%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU444+4 : 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 : n026.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 86.85s 47.39s
% Output : Refutation 90.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 598
% Syntax : Number of formulae : 1251 ( 172 unt; 0 typ; 12 def)
% Number of atoms : 6797 (1261 equ; 0 cnn)
% Maximal formula atoms : 48 ( 5 avg)
% Number of connectives : 24278 (1197 ~; 191 |;2688 &;17575 @)
% ( 106 <=>;2521 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 165 ( 162 usr; 48 con; 0-6 aty)
% Number of variables : 4162 ( 1 ^;3997 !; 152 ?;4162 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% 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_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
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(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k14_funct_3_decl,type,
k14_funct_3: $i > $i > $i > $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
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(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k4_relset_1_decl,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k4_finseq_4_decl,type,
k4_finseq_4: $i > $i > $i > $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(v2_funct_2_decl,type,
v2_funct_2: $i > $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k1_funct_3_decl,type,
k1_funct_3: $i > $i ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k15_pralg_1_decl,type,
k15_pralg_1: $i > $i > $i ).
thf(k10_relat_1_decl,type,
k10_relat_1: $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k16_funct_3_decl,type,
k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_card_1_decl,type,
k1_card_1: $i > $i ).
thf(k13_funct_3_decl,type,
k13_funct_3: $i > $i > $i ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k12_turing_1_decl,type,
k12_turing_1: $i > $i > $i > $i ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k11_cohsp_1_decl,type,
k11_cohsp_1: $i > $i > $i > $i ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(k2_oposet_1_decl,type,
k2_oposet_1: $i > $i > $i ).
thf(k1_bhsp_5_decl,type,
k1_bhsp_5: $i > $i > $i > $i ).
thf(r1_partit_2_decl,type,
r1_partit_2: $i > $i > $i > $i > $o ).
thf(k6_cohsp_1_decl,type,
k6_cohsp_1: $i > $i > $i > $i ).
thf(k8_cohsp_1_decl,type,
k8_cohsp_1: $i > $i > $i > $i ).
thf(v1_yellow18_decl,type,
v1_yellow18: $i > $i > $i > $i > $o ).
thf(k5_bhsp_5_decl,type,
k5_bhsp_5: $i > $i > $i > $i > $i > $i ).
thf(k9_relset_1_decl,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(k4_graphsp_decl,type,
k4_graphsp: $i > $i > $i > $i ).
thf(a_3_0_ami_1_decl,type,
a_3_0_ami_1: $i > $i > $i > $i ).
thf(f1_s2_seq_1_decl,type,
f1_s2_seq_1: $i ).
thf(f2_s2_seq_1_decl,type,
f2_s2_seq_1: $i ).
thf(p1_s2_seq_1_decl,type,
p1_s2_seq_1: $i > $i > $o ).
thf(p1_s1_abcmiz_0_decl,type,
p1_s1_abcmiz_0: $i > $o ).
thf(f1_s1_monoid_1_decl,type,
f1_s1_monoid_1: $i ).
thf(f2_s1_monoid_1_decl,type,
f2_s1_monoid_1: $i ).
thf(p1_s1_monoid_1_decl,type,
p1_s1_monoid_1: $i > $i > $o ).
thf(k2_monoid_0_decl,type,
k2_monoid_0: $i > $i > $i > $i ).
thf(k1_oposet_1_decl,type,
k1_oposet_1: $i > $i > $i ).
thf(f1_s2_lmod_7_decl,type,
f1_s2_lmod_7: $i ).
thf(f2_s2_lmod_7_decl,type,
f2_s2_lmod_7: $i > $i ).
thf(r1_qmax_1_decl,type,
r1_qmax_1: $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(k1_polynom1_decl,type,
k1_polynom1: $i > $i > $i > $i > $i > $i ).
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_s14_scheme1_decl,type,
f1_s14_scheme1: $i ).
thf(p1_s14_scheme1_decl,type,
p1_s14_scheme1: $i > $o ).
thf(p2_s14_scheme1_decl,type,
p2_s14_scheme1: $i > $o ).
thf(p3_s14_scheme1_decl,type,
p3_s14_scheme1: $i > $o ).
thf(p4_s14_scheme1_decl,type,
p4_s14_scheme1: $i > $o ).
thf(f3_s14_scheme1_decl,type,
f3_s14_scheme1: $i > $i ).
thf(f2_s14_scheme1_decl,type,
f2_s14_scheme1: $i ).
thf(f4_s14_scheme1_decl,type,
f4_s14_scheme1: $i > $i ).
thf(f5_s14_scheme1_decl,type,
f5_s14_scheme1: $i > $i ).
thf(f6_s14_scheme1_decl,type,
f6_s14_scheme1: $i > $i ).
thf(f1_s19_scheme1_decl,type,
f1_s19_scheme1: $i ).
thf(p1_s19_scheme1_decl,type,
p1_s19_scheme1: $i > $o ).
thf(p2_s19_scheme1_decl,type,
p2_s19_scheme1: $i > $o ).
thf(p3_s19_scheme1_decl,type,
p3_s19_scheme1: $i > $o ).
thf(f2_s19_scheme1_decl,type,
f2_s19_scheme1: $i ).
thf(f3_s19_scheme1_decl,type,
f3_s19_scheme1: $i > $i ).
thf(f4_s19_scheme1_decl,type,
f4_s19_scheme1: $i > $i ).
thf(f5_s19_scheme1_decl,type,
f5_s19_scheme1: $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(f3_s1_rlvect_4_decl,type,
f3_s1_rlvect_4: $i ).
thf(f4_s1_rlvect_4_decl,type,
f4_s1_rlvect_4: $i ).
thf(f5_s1_rlvect_4_decl,type,
f5_s1_rlvect_4: $i ).
thf(f1_s1_rlvect_4_decl,type,
f1_s1_rlvect_4: $i ).
thf(f2_s1_rlvect_4_decl,type,
f2_s1_rlvect_4: $i ).
thf(f6_s1_rlvect_4_decl,type,
f6_s1_rlvect_4: $i ).
thf(f7_s1_rlvect_4_decl,type,
f7_s1_rlvect_4: $i ).
thf(f8_s1_rlvect_4_decl,type,
f8_s1_rlvect_4: $i ).
thf(f9_s1_rlvect_4_decl,type,
f9_s1_rlvect_4: $i > $i ).
thf(f1_s11_scheme1_decl,type,
f1_s11_scheme1: $i ).
thf(p1_s11_scheme1_decl,type,
p1_s11_scheme1: $i > $o ).
thf(p2_s11_scheme1_decl,type,
p2_s11_scheme1: $i > $o ).
thf(p3_s11_scheme1_decl,type,
p3_s11_scheme1: $i > $o ).
thf(p4_s11_scheme1_decl,type,
p4_s11_scheme1: $i > $o ).
thf(f2_s11_scheme1_decl,type,
f2_s11_scheme1: $i ).
thf(f3_s11_scheme1_decl,type,
f3_s11_scheme1: $i > $i ).
thf(f4_s11_scheme1_decl,type,
f4_s11_scheme1: $i > $i ).
thf(f5_s11_scheme1_decl,type,
f5_s11_scheme1: $i > $i ).
