @ k6_relset_1 ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(2953,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)],[473]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(741,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)],[65]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(2014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1728,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)],[254]) ).
thf(456,axiom,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).
thf(2834,plain,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(2835,plain,
! [A: $i] :
( ( ( ( A @ ( sk178 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk176 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk178 @ m2_relset_1 ) ) )
| ~ sk176 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk178 @ v1_funct_2 ) ) )
| ~ sk176 )
& ( ( sk178 @ v1_funct_1 )
| ~ sk176 )
& ( sk176
| ~ ( f2_s12_funct_2 @ ( sk177 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk176
| ( f1_s12_funct_2 @ ( sk177 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[2834]) ).
thf(2837,plain,
( ( sk178 @ v1_funct_1 )
| ~ sk176 ),
inference(cnfConj,[status(thm)],[2835]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(510,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[510]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).
thf(1437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(1041,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)],[128]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(2231,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)],[339]) ).
thf(417,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).
thf(2622,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(2248,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)],[342]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_sysrel) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(265,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(1788,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(2740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(1999,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(715,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)],[59]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(1275,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_partfun1) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
thf(1954,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(48,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(670,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(1867,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)],[280]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(2184,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)],[328]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(709,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(229,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(1613,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(1601,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)],[226]) ).
thf(135,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(1091,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1092,plain,
sk44 @ v1_xboole_0,
inference(cnf,[status(esa)],[1091]) ).
thf(1789,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[1788]) ).
thf(1790,plain,
~ ( sk92 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[1789]) ).
thf(3138,plain,
( ( ( sk92 @ v1_xboole_0 )
!= ( sk44 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1092,1790]) ).
thf(3139,plain,
( ( sk92 @ v1_xboole_0 )
!= ( sk44 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3140,plain,
sk92 != sk44,
inference(simp,[status(thm)],[3139]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_1) ).
thf(2400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).
thf(1518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_subset_1) ).
thf(2531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_realset1) ).
thf(651,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(2985,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)],[475]) ).
thf(337,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2227,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(1055,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)],[130]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( C = k1_xboole_0 ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( ( C = k1_xboole_0 )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( C = k1_xboole_0 ) ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(452,axiom,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).
thf(2811,plain,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(2812,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk174 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk172 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk174 @ m2_relset_1 ) ) )
| ~ sk172 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk174 @ v1_funct_2 ) ) )
| ~ sk172 )
& ( ( sk174 @ v1_funct_1 )
| ~ sk172 )
& ( sk172
| ~ ( A @ ( sk173 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk172
| ( f1_s14_funct_2 @ ( sk173 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[2811]) ).
thf(2814,plain,
( sk172
| ( f1_s14_funct_2 @ ( sk173 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[2812]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(2269,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)],[347]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_2) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(1511,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)],[205]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(1992,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)],[298]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(1264,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)],[171]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_2) ).
thf(2217,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(587,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1581,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)],[222]) ).
thf(1582,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[1581]) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1582]) ).
thf(1585,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1583]) ).
thf(1587,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1585]) ).
thf(1588,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[1587]) ).
thf(129,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(1051,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1052,plain,
( ( sk43 @ v1_finset_1 )
& ~ ( sk43 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1051]) ).
thf(1053,plain,
~ ( sk43 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1052]) ).
thf(3143,plain,
( ( ( sk43 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1588,1053]) ).
thf(3144,plain,
( ( sk43 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3143]) ).
thf(3148,plain,
sk43 != k1_xboole_0,
inference(simp,[status(thm)],[3144]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
thf(559,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(1319,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k5_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k5_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_5) ).
thf(3084,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k5_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k5_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(2520,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)],[397]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(2301,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)],[356]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(1778,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)],[262]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).
thf(1100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(1847,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)],[277]) ).
thf(106,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(922,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(923,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk34 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk34 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk34 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[922]) ).
thf(924,plain,
~ ( sk34 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[923]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(2893,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(1682,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)],[243]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).
thf(1978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k3_subset_1 ) )
= ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_2) ).
thf(514,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k3_subset_1 ) )
= ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_funct_2) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(756,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)],[68]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(2794,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(2335,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).
thf(966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(692,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)],[52]) ).
thf(114,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(956,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)],[114]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(2002,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ k2_funct_5 @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ k2_funct_5 @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(505,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ k2_funct_5 @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(506,plain,
( ( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k2_funct_5 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) )
| ( ( sk3 @ k1_funct_5 )
!= ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) ) )
& ( sk1 @ ( sk2 @ ( sk3 @ m2_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[505]) ).
thf(507,plain,
sk1 @ ( sk2 @ ( sk3 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[506]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(981,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k2_funct_5 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_5) ).
thf(2964,plain,
! [A: $i,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_funct_5 ) ) )
& ( ( B
= ( A @ k2_funct_5 ) )
=> ! [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)],[474]) ).
thf(381,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(2424,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(2371,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(988,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)],[120]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(2639,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)],[421]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_2) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_partfun1) ).
thf(2205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_2) ).