thf(f6_s11_scheme1_decl,type,
f6_s11_scheme1: $i > $i ).
thf(f1_s20_scheme1_decl,type,
f1_s20_scheme1: $i ).
thf(p1_s20_scheme1_decl,type,
p1_s20_scheme1: $i > $o ).
thf(p2_s20_scheme1_decl,type,
p2_s20_scheme1: $i > $o ).
thf(p3_s20_scheme1_decl,type,
p3_s20_scheme1: $i > $o ).
thf(p4_s20_scheme1_decl,type,
p4_s20_scheme1: $i > $o ).
thf(f2_s20_scheme1_decl,type,
f2_s20_scheme1: $i ).
thf(f3_s20_scheme1_decl,type,
f3_s20_scheme1: $i > $i ).
thf(f4_s20_scheme1_decl,type,
f4_s20_scheme1: $i > $i ).
thf(f5_s20_scheme1_decl,type,
f5_s20_scheme1: $i > $i ).
thf(f6_s20_scheme1_decl,type,
f6_s20_scheme1: $i > $i ).
thf(f1_s13_scheme1_decl,type,
f1_s13_scheme1: $i ).
thf(p1_s13_scheme1_decl,type,
p1_s13_scheme1: $i > $o ).
thf(p2_s13_scheme1_decl,type,
p2_s13_scheme1: $i > $o ).
thf(p3_s13_scheme1_decl,type,
p3_s13_scheme1: $i > $o ).
thf(f3_s13_scheme1_decl,type,
f3_s13_scheme1: $i > $i ).
thf(f2_s13_scheme1_decl,type,
f2_s13_scheme1: $i ).
thf(f4_s13_scheme1_decl,type,
f4_s13_scheme1: $i > $i ).
thf(f5_s13_scheme1_decl,type,
f5_s13_scheme1: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk94_decl,type,
sk94: $i ).
thf(sk96_decl,type,
sk96: $i ).
thf(sk158_decl,type,
sk158: $i ).
thf(sk159_decl,type,
sk159: $i ).
thf(sk199_decl,type,
sk199: $i ).
thf(sk200_decl,type,
sk200: $i > $i ).
thf(sk222_decl,type,
sk222: $i ).
thf(sk230_decl,type,
sk230: $o ).
thf(sk231_decl,type,
sk231: $i ).
thf(sk232_decl,type,
sk232: $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(sk94_def,definition,
( sk94
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk96_def,definition,
( sk96
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk158_def,definition,
( sk158
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk159_def,definition,
( sk159
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk199_def,definition,
( sk199
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s2_seq_1 ) ) ) )
& ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) ) )
& ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ ( B @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( C @ m1_subset_1 ) ) ) ) ) )
& ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk200_def,definition,
( sk200
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk222_def,definition,
( sk222
= ( @+[A: $i] :
~ ( A @ v1_finset_1 ) ) ) ).
thf(sk231_def,definition,
( sk231
= ( @+[A: $i] :
( ! [B: $i] :
( ( f2_s1_monoid_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ p1_s1_monoid_1 ) ) )
& ( f1_s1_monoid_1 @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk232_def,definition,
( sk232
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s1_monoid_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_monoid_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(299,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(2163,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)],[299]) ).
thf(422,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(2822,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)],[422]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_3) ).
thf(809,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(282,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(2094,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(462,axiom,
( ? [A: $i] :
( ( A @ p1_s1_abcmiz_0 )
& ( A @ v1_finset_1 ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( ( B @ p1_s1_abcmiz_0 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( B = A ) )
& ( A @ p1_s1_abcmiz_0 )
& ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_abcmiz_0) ).
thf(3053,plain,
( ? [A: $i] :
( ( A @ p1_s1_abcmiz_0 )
& ( A @ v1_finset_1 ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( ( B @ p1_s1_abcmiz_0 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( B = A ) )
& ( A @ p1_s1_abcmiz_0 )
& ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(561,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(3666,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)],[561]) ).
thf(579,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k2_funct_5 @ v1_finset_1 )
& ( A @ k1_funct_5 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_waybel26) ).
thf(3830,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k2_funct_5 @ v1_finset_1 )
& ( A @ k1_funct_5 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
& ( F @ ( C @ ( B @ k4_relset_1 ) ) @ ( E @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( F @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun2) ).
thf(1083,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
& ( F @ ( C @ ( B @ k4_relset_1 ) ) @ ( E @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( F @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(373,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(2559,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)],[373]) ).
thf(188,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(1549,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)],[188]) ).
thf(114,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(1110,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)],[114]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_2) ).
thf(1369,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] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(131,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(1190,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)],[131]) ).
thf(275,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(2072,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)],[275]) ).
thf(559,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(3661,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)],[559]) ).
thf(529,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(3477,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)],[529]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(1031,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(136,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(1211,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)],[136]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cat_3) ).
thf(762,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(86,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 @ k1_card_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_topgen_2) ).
thf(1005,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 @ k1_card_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(436,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(2908,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)],[436]) ).
thf(237,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(1808,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)],[237]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_finset_1 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_sf_mastr) ).
thf(3509,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_finset_1 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(382,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(2590,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(741,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(134,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(1205,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)],[134]) ).
thf(428,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(2854,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)],[428]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_jordan1k) ).
thf(677,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_funct_3) ).
thf(593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(594,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) )
& ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[593]) ).
thf(597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[594]) ).
thf(58,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(861,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)],[58]) ).
thf(287,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(2117,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)],[287]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) )
=> ( ( ( A @ k3_tarski )
= B )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_setlim_1) ).
thf(1596,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) )
=> ( ( ( A @ k3_tarski )
= B )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_card_1) ).
thf(2495,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(334,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(2381,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)],[334]) ).
thf(398,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(2671,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(399,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(2676,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(267,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(2014,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)],[267]) ).
thf(403,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(2686,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)],[403]) ).
thf(555,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(3648,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)],[555]) ).
thf(475,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(3135,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)],[475]) ).
thf(245,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(1867,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)],[245]) ).
thf(143,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_orders_1) ).
thf(1233,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(160,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 @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_2) ).
thf(1327,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 @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(578,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(3826,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)],[578]) ).
thf(228,axiom,
! [A: $i,B: $i] :
~ ( ? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( C
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_mcart_2) ).
thf(1761,plain,
! [A: $i,B: $i] :
~ ( ? [C: $i] :
( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( C
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(261,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(1954,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)],[261]) ).
thf(105,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(1078,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)],[105]) ).
thf(488,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor0) ).
thf(3217,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(538,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(3530,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)],[538]) ).
thf(507,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(3338,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)],[507]) ).
thf(441,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2933,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(247,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(1872,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)],[247]) ).
thf(406,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(2712,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)],[406]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(2627,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).
thf(698,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(552,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(3629,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)],[552]) ).
thf(327,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(2348,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)],[327]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2222,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)],[312]) ).
thf(2223,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)],[2222]) ).
thf(2224,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)],[2223]) ).
thf(2226,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2224]) ).
thf(2228,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2226]) ).
thf(2229,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[2228]) ).
thf(363,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2506,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(2507,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2506]) ).
thf(2508,plain,
~ ( sk158 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2507]) ).
thf(3991,plain,
( ( ( sk158 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2229,2508]) ).
thf(3992,plain,
( ( sk158 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3991]) ).
thf(3994,plain,
sk158 != k1_xboole_0,
inference(simp,[status(thm)],[3992]) ).
thf(360,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(2491,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)],[360]) ).
thf(195,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(1576,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)],[195]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_cohsp_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_cohsp_1) ).
thf(2010,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_cohsp_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(208,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(1650,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)],[208]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(2082,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(166,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ k1_tarski @ ( D @ k9_relat_1 ) )
= ( C @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) @ k1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_partfun2) ).
thf(1366,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ k1_tarski @ ( D @ k9_relat_1 ) )
= ( C @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) @ k1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(290,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( B @ m2_relset_1 ) ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_armstrng) ).
thf(2136,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( B @ m2_relset_1 ) ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(370,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(2531,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)],[370]) ).
thf(83,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(973,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)],[83]) ).
thf(468,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(3088,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)],[468]) ).
thf(184,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_setwiseo) ).
thf(1529,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k2_funcop_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_amistd_1) ).
thf(2067,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k2_funcop_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ m2_relset_1 ) ) )
=> ~ ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( B
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_armstrng) ).
thf(2825,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ m2_relset_1 ) ) )
=> ~ ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( B
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(421,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(2819,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(235,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(1803,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(142,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(1228,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)],[142]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(1482,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(548,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(3597,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)],[548]) ).
thf(577,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(3820,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)],[577]) ).
thf(485,axiom,
( ! [A: $i] :
~ ( ! [B: $i] :
( ( f2_s1_monoid_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ p1_s1_monoid_1 ) ) )
& ( f1_s1_monoid_1 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_monoid_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_monoid_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_monoid_1) ).
thf(3200,plain,
( ! [A: $i] :
~ ( ! [B: $i] :
( ( f2_s1_monoid_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ p1_s1_monoid_1 ) ) )
& ( f1_s1_monoid_1 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_monoid_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_monoid_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(3201,plain,
( ~ ? [A: $i] :
( ! [B: $i] :
( ( f2_s1_monoid_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ p1_s1_monoid_1 ) ) )
& ( f1_s1_monoid_1 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_monoid_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_monoid_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(miniscope,[status(thm)],[3200]) ).
thf(3202,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk232 @ k1_funct_1 ) @ ( B @ p1_s1_monoid_1 ) )
| ~ ( f1_s1_monoid_1 @ ( B @ r2_hidden ) )
| ~ sk230 )
& ( ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( sk232 @ m2_relset_1 ) ) )
| ~ sk230 )
& ( ( f2_s1_monoid_1 @ ( f1_s1_monoid_1 @ ( sk232 @ v1_funct_2 ) ) )
| ~ sk230 )
& ( ( sk232 @ v1_funct_1 )
| ~ sk230 )
& ( sk230
| ~ ( A @ ( sk231 @ p1_s1_monoid_1 ) )
| ~ ( f2_s1_monoid_1 @ ( A @ m1_subset_1 ) ) )
& ( sk230
| ( f1_s1_monoid_1 @ ( sk231 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[3201]) ).
thf(3204,plain,
( ( sk232 @ v1_funct_1 )
| ~ sk230 ),
inference(cnfConj,[status(thm)],[3202]) ).
thf(520,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(3425,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)],[520]) ).
thf(493,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(3275,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)],[493]) ).
thf(349,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(2444,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)],[349]) ).
thf(495,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(3280,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)],[495]) ).
thf(461,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(3043,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)],[461]) ).
thf(211,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 @ k1_funct_4 ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_4) ).
thf(1660,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 @ k1_funct_4 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(1298,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) )
| ( C @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_kurato_2) ).
thf(702,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) )
| ( C @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(530,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finset_1) ).
thf(3485,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ! [F: $i] :
( ( ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ( ( C @ ( F @ k1_funct_1 ) )
= D )
& ( ( A @ ( F @ ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ k2_partfun1 ) ) ) )
= E ) ) )
& ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( ( B @ v1_xboole_0 )
=> ( A @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_stirl2_1) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ! [F: $i] :
( ( ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ( ( C @ ( F @ k1_funct_1 ) )
= D )
& ( ( A @ ( F @ ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ k2_partfun1 ) ) ) )
= E ) ) )
& ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( ( B @ v1_xboole_0 )
=> ( A @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(434,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(2897,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)],[434]) ).
thf(75,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(949,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)],[75]) ).
thf(376,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
<=> ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun2) ).
thf(2571,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( D @ r2_hidden ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) )
& ( ( ( C @ ( D @ r2_hidden ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(234,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(1800,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)],[234]) ).
thf(7,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(638,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)],[7]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D
= ( A @ ( E @ ( B @ ( C @ k3_funct_2 ) ) ) ) )
<=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
<=> ( ( A @ ( F @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_partfun2) ).
thf(1892,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ( ( A @ ( F @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) )
& ( ( D @ ( F @ r2_hidden ) )
=> ( ( A @ ( F @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) ) ) ) )
=> ( D
= ( A @ ( E @ ( B @ ( C @ k3_funct_2 ) ) ) ) ) )
& ( ( D
= ( A @ ( E @ ( B @ ( C @ k3_funct_2 ) ) ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ( ( A @ ( F @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) )
& ( ( D @ ( F @ r2_hidden ) )
=> ( ( A @ ( F @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ( ~ ( A @ k1_zfmisc_1 @ v1_finset_1 )
& ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_topgen_3) ).
thf(2552,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ( ~ ( A @ k1_zfmisc_1 @ v1_finset_1 )
& ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(200,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(1607,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1608,plain,
( ( sk94 @ v1_finset_1 )
& ~ ( sk94 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1607]) ).
thf(1609,plain,
~ ( sk94 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1608]) ).
thf(162,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(1347,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)],[162]) ).
thf(584,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(3902,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)],[584]) ).
thf(366,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(2520,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)],[366]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(492,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 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_4) ).
thf(3268,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 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ k13_funct_3 ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_finseqop) ).
thf(1922,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ k13_funct_3 ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(405,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(2691,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)],[405]) ).
thf(219,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(1704,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)],[219]) ).
thf(251,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(1890,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(452,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(2989,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)],[452]) ).
thf(263,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(1963,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)],[263]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( A @ k1_funct_2 ) )
= k1_xboole_0 )
& ( ( C @ ( B @ k1_funct_2 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_altcat_1) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( A @ k1_funct_2 ) )
= k1_xboole_0 )
& ( ( C @ ( B @ k1_funct_2 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(178,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k12_turing_1 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( E @ k4_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_turing_1) ).
thf(1489,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( E @ k4_tarski ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k12_turing_1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k12_turing_1 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( E @ k4_tarski ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ k5_finsub_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_cohsp_1) ).
thf(924,plain,
! [A: $i] :
( ( A @ k5_finsub_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(521,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(3431,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)],[521]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_oposet_1 ) )
= ( B @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_oposet_1) ).
thf(1632,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_oposet_1 ) )
= ( B @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(479,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(3163,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)],[479]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2925,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_partfun1) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k8_cohsp_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_cohsp_1) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k8_cohsp_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( ( C @ k1_tarski @ ( A @ k2_xboole_0 ) )
!= B )
& ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_borsuk_5) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( ( C @ k1_tarski @ ( A @ k2_xboole_0 ) )
!= B )
& ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski @ ( C @ ( A @ ( B @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setwiseo) ).