thf(512,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(661,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)],[45]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(546,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(70,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(761,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)],[70]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(2093,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(489,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3054,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(2790,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)],[447]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(1074,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)],[133]) ).
thf(227,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_1) ).
thf(1604,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(508,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k2_funct_5 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) )
| ( ( sk3 @ k1_funct_5 )
!= ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[506]) ).
thf(509,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k2_funct_5 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) ) )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k1_funct_5 ) ) ),
inference(lifteq,[status(thm)],[508]) ).
thf(3150,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k2_funct_5 ) )
| ( ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) ) )
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k1_funct_5 ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(3151,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k2_funct_5 ) )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ k6_relset_1 ) ) @ ( sk2 @ ( sk1 @ k10_relset_1 ) ) ) )
!= ( sk3 @ k1_funct_5 ) ) ),
inference(simp,[status(thm)],[3150]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).
thf(2011,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(2660,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(1768,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)],[260]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(2382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(172,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(1273,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1274,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1273]) ).
thf(30,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(598,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_1) ).
thf(3069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(1619,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)],[231]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(746,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)],[66]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(1570,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)],[220]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_2) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_partfun1) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(484,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_1) ).
thf(3022,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(1502,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(820,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)],[87]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).
thf(630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(2937,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)],[469]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(426,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(2670,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(496,axiom,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_5) ).
thf(3090,plain,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(3134,plain,
( ( ( sk44 @ v1_xboole_0 )
!= ( sk43 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1092,1053]) ).
thf(3135,plain,
( ( sk44 @ v1_xboole_0 )
!= ( sk43 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3134]) ).
thf(3137,plain,
sk44 != sk43,
inference(simp,[status(thm)],[3135]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2068,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(326,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(2179,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(1656,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(682,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)],[49]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(1740,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(443,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(2769,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)],[443]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(1938,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(2758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).
thf(566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(2663,plain,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).
thf(522,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_sysrel) ).
thf(830,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).
thf(2344,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(393,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(2492,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1128,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)],[144]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(948,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_partfun1) ).
thf(2685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(1227,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(63,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(725,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(1498,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)],[200]) ).
thf(186,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(1425,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(211,axiom,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).
thf(1540,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(1138,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)],[146]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(783,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(3001,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)],[479]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).
thf(857,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)],[95]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( C @ ( D @ k9_relat_1 ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_relset_2) ).
thf(519,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( C @ ( D @ k9_relat_1 ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(1592,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(1567,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)],[219]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(2798,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)],[449]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).
thf(933,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(2419,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)],[380]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= k1_xboole_0 )
| ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relset_2) ).
thf(526,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D = k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= k1_xboole_0 )
| ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(637,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(1700,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)],[247]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_5) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ k1_eqrel_1 )
= ( A @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_eqrel_1) ).
thf(1016,plain,
! [A: $i] :
( ( A @ k1_eqrel_1 )
= ( A @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(2666,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)],[425]) ).
thf(127,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(1039,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(1744,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)],[257]) ).
thf(56,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(706,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(184,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(1419,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(1082,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)],[134]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_funct_5 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_5) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k1_funct_5 ) ) )
& ( ( B
= ( A @ k1_funct_5 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(3091,plain,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3090]) ).
thf(3092,plain,
( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3091]) ).
thf(3094,plain,
( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3092]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(1461,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)],[192]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(1214,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(2349,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)],[367]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(2304,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)],[357]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
<=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_2) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) )
& ( ( C @ ( B @ r1_partfun1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(1668,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
thf(1192,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(721,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)],[61]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).
thf(1799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(290,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(1947,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ k2_funct_5 )
= ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k2_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k1_funct_5 )
= ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_5) ).
thf(3115,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ k2_funct_5 )
= ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k2_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k1_funct_5 )
= ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_sysrel) ).
thf(569,plain,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2766,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(2504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(1114,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)],[140]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_funct_5 @ ( B @ r2_hidden ) )
& ( C @ k1_funct_5 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_5) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_funct_5 @ ( B @ r2_hidden ) )
& ( C @ k1_funct_5 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).
thf(2900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(2387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(2581,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)],[409]) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(2465,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)],[388]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ( ( D @ k1_funct_5 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k1_funct_5 @ r1_tarski ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k1_funct_5 )
= ( E @ k1_funct_5 @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k10_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_2) ).
thf(3064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ( ( D @ k1_funct_5 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k1_funct_5 @ r1_tarski ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k1_funct_5 )
= ( E @ k1_funct_5 @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k10_relset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_realset1) ).
thf(1720,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(2140,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)],[324]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(2756,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)],[438]) ).
thf(3141,plain,
( ( ( sk34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1588,924]) ).
thf(3142,plain,
( ( sk34 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3141]) ).
thf(3147,plain,
sk34 != k1_xboole_0,
inference(simp,[status(thm)],[3142]) ).
thf(440,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_boole) ).
thf(2761,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).
thf(633,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(1695,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(541,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(1663,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)],[238]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(530,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(953,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(255,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(1732,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 @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(107,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(926,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(2634,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1857,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)],[278]) ).