thf(2451,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski @ ( C @ ( A @ ( B @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(315,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(2236,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)],[315]) ).
thf(537,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(3527,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)],[537]) ).
thf(568,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ k1_oposet_1 ) @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_oposet_1) ).
thf(3702,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ k1_oposet_1 ) @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(432,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(2880,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)],[432]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice2) ).
thf(1682,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(117,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(1136,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)],[117]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(687,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(465,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(3068,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)],[465]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D
= ( A @ ( E @ k9_relat_1 ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
<=> ? [G: $i] :
( ( F
= ( G @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( A @ ( G @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
& ( C @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_partfun2) ).
thf(2281,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ? [G: $i] :
( ( F
= ( G @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( A @ ( G @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
& ( C @ ( G @ m1_subset_1 ) ) )
=> ( D @ ( F @ r2_hidden ) ) )
& ( ( D @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ( F
= ( G @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( A @ ( G @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
& ( C @ ( G @ m1_subset_1 ) ) ) ) ) )
=> ( D
= ( A @ ( E @ k9_relat_1 ) ) ) )
& ( ( D
= ( A @ ( E @ k9_relat_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ? [G: $i] :
( ( F
= ( G @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( A @ ( G @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
& ( C @ ( G @ m1_subset_1 ) ) )
=> ( D @ ( F @ r2_hidden ) ) )
& ( ( D @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ( F
= ( G @ ( E @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( A @ ( G @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
& ( C @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(137,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(1215,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)],[137]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( B @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( F @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( E @ ( D @ ( F @ ( B @ ( A @ k4_finseq_4 ) ) ) @ k4_tarski ) @ r2_hidden ) )
& ( F @ ( D @ ( F @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun2) ).
thf(692,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( B @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( F @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( E @ ( D @ ( F @ ( B @ ( A @ k4_finseq_4 ) ) ) @ k4_tarski ) @ r2_hidden ) )
& ( F @ ( D @ ( F @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(734,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(173,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(1447,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)],[173]) ).
thf(563,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(3676,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)],[563]) ).
thf(316,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_orders_1) ).
thf(2242,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_4) ).
thf(1697,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(531,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(3492,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)],[531]) ).
thf(367,axiom,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_gate_1) ).
thf(2523,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(103,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(1072,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)],[103]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(2424,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(259,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(1943,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(133,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(1201,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)],[133]) ).
thf(456,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(3011,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)],[456]) ).
thf(571,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(3720,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)],[571]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_funct_2 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( E @ ( D @ k15_pralg_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_hilbert3) ).
thf(793,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_funct_2 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( E @ ( D @ k15_pralg_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(253,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(1915,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)],[253]) ).
thf(491,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(3265,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)],[491]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k2_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow_3) ).
thf(2646,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k2_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i] :
~ ( ( B @ ( D @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( C @ ( D @ r1_tarski ) )
& ( D @ v1_finset_1 ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_cqc_the1) ).
thf(2061,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i] :
~ ( ( B @ ( D @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( C @ ( D @ r1_tarski ) )
& ( D @ v1_finset_1 ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(205,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(1635,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1636,plain,
sk96 @ v1_xboole_0,
inference(cnf,[status(esa)],[1635]) ).
thf(101,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v6_ordinal1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_hahnban) ).
thf(1057,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v6_ordinal1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(564,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(3679,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)],[564]) ).
thf(64,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 @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(894,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 @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_triang_1) ).
thf(746,plain,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(90,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(1021,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)],[90]) ).
thf(583,axiom,
( ! [A: $i] :
( ( f1_s11_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p3_s11_scheme1 ) )
& ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p2_s11_scheme1 ) )
& ~ ( ( A @ p3_s11_scheme1 )
& ( A @ p2_s11_scheme1 ) )
& ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) )
& ~ ( ( A @ p3_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) )
& ~ ( ( A @ p2_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p4_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f6_s11_scheme1 ) ) )
& ( ( B @ p3_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s11_scheme1 ) ) )
& ( ( B @ p2_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s11_scheme1 ) ) )
& ( ( B @ p1_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s11_scheme1 ) ) ) ) ) )
& ! [B: $i] :
( ( f1_s11_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
<=> ~ ( ~ ( B @ p4_s11_scheme1 )
& ~ ( B @ p3_s11_scheme1 )
& ~ ( B @ p2_s11_scheme1 )
& ~ ( B @ p1_s11_scheme1 ) ) ) )
& ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_scheme1) ).
thf(3867,plain,
( ! [A: $i] :
( ( f1_s11_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p3_s11_scheme1 ) )
& ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p2_s11_scheme1 ) )
& ~ ( ( A @ p3_s11_scheme1 )
& ( A @ p2_s11_scheme1 ) )
& ~ ( ( A @ p4_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) )
& ~ ( ( A @ p3_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) )
& ~ ( ( A @ p2_s11_scheme1 )
& ( A @ p1_s11_scheme1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p4_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f6_s11_scheme1 ) ) )
& ( ( B @ p3_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s11_scheme1 ) ) )
& ( ( B @ p2_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s11_scheme1 ) ) )
& ( ( B @ p1_s11_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s11_scheme1 ) ) ) ) ) )
& ! [B: $i] :
( ( f1_s11_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( ~ ( B @ p4_s11_scheme1 )
& ~ ( B @ p3_s11_scheme1 )
& ~ ( B @ p2_s11_scheme1 )
& ~ ( B @ p1_s11_scheme1 ) )
=> ( A @ ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) ) )
& ( ( A @ ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ~ ( ~ ( B @ p4_s11_scheme1 )
& ~ ( B @ p3_s11_scheme1 )
& ~ ( B @ p2_s11_scheme1 )
& ~ ( B @ p1_s11_scheme1 ) ) ) ) )
& ( f2_s11_scheme1 @ ( f1_s11_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(49,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(820,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)],[49]) ).
thf(474,axiom,
? [A: $i] :
~ ( A @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_5) ).
thf(3132,plain,
? [A: $i] :
~ ( A @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(3133,plain,
~ ! [A: $i] : ( A @ v1_finset_1 ),
inference(miniscope,[status(thm)],[3132]) ).
thf(3134,plain,
~ ( sk222 @ v1_finset_1 ),
inference(cnf,[status(esa)],[3133]) ).
thf(203,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(1619,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)],[203]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_4) ).
thf(2528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(338,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(2396,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)],[338]) ).
thf(527,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_hilbert3) ).
thf(3471,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(148,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(1274,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)],[148]) ).
thf(348,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_3) ).
thf(2441,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ k2_relat_1 @ ( C @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_isocat_2) ).
thf(1042,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ k2_relat_1 @ ( C @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(76,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 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( A @ k3_subset_1 ) )
= ( D @ ( B @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_jct_misc) ).
thf(952,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 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( A @ k3_subset_1 ) )
= ( D @ ( B @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_3) ).
thf(1217,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(4,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(598,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)],[4]) ).
thf(295,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(2147,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)],[295]) ).