thf(1054,plain,
sk43 @ v1_finset_1,
inference(cnfConj,[status(thm)],[1052]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2057,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).
thf(765,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(1466,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)],[194]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(2402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).
thf(1616,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(2995,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)],[477]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(794,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
thf(1996,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(2529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).
thf(718,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(1648,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)],[235]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( C @ ( B @ ( B @ ( D @ ( C @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relset_1) ).
thf(3130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( C @ ( B @ ( B @ ( D @ ( C @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k5_relset_1 ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k4_relset_1 ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relset_1) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k5_relset_1 ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( A @ ( B @ k4_relset_1 ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(2570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_subset_1) ).
thf(2602,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(499,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/sandbox/benchmark/theBenchmark.p',s1_relset_1) ).
thf(3104,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)],[499]) ).
thf(3105,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 ) ) )
& ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[3104]) ).
thf(3106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk197 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
| ~ ( D @ ( C @ p1_s1_relset_1 ) )
| ~ ( f2_s1_relset_1 @ ( D @ r2_hidden ) )
| ~ ( f1_s1_relset_1 @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ p1_s1_relset_1 ) )
| ~ ( sk197 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f2_s1_relset_1 @ ( B @ r2_hidden ) )
| ~ ( sk197 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f1_s1_relset_1 @ ( A @ r2_hidden ) )
| ~ ( sk197 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( sk197 @ m2_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[3105]) ).
thf(3111,plain,
f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( sk197 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[3106]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_2) ).
thf(1374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(1631,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)],[234]) ).
thf(346,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(2260,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) )
| ~ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[512]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(2292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( D @ ( A @ ( B @ k8_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relset_1) ).
thf(2391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( D @ ( A @ ( B @ k8_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(465,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_subset_1) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).
thf(584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(562,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)],[21]) ).
thf(310,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(2048,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_2) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(2489,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)],[392]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(1795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(875,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)],[100]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(826,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1520,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)],[208]) ).
thf(2817,plain,
( ( sk174 @ v1_funct_1 )
| ~ sk172 ),
inference(cnfConj,[status(thm)],[2812]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(1256,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)],[169]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).
thf(1488,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(641,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)],[41]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(2193,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)],[331]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
<=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_2) ).
thf(572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) )
& ( ( D @ ( C @ r1_partfun1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(79,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(787,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
thf(1865,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_5) ).
thf(1058,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ k2_funct_5 @ ( C @ r1_tarski ) )
<=> ( C @ ( D @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ ( B @ k9_relset_2 ) ) ) ) @ ( B @ ( B @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_relset_2) ).
thf(3123,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( ( C @ ( D @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ ( B @ k9_relset_2 ) ) ) ) @ ( B @ ( B @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) )
=> ( D @ k2_funct_5 @ ( C @ r1_tarski ) ) )
& ( ( D @ k2_funct_5 @ ( C @ r1_tarski ) )
=> ( C @ ( D @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ ( B @ k9_relset_2 ) ) ) ) @ ( B @ ( B @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).
thf(1224,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(1209,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(2478,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)],[391]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(2229,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(2623,plain,
! [A: $i] :
( ( ( ( A @ ( sk155 @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s4_funct_2 ) )
| ~ ( f1_s4_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk155 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk155 @ v1_funct_2 ) ) )
& ( sk155 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[2622]) ).
thf(2624,plain,
sk155 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2623]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(1011,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(736,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1492,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)],[198]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(470,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/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(2945,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)],[470]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(1122,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)],[142]) ).
thf(2894,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[2893]) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[2894]) ).
thf(2896,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2895]) ).
thf(599,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[598]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(1589,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)],[223]) ).
thf(351,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2284,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(286,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(1933,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(1801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(2824,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)],[454]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(2182,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)],[327]) ).
thf(436,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/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(2742,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)],[436]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2605,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)],[415]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_1) ).
thf(2780,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( A = k1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 )
= B )
& ( ( A @ ( B @ k2_zfmisc_1 ) @ k1_funct_5 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_5) ).
thf(1162,plain,
! [A: $i,B: $i] :
( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( A = k1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 )
= B )
& ( ( A @ ( B @ k2_zfmisc_1 ) @ k1_funct_5 )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_2) ).
thf(1325,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(769,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(110,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
<=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_2) ).
thf(943,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) )
=> ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) ) )
& ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).
thf(2278,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_2) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).
thf(1688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(2129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2625,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk155 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[2623]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relset_1) ).
thf(2785,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( C @ k2_relat_1 )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_2) ).
thf(895,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
=> ( ( C @ k2_relat_1 )
= B ) )
& ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(481,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(3006,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_realset1) ).
thf(685,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(1198,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)],[155]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_1) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(695,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).
thf(2086,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)],[317]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(2369,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)],[368]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1176,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)],[151]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(1775,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)],[261]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun1) ).
thf(868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(1528,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)],[209]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(1726,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)],[253]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(1250,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)],[167]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(2867,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( 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)],[459]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(658,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun1) ).
thf(3009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(2054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(2239,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)],[341]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(1809,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)],[272]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(2096,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)],[319]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1873,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(589,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)],[28]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(968,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)],[117]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun1) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(1413,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)],[182]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).
thf(2471,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) @ ( B @ k3_subset_1 ) )
= ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_2) ).
thf(548,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) @ ( B @ k3_subset_1 ) )
= ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(749,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)],[67]) ).
thf(418,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relset_1) ).
thf(2629,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( C @ k2_funct_5 )
= ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_2) ).
thf(3048,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( C @ k2_funct_5 )
= ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) ) )
& ( ( C @ k1_funct_5 )
= ( A @ ( C @ ( A @ ( B @ k6_relset_1 ) ) @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(617,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)],[33]) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k3_subset_1 ) )
= ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) ) )
| ~ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[514]) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k3_subset_1 ) )
= ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) ) ) ),
inference(lifteq,[status(thm)],[515]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(2564,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(836,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)],[92]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(1551,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)],[215]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).
thf(2567,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)],[404]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(2298,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)],[355]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_2) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(2715,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)],[433]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(1961,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)],[294]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(1025,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)],[125]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_partfun1) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).
thf(2060,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).
thf(887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(1531,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)],[210]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).
thf(2888,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(430,axiom,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
| ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
=> ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_5) ).
thf(2689,plain,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
| ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
=> ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).
thf(690,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)],[51]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(1598,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)],[225]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(1449,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1450,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[1449]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1450]) ).
thf(1452,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1451]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(791,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)],[80]) ).
thf(485,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).
thf(3026,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(1262,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2276,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(112,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(951,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(2044,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)],[309]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).
thf(2468,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(1711,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).
thf(1987,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m3_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_2) ).
thf(2224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(840,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_5) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).
thf(1830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ k6_relset_1 ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_relset_1 ) ) @ ( B @ ( A @ k6_relset_1 ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).
thf(1218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(3093,plain,
( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3091]) ).
thf(3095,plain,
( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3093]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(2675,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(703,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).
thf(656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(1702,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)],[248]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(1221,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)],[160]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(1506,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(2579,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
thf(1504,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(978,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)],[118]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_5 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_5) ).
thf(1670,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_5 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_partfun1) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ( ( E @ k2_funct_5 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k2_funct_5 @ r1_tarski ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k2_funct_5 )
= ( D @ k2_funct_5 @ ( E @ ( C @ ( B @ k10_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_2) ).
thf(3071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ( ( E @ k2_funct_5 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k2_funct_5 @ r1_tarski ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ k2_funct_5 )
= ( D @ k2_funct_5 @ ( E @ ( C @ ( B @ k10_relset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(1372,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)],[178]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_2) ).
thf(859,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(1934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_1) ).
thf(2948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(1141,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)],[147]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(2426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k4_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k4_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_5) ).
thf(1981,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k4_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k4_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(457,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(2843,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)],[457]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(1240,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)],[165]) ).
thf(121,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 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_subset_1) ).
thf(991,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 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relset_2) ).
thf(627,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2626,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk155 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[2623]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(1685,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)],[244]) ).
thf(431,axiom,
! [A: $i] :
( ( A @ v1_funct_1 )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(2696,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
=> ( A @ v1_funct_1 ) )
& ( ( A @ v1_funct_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(1844,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)],[276]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relset_2) ).
thf(524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k2_funct_5 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_funct_5 )
= ( C @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_5) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k2_funct_5 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_funct_5 )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( B @ k1_tarski @ ( E @ ( D @ ( C @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ( ( D @ ( A @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ~ ( E @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_relset_2) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( A @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ~ ( E @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ k1_tarski @ ( E @ ( D @ ( C @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_tarski @ ( E @ ( D @ ( C @ k2_zfmisc_1 ) @ k3_subset_1 ) @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ( ( D @ ( A @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ~ ( E @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(2828,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
thf(2078,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(274,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(1834,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(362,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/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(2325,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)],[362]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(759,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(1781,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1216,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)],[158]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(2209,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(2187,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)],[329]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).
thf(1189,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).
thf(2658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(2770,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[2769]) ).
thf(2771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk168 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2770]) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2771]) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2772]) ).
thf(2775,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[2774]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(1807,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(771,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)],[73]) ).
thf(466,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(2907,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(2591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(2389,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)],[374]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_5) ).
thf(1508,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_partfun1) ).
thf(2431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ ( B @ ( A @ k8_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(3132,plain,
( ( ( sk44 @ v1_xboole_0 )
!= ( sk34 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1092,924]) ).
thf(3133,plain,
( ( sk44 @ v1_xboole_0 )
!= ( sk34 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3132]) ).
thf(3136,plain,
sk44 != sk34,
inference(simp,[status(thm)],[3133]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(781,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)],[76]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_subset_1) ).
thf(2526,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(376,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_1) ).
thf(2394,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(1253,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(699,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)],[54]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_1) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_2) ).
thf(813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).
thf(2988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(963,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)],[115]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_relset_2) ).
thf(517,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(2167,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)],[325]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(2273,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_partfun1) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).
thf(2135,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
thf(1629,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(480,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/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(3003,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)],[480]) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(2764,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)],[441]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(2447,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(2576,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(2315,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)],[360]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).