thf(500,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(3307,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)],[500]) ).
thf(480,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(3166,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)],[480]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_funct_3) ).
thf(847,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(199,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ m1_orders_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_orders_1) ).
thf(1602,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( A @ ( B @ m1_orders_1 ) ) )
& ( ( A @ ( B @ m1_orders_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(254,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(1920,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)],[254]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lopclset) ).
thf(852,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(509,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(3349,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(303,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(2179,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)],[303]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_7) ).
thf(1159,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(539,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(3535,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)],[539]) ).
thf(93,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_measure1) ).
thf(1027,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(14,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(682,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)],[14]) ).
thf(152,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(1291,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k1_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow_3) ).
thf(1888,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k1_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(570,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(3718,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)],[570]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_polynom1) ).
thf(3600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k1_polynom1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(174,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(1457,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)],[174]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_jordan1k) ).
thf(757,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(326,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(2345,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(458,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(3033,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)],[458]) ).
thf(518,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(3408,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)],[518]) ).
thf(226,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 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( A @ ( E @ ( C @ ( B @ k2_partfun1 ) ) ) @ k2_relat_1 @ ( D @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_partfun2) ).
thf(1740,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 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( A @ ( E @ ( C @ ( B @ k2_partfun1 ) ) ) @ k2_relat_1 @ ( D @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(52,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(842,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)],[52]) ).
thf(170,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ ( D @ ( E @ m2_relset_1 ) ) )
& ( B @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tmap_1) ).
thf(1402,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ ( D @ ( E @ m2_relset_1 ) ) )
& ( B @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(165,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(1360,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)],[165]) ).
thf(187,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(1541,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)],[187]) ).
thf(283,axiom,
! [A: $i] :
~ ( ( A @ v1_xboole_0 )
& ( A
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_gate_1) ).
thf(2100,plain,
! [A: $i] :
~ ( ( A @ v1_xboole_0 )
& ( A
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(446,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_graphsp ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_graphsp ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_graphsp ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_graphsp) ).
thf(2946,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_graphsp ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_graphsp ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_graphsp ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(8,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(650,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)],[8]) ).
thf(260,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(1952,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1953,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1952]) ).
thf(513,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(3381,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)],[513]) ).
thf(179,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_fraenkel) ).
thf(1498,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(248,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(1878,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)],[248]) ).
thf(587,axiom,
( ( ! [A: $i] :
( ( ( A @ p3_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f5_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p2_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f4_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p1_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f3_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( f1_s13_scheme1 @ ( A @ r2_hidden ) )
=> ( ~ ( ( A @ p3_s13_scheme1 )
& ( A @ p2_s13_scheme1 ) )
& ~ ( ( A @ p3_s13_scheme1 )
& ( A @ p1_s13_scheme1 ) )
& ~ ( ( A @ p2_s13_scheme1 )
& ( A @ p1_s13_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( A @ ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p3_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s13_scheme1 ) ) )
& ( ( B @ p2_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s13_scheme1 ) ) )
& ( ( B @ p1_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s13_scheme1 ) ) ) ) )
& ! [B: $i] :
( ( A @ ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
<=> ( ~ ( ~ ( B @ p3_s13_scheme1 )
& ~ ( B @ p2_s13_scheme1 )
& ~ ( B @ p1_s13_scheme1 ) )
& ( f1_s13_scheme1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_scheme1) ).
thf(3941,plain,
( ( ! [A: $i] :
( ( ( A @ p3_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f5_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p2_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f4_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p1_s13_scheme1 )
& ( f1_s13_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s13_scheme1 @ ( A @ f3_s13_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( f1_s13_scheme1 @ ( A @ r2_hidden ) )
=> ( ~ ( ( A @ p3_s13_scheme1 )
& ( A @ p2_s13_scheme1 ) )
& ~ ( ( A @ p3_s13_scheme1 )
& ( A @ p1_s13_scheme1 ) )
& ~ ( ( A @ p2_s13_scheme1 )
& ( A @ p1_s13_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( A @ ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p3_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s13_scheme1 ) ) )
& ( ( B @ p2_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s13_scheme1 ) ) )
& ( ( B @ p1_s13_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s13_scheme1 ) ) ) ) )
& ! [B: $i] :
( ( ( ~ ( ~ ( B @ p3_s13_scheme1 )
& ~ ( B @ p2_s13_scheme1 )
& ~ ( B @ p1_s13_scheme1 ) )
& ( f1_s13_scheme1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) ) )
& ( ( A @ ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ~ ( ~ ( B @ p3_s13_scheme1 )
& ~ ( B @ p2_s13_scheme1 )
& ~ ( B @ p1_s13_scheme1 ) )
& ( f1_s13_scheme1 @ ( B @ r2_hidden ) ) ) ) )
& ( f2_s13_scheme1 @ ( f1_s13_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice2) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(470,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(3105,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)],[470]) ).
thf(525,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(3467,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(574,axiom,
( ( ! [A: $i] :
( ( f1_s19_scheme1 @ ( A @ m1_subset_1 ) )
=> ~ ( ~ ( A @ p3_s19_scheme1 )
& ~ ( A @ p2_s19_scheme1 )
& ~ ( A @ p1_s19_scheme1 ) ) )
& ! [A: $i] :
( ( f1_s19_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p3_s19_scheme1 )
& ( A @ p2_s19_scheme1 ) )
& ~ ( ( A @ p3_s19_scheme1 )
& ( A @ p1_s19_scheme1 ) )
& ~ ( ( A @ p2_s19_scheme1 )
& ( A @ p1_s19_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s19_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p3_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f5_s19_scheme1 ) ) )
& ( ( B @ p2_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f4_s19_scheme1 ) ) )
& ( ( B @ p1_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f3_s19_scheme1 ) ) ) ) )
& ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s19_scheme1) ).
thf(3784,plain,
( ( ! [A: $i] :
( ( f1_s19_scheme1 @ ( A @ m1_subset_1 ) )
=> ~ ( ~ ( A @ p3_s19_scheme1 )
& ~ ( A @ p2_s19_scheme1 )
& ~ ( A @ p1_s19_scheme1 ) ) )
& ! [A: $i] :
( ( f1_s19_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p3_s19_scheme1 )
& ( A @ p2_s19_scheme1 ) )
& ~ ( ( A @ p3_s19_scheme1 )
& ( A @ p1_s19_scheme1 ) )
& ~ ( ( A @ p2_s19_scheme1 )
& ( A @ p1_s19_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s19_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p3_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f5_s19_scheme1 ) ) )
& ( ( B @ p2_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f4_s19_scheme1 ) ) )
& ( ( B @ p1_s19_scheme1 )
=> ( ( B @ ( A @ ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f3_s19_scheme1 ) ) ) ) )
& ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s19_scheme1 @ ( f1_s19_scheme1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(874,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,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(1143,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)],[119]) ).
thf(286,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(2115,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)],[286]) ).
thf(110,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(1096,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)],[110]) ).
thf(364,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(2509,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)],[364]) ).
thf(569,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(3704,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)],[569]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ? [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',rc1_topgen_3) ).
thf(1138,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ? [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)],[118]) ).
thf(407,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(2724,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)],[407]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ v1_finset_1 )
| ( ~ ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
& ~ ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_card_2) ).