thf(667,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(2462,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)],[387]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).
thf(929,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3145,plain,
( ( ( sk92 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1588,1790]) ).
thf(3146,plain,
( ( sk92 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3145]) ).
thf(3149,plain,
sk92 != k1_xboole_0,
inference(simp,[status(thm)],[3146]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(536,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(1116,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)],[141]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k2_funct_5 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k1_funct_5 )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_5) ).
thf(2374,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k2_funct_5 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k1_funct_5 )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(620,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)],[34]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_tarski ) )
<=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( D = F )
<=> ( E = G ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_tarski) ).
thf(1280,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) )
=> ( B @ ( A @ r2_tarski ) ) )
& ( ( B @ ( A @ r2_tarski ) )
=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(2385,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)],[372]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_2) ).
thf(2534,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(91,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(833,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(834,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[833]) ).
thf(835,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[834]) ).
thf(213,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).
thf(1546,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(1625,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ k1_funct_5 @ ( C @ r1_tarski ) )
<=> ( C @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( D @ ( A @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ ( A @ ( A @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_relset_2) ).
thf(3100,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( D @ ( A @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ ( A @ ( A @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) )
=> ( D @ k1_funct_5 @ ( C @ r1_tarski ) ) )
& ( ( D @ k1_funct_5 @ ( C @ r1_tarski ) )
=> ( C @ ( D @ ( B @ ( A @ k6_relset_1 ) ) @ ( D @ ( A @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ ( A @ ( A @ k10_relset_1 ) ) ) @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(2951,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)],[472]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1876,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)],[283]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1757,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)],[259]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(865,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)],[97]) ).
thf(320,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2123,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(2258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(1578,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)],[221]) ).
thf(293,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(1957,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)],[293]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(1229,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)],[163]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relset_1) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_sysrel) ).
thf(1248,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_1) ).
thf(2050,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(2800,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)],[450]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).
thf(807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(2572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(217,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(1561,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)],[217]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(664,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)],[46]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(828,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)],[89]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_2) ).
thf(532,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).
thf(796,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(564,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(420,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(2636,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(918,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)],[105]) ).
thf(83,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(801,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2021,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)],[307]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(1610,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).
thf(2803,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(1378,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)],[180]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).
thf(1019,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1550,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1549]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).
thf(2583,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(62,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(723,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_2) ).
thf(2507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(2864,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)],[458]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(871,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(607,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)],[32]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(1093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(624,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
thf(2600,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(2898,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(494,axiom,
! [A: $i] :
( ( ( A @ k1_funct_5 )
= k1_xboole_0 )
<=> ( ( A @ k2_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_5) ).
thf(3076,plain,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
=> ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_funct_5 )
= k1_xboole_0 )
=> ( ( A @ k2_funct_5 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(500,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k1_eqrel_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_eqrel_1) ).
thf(3113,plain,
! [A: $i] : ( A @ ( A @ ( A @ k1_eqrel_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(483,axiom,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).
thf(3013,plain,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(803,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_1) ).
thf(2321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(460,axiom,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).
thf(2879,plain,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(2880,plain,
! [A: $i] :
( ( ( ( A @ ( sk184 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk182 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk184 @ m2_relset_1 ) ) )
| ~ sk182 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk184 @ v1_funct_2 ) ) )
| ~ sk182 )
& ( ( sk184 @ v1_funct_1 )
| ~ sk182 )
& ( sk182
| ~ ( f2_s13_funct_2 @ ( sk183 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk182
| ( f1_s13_funct_2 @ ( sk183 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[2879]) ).
thf(2881,plain,
( ( sk184 @ v1_funct_1 )
| ~ sk182 ),
inference(cnfConj,[status(thm)],[2880]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_5) ).
thf(3096,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).
thf(1184,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(1416,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)],[183]) ).
thf(416,axiom,
! [A: $i] :
( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
& ( ( A @ k1_funct_5 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_5) ).
thf(2615,plain,
! [A: $i] :
( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
& ( ( A @ k1_funct_5 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(882,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)],[101]) ).
thf(281,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(1870,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(427,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2672,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(1463,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(2998,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(218,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(1565,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)],[218]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_partfun1) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(775,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)],[74]) ).
thf(4132,plain,
$false,
inference(e,[status(thm)],[1036,2452,1411,2778,1559,893,2499,1549,2295,2306,2412,1237,846,777,555,2309,3040,2953,741,2014,1728,2837,511,1437,1041,2231,2622,1422,2248,1705,1788,2740,1999,715,1275,1327,1954,1458,670,1867,2184,709,1613,1601,3140,2400,1518,2531,651,2985,2227,1055,2916,2814,1660,785,2269,2708,1511,1455,1992,1264,2217,587,3148,559,1319,1479,3084,2520,2301,1778,1100,1847,924,591,2893,1682,1978,514,2254,1051,756,2794,1581,2335,966,692,956,2002,2750,507,981,2964,2424,2371,988,2286,2639,2718,2205,512,661,546,761,2093,3054,2790,1074,1604,3151,2011,2660,1768,2382,1274,598,1666,3069,1619,746,1091,1570,1174,1676,3022,1502,820,630,2937,1837,2670,3090,3137,2068,2179,1656,682,1740,2769,1938,2758,566,2663,2332,2820,522,830,2344,2492,551,1128,948,2685,1804,1227,725,1498,1425,1096,1540,1138,783,3001,857,519,1592,1567,2798,933,2561,2419,526,637,1700,1791,1016,2666,1039,1744,706,1419,1082,2023,3094,1461,1214,2349,622,2304,1131,1668,1192,721,1799,1947,3115,569,2766,2504,1114,2125,1588,2900,2387,2581,2465,3064,1720,2140,2756,3147,2761,633,1695,541,1663,530,953,1732,926,2634,1857,1054,2057,765,1466,2402,2189,1616,2995,794,2338,1996,2529,718,1648,3130,3042,1273,2570,2602,3111,1374,1631,2260,513,2292,2391,2904,584,562,2048,1125,2489,1752,2016,1795,875,826,1520,2817,1256,1488,641,2193,572,787,1865,1058,3123,1092,1224,1209,2478,2229,2624,1011,736,1492,1542,2945,1122,2896,599,1589,2284,1933,509,1801,2824,2182,2742,2605,2780,1162,1325,769,943,2278,1061,1688,2129,2625,2785,895,3006,685,1198,2212,695,2086,2369,1176,1775,505,922,868,1445,1528,1726,1250,2867,658,3009,2054,2239,1809,2096,1873,589,553,968,2005,1413,2471,548,749,2629,3048,617,516,2256,2564,836,1551,2567,2298,712,2715,1961,1025,1156,2060,887,1531,2888,2689,690,1598,1452,791,3026,1262,2276,951,2044,2468,1711,1053,1790,1987,2224,840,1785,1830,3127,1218,3095,2675,703,656,1702,1221,1506,2579,1504,978,1670,1717,3071,1372,859,1934,2948,1141,2426,1981,600,2843,1240,991,1940,2435,627,2626,1685,2696,1844,524,3056,1108,1949,2828,2078,1834,2325,759,1781,1216,2209,2187,1189,2658,2775,1807,771,2907,2591,2389,1508,2431,3136,781,2526,2934,2394,1253,699,2594,813,2988,963,517,2167,2273,1903,2135,2811,1629,3104,3003,2764,2447,510,2576,1513,2315,667,2462,929,3149,536,2019,1116,2374,620,1280,2385,2534,833,835,1546,1625,3100,2951,1876,1757,865,2123,2258,1578,1957,1229,2233,1248,2050,2800,1495,807,2572,1561,664,828,532,796,564,2636,918,801,2021,1610,2803,1378,1019,1550,2583,723,2507,2864,871,607,1093,1930,624,2600,2898,3076,3113,3013,803,2321,2881,3096,1184,1416,2615,2834,1449,882,1870,2672,2879,1463,2998,1565,1490,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU444+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 09:58:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 4.23/1.87 % [INFO] Parsing done (870ms).
% 4.23/1.88 % [INFO] Running in sequential loop mode.
% 5.16/2.25 % [INFO] eprover registered as external prover.
% 5.16/2.26 % [INFO] Scanning for conjecture ...
% 6.58/2.70 % [INFO] Found a conjecture (or negated_conjecture) and 4527 axioms. Running axiom selection ...
% 9.11/3.31 % [INFO] Axiom selection finished. Selected 502 axioms (removed 4025 axioms).
% 10.54/3.71 % [INFO] Problem is first-order (TPTP FOF).
% 10.54/3.74 % [INFO] Type checking passed.
% 10.54/3.75 % [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 ...
% 38.05/9.73 % External prover 'e' found a proof!
% 38.05/9.73 % [INFO] Killing All external provers ...