thf(1567,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( ( A @ v1_finset_1 )
| ( ~ ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) )
& ~ ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(355,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(2460,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)],[355]) ).
thf(455,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ r1_tarski ) )
& ~ ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v1_finset_1 ) )
=> ( ( A @ ( A @ k3_tarski @ r2_hidden ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_card_2) ).
thf(3000,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ r1_tarski ) )
& ~ ( C @ ( B @ r1_tarski ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v1_finset_1 ) )
=> ( ( A @ ( A @ k3_tarski @ r2_hidden ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(486,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(3210,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)],[486]) ).
thf(217,axiom,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_card_1) ).
thf(1700,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
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(588,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(589,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)],[588]) ).
thf(590,plain,
sk1 @ ( sk2 @ ( sk3 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[589]) ).
thf(396,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_card_5) ).
thf(2666,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_funct_3) ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,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 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_3) ).
thf(706,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 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(269,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(2023,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(503,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(3326,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)],[503]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= ( D @ ( A @ ( B @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_partfun2) ).
thf(669,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= ( D @ ( A @ ( B @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(573,axiom,
( ( ! [A: $i] :
( ( ( A @ p4_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f6_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p3_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f5_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p2_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f4_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p1_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f3_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( f1_s14_scheme1 @ ( A @ r2_hidden ) )
=> ( ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p3_s14_scheme1 ) )
& ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p2_s14_scheme1 ) )
& ~ ( ( A @ p3_s14_scheme1 )
& ( A @ p2_s14_scheme1 ) )
& ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) )
& ~ ( ( A @ p3_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) )
& ~ ( ( A @ p2_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( A @ ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p4_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f6_s14_scheme1 ) ) )
& ( ( B @ p3_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s14_scheme1 ) ) )
& ( ( B @ p2_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s14_scheme1 ) ) )
& ( ( B @ p1_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s14_scheme1 ) ) ) ) )
& ! [B: $i] :
( ( A @ ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
<=> ( ~ ( ~ ( B @ p4_s14_scheme1 )
& ~ ( B @ p3_s14_scheme1 )
& ~ ( B @ p2_s14_scheme1 )
& ~ ( B @ p1_s14_scheme1 ) )
& ( f1_s14_scheme1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_scheme1) ).
thf(3728,plain,
( ( ! [A: $i] :
( ( ( A @ p4_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f6_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p3_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f5_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p2_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f4_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( ( A @ p1_s14_scheme1 )
& ( f1_s14_scheme1 @ ( A @ r2_hidden ) ) )
=> ( f2_s14_scheme1 @ ( A @ f3_s14_scheme1 @ r2_hidden ) ) )
& ! [A: $i] :
( ( f1_s14_scheme1 @ ( A @ r2_hidden ) )
=> ( ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p3_s14_scheme1 ) )
& ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p2_s14_scheme1 ) )
& ~ ( ( A @ p3_s14_scheme1 )
& ( A @ p2_s14_scheme1 ) )
& ~ ( ( A @ p4_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) )
& ~ ( ( A @ p3_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) )
& ~ ( ( A @ p2_s14_scheme1 )
& ( A @ p1_s14_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( A @ ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ( ( B @ p4_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f6_s14_scheme1 ) ) )
& ( ( B @ p3_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f5_s14_scheme1 ) ) )
& ( ( B @ p2_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f4_s14_scheme1 ) ) )
& ( ( B @ p1_s14_scheme1 )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s14_scheme1 ) ) ) ) )
& ! [B: $i] :
( ( ( ~ ( ~ ( B @ p4_s14_scheme1 )
& ~ ( B @ p3_s14_scheme1 )
& ~ ( B @ p2_s14_scheme1 )
& ~ ( B @ p1_s14_scheme1 ) )
& ( f1_s14_scheme1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) ) )
& ( ( A @ ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( ~ ( ~ ( B @ p4_s14_scheme1 )
& ~ ( B @ p3_s14_scheme1 )
& ~ ( B @ p2_s14_scheme1 )
& ~ ( B @ p1_s14_scheme1 ) )
& ( f1_s14_scheme1 @ ( B @ r2_hidden ) ) ) ) )
& ( f2_s14_scheme1 @ ( f1_s14_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) ) )
=> ( ( F = G )
& ( D = E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_3) ).
thf(901,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) ) )
=> ( ( F = G )
& ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(104,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 @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_2) ).
thf(1075,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 @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ ( A @ k12_turing_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ ( A @ k12_turing_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k12_turing_1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_turing_1) ).
thf(997,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ ( A @ k12_turing_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ ( A @ k12_turing_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k12_turing_1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(557,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(3654,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)],[557]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r1_tarski ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_7) ).
thf(1249,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r1_tarski ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(186,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(1539,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)],[186]) ).
thf(463,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(3059,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)],[463]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) )
<=> ( D @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v1_yellow18) ).
thf(2387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( D @ v2_funct_1 )
=> ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) )
=> ( D @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) ) )
& ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_partfun2) ).
thf(654,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) ) )
& ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(427,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(2851,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)],[427]) ).
thf(258,axiom,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(1932,plain,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(374,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(2566,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)],[374]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
<=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setwiseo) ).
thf(1852,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(471,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] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ k13_funct_3 ) )
= ( G @ ( E @ k13_funct_3 ) ) )
=> ( ( ( F = G )
& ( D = E ) )
| ( ( A != k1_xboole_0 )
& ( C = k1_xboole_0 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_3) ).
thf(3109,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] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ k13_funct_3 ) )
= ( G @ ( E @ k13_funct_3 ) ) )
=> ( ( ( F = G )
& ( D = E ) )
| ( ( A != k1_xboole_0 )
& ( C = k1_xboole_0 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(319,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(2272,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)],[319]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k2_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_3) ).
thf(2140,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k2_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(472,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(3126,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)],[472]) ).
thf(401,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(2681,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)],[401]) ).
thf(379,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(2581,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)],[379]) ).
thf(356,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( C != D ) )
& ( ( B @ k1_tarski )
!= A ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_collsp) ).
thf(2465,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( C != D ) )
& ( ( B @ k1_tarski )
!= A ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(540,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(3540,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)],[540]) ).
thf(24,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(721,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)],[24]) ).
thf(580,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(3834,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)],[580]) ).
thf(307,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(2203,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)],[307]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_sgraph1) ).
thf(1086,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [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 ) )
=> ( C @ ( E @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_heyting1) ).
thf(2761,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [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 ) )
=> ( C @ ( E @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(481,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(3173,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)],[481]) ).
thf(2524,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[2523]) ).
thf(2525,plain,
~ ( sk159 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2524]) ).
thf(3995,plain,
( ( ( sk159 @ v1_xboole_0 )
!= ( sk96 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1636,2525]) ).
thf(3996,plain,
( ( sk159 @ v1_xboole_0 )
!= ( sk96 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3995]) ).
thf(3999,plain,
sk159 != sk96,
inference(simp,[status(thm)],[3996]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k1_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_3) ).
thf(2402,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k1_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(202,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(1616,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_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',t18_setwiseo) ).
thf(888,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_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)],[63]) ).
thf(575,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(3807,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)],[575]) ).