% 38.05/9.73 % Time passed: 9171ms (effective reasoning time: 7839ms)
% 38.05/9.73 % 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)>
% 38.05/9.73 % Axioms used in derivation (502): t119_funct_2, t62_partfun1, t42_xboole_1, t39_relset_1, t34_sysrel, t21_zfmisc_1, t44_xboole_1, t5_boole, t13_zfmisc_1, t50_relset_2, t51_partfun1, redefinition_m2_relset_1, fc1_zfmisc_1, t35_subset_1, d1_tarski, t66_funct_2, t14_finset_1, t53_subset_1, cc2_finset_1, t20_zfmisc_1, t135_zfmisc_1, dt_k6_relset_1, fc3_finset_1, t25_relset_1, dt_k5_relset_1, t105_zfmisc_1, t140_zfmisc_1, t109_xboole_1, t110_xboole_1, t20_funct_2, dt_k8_funcop_1, dt_k4_relset_1, d1_funct_5, rc4_finset_1, t57_funcop_1, t47_relset_1, t1_boole, t7_subset_1, t92_xboole_1, t2_realset1, t3_xboole_1, t97_xboole_1, fc1_xboole_0, t32_relset_2, t113_xboole_1, t111_zfmisc_1, t64_funct_5, t56_partfun1, t8_subset_1, t4_ordinal1, s12_funct_2, t1_subset, s3_funct_2, t10_partfun1, t16_funct_2, t113_zfmisc_1, t34_xboole_1, dt_k7_subset_1, t53_funct_2, d5_tarski, t158_partfun1, fc4_subset_1, dt_k3_funct_2, t7_funct_2, t146_funct_2, t42_zfmisc_1, dt_k9_relset_1, t13_funcop_1, t6_xboole_1, t41_funct_2, d5_xboole_0, t54_relset_2, t168_funct_2, t43_xboole_1, t54_partfun1, t81_zfmisc_1, t166_funct_2, t148_partfun1, fc5_finset_1, t19_finset_1, t35_zfmisc_1, t117_zfmisc_1, t15_funct_5, dt_k8_relset_1, t24_relset_2, t43_zfmisc_1, t65_partfun1, t44_funct_2, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, t15_relset_1, t61_subset_1, t49_funct_2, t6_mssubfam, t162_partfun1, t45_zfmisc_1, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, t27_zfmisc_1, t37_xboole_1, t9_xboole_1, redefinition_k2_funct_2, d7_partfun1, t36_subset_1, t49_zfmisc_1, t55_relset_2, t130_funct_2, t29_relset_2, t59_subset_1, t41_zfmisc_1, dt_m2_relset_1, t9_mssubfam, t18_finset_1, t12_funct_5, t50_zfmisc_1, fc8_finset_1, t16_funct_5, t29_partfun1, t31_relset_1, t176_partfun1, t62_funct_2, t115_zfmisc_1, t152_funct_2, t65_funct_2, t25_relset_2, s13_funct_2, dt_k8_relset_2, d2_tarski, t129_zfmisc_1, fc2_xboole_0, d1_relset_2, involutiveness_k6_relset_1, dt_m2_realset1, t64_funct_2, t30_relset_2, involutiveness_k3_subset_1, t175_partfun1, d1_xboole_0, t5_mssubfam, t34_partfun1, t2_mssubfam, t3_mssubfam, t138_zfmisc_1, d2_funcop_1, t130_zfmisc_1, t154_funct_2, t48_funct_2, t156_funct_2, t18_funct_5, t108_zfmisc_1, t165_funct_2, t27_relset_1, t52_relset_1, t60_partfun1, t118_funct_2, existence_m1_realset1, t16_relset_1, t53_relset_1, t30_sysrel, t46_zfmisc_1, t31_partfun1, t6_boole, t18_subset_1, t4_funct_5, t59_setfam_1, dt_k3_relset_2, t118_zfmisc_1, t8_funct_2, t14_relset_1, t24_relset_1, dt_k2_relset_2, t164_funct_2, fc2_funct_2, rc2_subset_1, fc9_finset_1, t1_xboole_1, t26_relset_1, t66_funct_5, t64_partfun1, t32_relset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t32_partfun1, d6_tarski, fc3_subset_1, t128_zfmisc_1, t25_zfmisc_1, t75_zfmisc_1, t48_zfmisc_1, t1_zfmisc_1, t46_partfun1, fc2_subset_1, t45_funct_2, t79_zfmisc_1, dt_k8_funct_2, d2_realset1, t53_relset_2, fc6_finset_1, t63_funct_5, t150_relat_1, existence_m1_relset_1, t167_funct_2, t24_finset_1, t11_funct_2, t28_partfun1, t40_funct_2, t102_zfmisc_1, t28_relset_1, t2_tarski, t33_xboole_1, t62_subset_1, t28_zfmisc_1, t72_zfmisc_1, t142_funct_2, t82_funct_2, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, dt_k1_partfun1, t52_subset_1, t42_relset_2, t23_zfmisc_1, dt_k9_relset_2, t4_subset, fc3_xboole_0, t33_sysrel, d2_xboole_0, t74_zfmisc_1, cc1_funct_2, t32_xboole_1, t5_ordinal1, t4_boole, dt_k11_relset_1, t162_funct_1, t141_zfmisc_1, t51_funct_2, t12_zfmisc_1, existence_m2_realset1, existence_m3_realset1, t56_subset_1, t8_funct_5, t17_funct_2, t96_xboole_1, t11_funct_5, commutativity_k5_xboole_0, t132_funct_2, t9_zfmisc_1, t148_funct_2, redefinition_k10_relset_1, s1_relset_1, t1_xboole_0, d4_partfun1, t139_zfmisc_1, t7_boole, cc1_funct_1, t17_funct_5, s11_funct_2, t13_finset_1, t3_ordinal1, t9_domain_1, d2_subset_1, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, dt_k2_partfun1, t6_funct_5, t26_zfmisc_1, t49_partfun1, t9_funct_2, rc1_subset_1, t149_funct_2, t158_funct_2, t51_relset_2, t49_relset_1, t22_finset_1, t69_partfun1, t7_ordinal1, t38_relset_1, t4_subset_1, t19_funct_2, t30_relset_1, t14_zfmisc_1, t64_zfmisc_1, d1_eqrel_1, d2_funct_5, t60_funct_2, t38_relset_2, dt_k1_eqrel_1, t113_funct_2, t71_partfun1, t159_funct_2, t116_zfmisc_1, t14_funct_2, t155_funct_2, t120_zfmisc_1, t169_partfun1, t5_realset1, t22_relset_1, t31_sysrel, s4_funct_2, t10_funct_5, t52_relset_2, t136_funct_2, commutativity_k7_subset_1, d2_zfmisc_1, existence_m1_subset_1, commutativity_k2_tarski, t8_relset_1, dt_k8_setfam_1, t4_relset_1, dt_k4_funct_2, t31_subset_1, t3_subset, t55_subset_1, t79_funct_2, t35_xboole_1, t106_zfmisc_1, d6_xboole_0, dt_k2_funct_2, t44_zfmisc_1, t5_funct_5, fc1_finset_1, t17_relset_1, t132_zfmisc_1, d5_subset_1, t29_zfmisc_1, t125_zfmisc_1, t73_funct_2, t14_xboole_1, t44_setfam_1, t99_partfun1, t107_zfmisc_1, t9_funct_5, t19_funct_5, t121_funct_2, t114_zfmisc_1, t58_partfun1, d1_zfmisc_1, t22_zfmisc_1, t15_xboole_1, t43_funct_2, t86_zfmisc_1, t38_zfmisc_1, redefinition_k7_subset_1, t116_funct_2, existence_m2_relset_1, t98_xboole_1, t168_partfun1, s14_funct_2, t73_partfun1, t51_subset_1, dt_k7_funcop_1, t6_funct_2, t36_zfmisc_1, t84_zfmisc_1, t13_funct_5, t8_xboole_1, d3_tarski, t74_partfun1, cc6_funct_2, t60_subset_1, d8_realset1, t13_xboole_1, t40_subset_1, reflexivity_r1_tarski, t8_realset1, t58_funcop_1, t6_relset_1, d1_relset_1, t39_zfmisc_1, d1_realset1, t131_funct_2, t119_zfmisc_1, dt_k10_relset_1, t37_relset_2, t143_funct_2, t18_funct_2, t1_realset1, t2_xboole_1, t9_mcart_1, d1_funct_2, t6_zfmisc_1, t1_mssubfam, t121_zfmisc_1, t10_subset_1, t57_partfun1, t4_xboole_1, t1_partfun1, t41_xboole_1, t57_subset_1, t47_zfmisc_1, t49_relset_2, d4_xboole_0, t35_funct_1, t29_relset_1, t45_partfun1, t36_xboole_1, t73_zfmisc_1, t151_funct_2, t46_relset_1, dt_k5_setfam_1, rc3_finset_1, t12_funct_2, t50_relset_1, cc1_finset_1, t35_partfun1, t40_relset_2, fc12_finset_1, t136_zfmisc_1, t4_mssubfam, t33_relset_1, t24_zfmisc_1, t68_zfmisc_1, t54_subset_1, rc1_finset_1, t8_boole, rc1_xboole_0, t11_xboole_1, t23_finset_1, redefinition_k8_funct_2, t35_relset_1, t34_zfmisc_1, t80_zfmisc_1, t120_funct_2, t38_funct_2, t16_finset_1, t14_funcop_1, t37_zfmisc_1, t43_relset_2, t109_zfmisc_1, t20_relset_2, t126_zfmisc_1, t10_realset1, t59_funct_2, t12_xboole_1, t10_zfmisc_1, t2_subset, t134_zfmisc_1, t28_finset_1, t48_subset_1, d1_funct_1, t44_partfun1, t34_relset_1, t9_tarski, t50_subset_1, t46_xboole_1, d10_xboole_0, fc2_finset_1, t115_funct_2, idempotence_k2_xboole_0, t43_partfun1, t7_xboole_1, t5_xboole_1, t145_funct_2, redefinition_k5_relset_1, t27_partfun1, t91_xboole_1, t67_partfun1, t3_boole, t6_ordinal1, t58_setfam_1, t21_relset_2, cc5_funct_2, t48_relset_1, t49_subset_1, t7_tarski, t22_funct_2, t99_xboole_1, fc14_finset_1, t36_relset_1, t30_zfmisc_1, fc7_finset_1, t143_partfun1, t81_relat_1, rc2_xboole_0, t174_partfun1, t45_xboole_1, t67_funct_2, t26_partfun1, t112_zfmisc_1, t40_xboole_1, t40_zfmisc_1, t72_funcop_1, dt_m3_realset1, t2_xboole_0, t61_funct_2, t10_xboole_1, t172_partfun1, t38_xboole_1, t39_xboole_1, antisymmetry_r2_hidden, t23_relset_1, dt_k3_subset_1, d2_relset_2, fc1_funct_2, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1
% 38.05/9.73 % No. of inferences in proof: 1084
% 38.05/9.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9171 ms resp. 7839 ms w/o parsing
% 40.61/10.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.61/10.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------