thf(3821,plain,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3820]) ).
thf(3822,plain,
( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3821]) ).
thf(3824,plain,
( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3822]) ).
thf(390,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(2634,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)],[390]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(765,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(100,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(1054,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)],[100]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(1663,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(280,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(2089,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(294,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(2144,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)],[294]) ).
thf(409,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(2729,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)],[409]) ).
thf(120,axiom,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_4) ).
thf(1146,plain,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(336,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 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ ( D @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_3) ).
thf(2391,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 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ ( D @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_4) ).
thf(2585,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(444,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(2941,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)],[444]) ).
thf(56,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(856,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)],[56]) ).
thf(498,axiom,
! [A: $i] :
( ( ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( A @ m2_relset_1 ) ) )
& ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ! [B: $i] :
( ( ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( B @ m2_relset_1 ) ) )
& ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_lmod_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ k8_funct_2 ) ) ) )
= ( C @ f2_s2_lmod_7 ) ) )
& ! [C: $i] :
( ( f1_s2_lmod_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ k8_funct_2 ) ) ) )
= ( C @ f2_s2_lmod_7 ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_lmod_7) ).
thf(3289,plain,
! [A: $i] :
( ( ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( A @ m2_relset_1 ) ) )
& ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ! [B: $i] :
( ( ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( B @ m2_relset_1 ) ) )
& ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_lmod_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ k8_funct_2 ) ) ) )
= ( C @ f2_s2_lmod_7 ) ) )
& ! [C: $i] :
( ( f1_s2_lmod_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( f1_s2_lmod_7 @ ( f1_s2_lmod_7 @ k8_funct_2 ) ) ) )
= ( C @ f2_s2_lmod_7 ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_card_1) ).
thf(1301,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(80,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(965,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(750,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(145,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( E @ ( D @ r1_tarski ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( B @ ( C @ r1_tarski ) ) )
& ( ( B @ k3_tarski )
= ( A @ k3_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
& ( A @ v6_ordinal1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_card_3) ).
thf(1251,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( E @ ( D @ r1_tarski ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( B @ ( C @ r1_tarski ) ) )
& ( ( B @ k3_tarski )
= ( A @ k3_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
& ( A @ v6_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(342,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(2413,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)],[342]) ).
thf(372,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(2556,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(112,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(1103,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)],[112]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cat_1) ).
thf(1927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(3983,plain,
( ( ( sk96 @ v1_xboole_0 )
!= ( sk94 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1636,1609]) ).
thf(3984,plain,
( ( sk96 @ v1_xboole_0 )
!= ( sk94 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3983]) ).
thf(3985,plain,
sk96 != sk94,
inference(simp,[status(thm)],[3984]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_cohsp_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_cohsp_1) ).
thf(1154,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_cohsp_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(408,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(2727,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(168,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(1389,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)],[168]) ).
thf(359,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( E @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_7) ).
thf(2489,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( E @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(337,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_msualg_9) ).
thf(2393,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(209,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(1652,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)],[209]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ k1_funct_2 ) @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k15_pralg_1 ) @ k2_relat_1 )
= ( k1_xboole_0 @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_hilbert3) ).
thf(2568,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ k1_funct_2 ) @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k15_pralg_1 ) @ k2_relat_1 )
= ( k1_xboole_0 @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(524,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3458,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)],[524]) ).
thf(116,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(1124,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)],[116]) ).
thf(141,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(1226,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)],[141]) ).
thf(289,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(2134,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)],[289]) ).
thf(3997,plain,
( ( ( sk159 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2229,2525]) ).
thf(3998,plain,
( ( sk159 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3997]) ).
thf(4000,plain,
sk159 != k1_xboole_0,
inference(simp,[status(thm)],[3998]) ).
thf(484,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(3187,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)],[484]) ).
thf(450,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s2_seq_1 ) ) ) )
& ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ ( B @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( C @ m1_subset_1 ) ) ) ) )
& ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_seq_1) ).
thf(2970,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s2_seq_1 ) ) ) )
& ! [B: $i] :
( ( f1_s2_seq_1 @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) ) )
& ( ( A @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ ( B @ p1_s2_seq_1 ) )
& ( f2_s2_seq_1 @ ( C @ m1_subset_1 ) ) ) ) ) )
& ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(502,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(3319,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)],[502]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).
thf(3636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(443,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(2938,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)],[443]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow15) ).
thf(1795,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1701,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1700]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(2161,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(181,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(1503,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
<=> ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_functor0) ).
thf(936,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) )
=> ( B @ ( A @ ( C @ v2_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(311,axiom,
! [A: $i,B: $i] : ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ v1_funct_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_heyting3) ).
thf(2220,plain,
! [A: $i,B: $i] : ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) @ v1_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(572,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(3726,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(554,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(3646,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)],[554]) ).
thf(556,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(3651,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)],[556]) ).
thf(560,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(3663,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)],[560]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(1107,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(547,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(3594,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)],[547]) ).
thf(567,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(3700,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)],[567]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( F @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_partfun2) ).
thf(804,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( F @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(519,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(3416,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)],[519]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( A @ k5_finsub_1 @ ( B @ r2_hidden ) ) )
=> ( A @ k5_finsub_1 @ ( C @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_8) ).
thf(704,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( A @ k5_finsub_1 @ ( B @ r2_hidden ) ) )
=> ( A @ k5_finsub_1 @ ( C @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(357,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(2474,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)],[357]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(1224,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(164,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(1356,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(442,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(2935,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)],[442]) ).
thf(224,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(1733,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)],[224]) ).
thf(300,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(2166,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)],[300]) ).
thf(108,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(1090,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)],[108]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( A @ ( B @ k4_relset_1 ) ) @ ( F @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= F )
<=> ( ( F @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= E ) ) ) ) )
& ( ( C @ k2_relat_1 )
= ( D @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ k2_relat_1 ) )
& ( C @ v2_funct_1 ) )
=> ( D
= ( C @ k2_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_partfun2) ).
thf(979,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( A @ ( B @ k4_relset_1 ) ) @ ( F @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
=> ( ( ( ( F @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= E )
=> ( ( E @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= F ) )
& ( ( ( E @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= F )
=> ( ( F @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= E ) ) ) ) ) )
& ( ( C @ k2_relat_1 )
= ( D @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ k2_relat_1 ) )
& ( C @ v2_funct_1 ) )
=> ( D
= ( C @ k2_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(331,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice4) ).
thf(2361,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_funct_5 @ ( C @ k1_funct_5 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_3) ).
thf(2679,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_funct_5 @ ( C @ k1_funct_5 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(150,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(1282,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)],[150]) ).
thf(223,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(1722,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)],[223]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( D
!= ( F @ ( E @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_grcat_1) ).
thf(3384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( D
!= ( F @ ( E @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(194,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(1571,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(59,axiom,
! [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 )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).
thf(863,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 )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(135,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(1209,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)],[135]) ).
thf(510,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(3352,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)],[510]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice2) ).
thf(2151,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ k3_tarski @ ( C @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_jordan1d) ).
thf(2084,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ k3_tarski @ ( C @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(490,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(3238,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)],[490]) ).
thf(417,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(2774,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)],[417]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(3287,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i,E: $i] :
~ ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( D != E )
& ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_4) ).
thf(3683,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i,E: $i] :
~ ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( D != E )
& ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(535,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(3515,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)],[535]) ).
thf(445,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(2943,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)],[445]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k3_subset_1 ) @ v1_finset_1 )
& ( B @ v1_finset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_topgen_3) ).
thf(737,plain,
! [A: $i] :
( ~ ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k3_subset_1 ) @ v1_finset_1 )
& ( B @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(429,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(2856,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)],[429]) ).
thf(533,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(3500,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)],[533]) ).
thf(476,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(3138,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)],[476]) ).
thf(333,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(2378,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)],[333]) ).
thf(464,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(3066,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(546,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(3586,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)],[546]) ).
thf(213,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(1667,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)],[213]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(811,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_borsuk_3) ).
thf(2632,plain,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( A @ ( E @ ( D @ ( C @ k4_finseq_4 ) ) ) )
= ( B @ ( E @ ( D @ ( C @ k4_finseq_4 ) ) ) ) )
& ( E @ ( D @ ( C @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
& ( E @ v2_funct_1 ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_partfun2) ).
thf(858,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( A @ ( E @ ( D @ ( C @ k4_finseq_4 ) ) ) )
= ( B @ ( E @ ( D @ ( C @ k4_finseq_4 ) ) ) ) )
& ( E @ ( D @ ( C @ k4_relset_1 ) ) @ ( B @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
& ( E @ v2_funct_1 ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) )
<=> ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_fin_topo) ).
thf(816,plain,
! [A: $i] :
( ~ ( A @ v1_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 ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) )
=> ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(466,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(3073,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)],[466]) ).
thf(418,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(2780,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)],[418]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(726,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(350,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(2446,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)],[350]) ).
thf(159,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(1325,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)],[159]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_2) ).
thf(915,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 )
=> ( B @ ( A @ ( C @ v2_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(545,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(3583,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ k1_funct_4 ) )
= ( C @ ( A @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_necklace) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ k1_funct_4 ) )
= ( C @ ( A @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( sk199 @ k1_funct_1 ) @ ( C @ p1_s2_seq_1 ) )
| ~ ( sk199 @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
| ~ ( f1_s2_seq_1 @ ( C @ m1_subset_1 ) ) )
& ( ( sk199 @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( B @ ( A @ p1_s2_seq_1 ) )
| ~ ( f2_s2_seq_1 @ ( B @ m1_subset_1 ) )
| ~ ( f1_s2_seq_1 @ ( A @ m1_subset_1 ) ) )
& ( ( A @ sk200 @ ( A @ p1_s2_seq_1 ) )
| ~ ( sk199 @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( f1_s2_seq_1 @ ( A @ m1_subset_1 ) ) )
& ( ( f2_s2_seq_1 @ ( A @ sk200 @ m1_subset_1 ) )
| ~ ( sk199 @ ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( f1_s2_seq_1 @ ( A @ m1_subset_1 ) ) )
& ( f2_s2_seq_1 @ ( f1_s2_seq_1 @ ( sk199 @ m2_relset_1 ) ) )
& ( sk199 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[2970]) ).
thf(2974,plain,
sk199 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2971]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_t_0topsp) ).
thf(1112,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_partit_2) ).
thf(2785,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(383,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(2593,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)],[383]) ).
thf(94,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1029,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(425,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(2835,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)],[425]) ).
thf(99,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(1044,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)],[99]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_partfun1) ).
thf(2620,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(88,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 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( ( D @ ( A @ ( E @ ( C @ ( B @ k2_partfun1 ) ) ) @ ( C @ ( B @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun2) ).
thf(1015,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 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( ( D @ ( A @ ( E @ ( C @ ( B @ k2_partfun1 ) ) ) @ ( C @ ( B @ k4_finseq_4 ) ) ) )
= ( D @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(127,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(1176,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)],[127]) ).
thf(449,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(2967,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)],[449]) ).
thf(482,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(3178,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)],[482]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(2207,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(69,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 @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(922,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 @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_partfun1) ).
thf(1805,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(15,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(685,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)],[15]) ).
thf(126,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(1171,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)],[126]) ).
thf(416,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(2770,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)],[416]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(2075,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(343,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_fraenkel) ).
thf(2418,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(310,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(2212,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)],[310]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(959,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(191,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(1562,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)],[191]) ).
thf(96,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(1034,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)],[96]) ).
thf(457,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(3031,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)],[457]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
~ ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( C @ ( E @ r1_tarski ) )
& ( E @ v1_finset_1 )
& ( B @ ( D @ r1_tarski ) )
& ( D @ v1_finset_1 ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_cqc_the1) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
~ ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( C @ ( E @ r1_tarski ) )
& ( E @ v1_finset_1 )
& ( B @ ( D @ r1_tarski ) )
& ( D @ v1_finset_1 ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(323,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(2318,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)],[323]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(927,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(362,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(2503,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)],[362]) ).
thf(351,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(2449,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)],[351]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_pscomp_1) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(161,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(1340,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)],[161]) ).
thf(523,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(3455,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(89,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(1018,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)],[89]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_lattice2) ).
thf(754,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(435,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(2899,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)],[435]) ).
thf(128,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(1181,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(189,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(1551,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)],[189]) ).
thf(440,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(2927,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)],[440]) ).
thf(388,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(2629,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)],[388]) ).
thf(39,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 ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(776,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 ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(515,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(3391,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)],[515]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) )
<=> ( D @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_partit_2) ).
thf(1770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) )
=> ( D @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(430,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(2863,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)],[430]) ).
thf(92,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(1025,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)],[92]) ).
thf(266,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_card_1) ).
thf(2012,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k3_subset_1 ) @ ( D @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_jordan1k) ).
thf(2588,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k3_subset_1 ) @ ( D @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(473,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(3129,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)],[473]) ).
thf(29,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(739,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(301,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(2175,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)],[301]) ).
thf(231,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 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k13_funct_3 ) @ v1_funct_1 ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_3) ).
thf(1780,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 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k13_funct_3 ) @ v1_funct_1 ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(147,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(1267,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)],[147]) ).
thf(433,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 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2882,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 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(3986,plain,
( ( ( sk94 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2229,1609]) ).
thf(3987,plain,
( ( sk94 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3986]) ).
thf(3988,plain,
sk94 != k1_xboole_0,
inference(simp,[status(thm)],[3987]) ).
thf(365,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(2513,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)],[365]) ).
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 ) )
=> ( ! [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(1611,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)],[201]) ).
thf(123,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(1156,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)],[123]) ).
thf(424,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(2831,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)],[424]) ).
thf(404,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(2689,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)],[404]) ).
thf(467,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(3080,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)],[467]) ).
thf(222,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(1716,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)],[222]) ).
thf(130,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(1188,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(51,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(840,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)],[51]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(2429,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(541,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(3544,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)],[541]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( C @ v1_finset_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_bhsp_5 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_bhsp_5) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( C @ v1_finset_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_bhsp_5 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(139,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(1220,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(206,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(1637,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)],[206]) ).
thf(505,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(3334,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)],[505]) ).
thf(591,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)],[589]) ).
thf(592,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)],[591]) ).
thf(4002,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)],[592]) ).
thf(4003,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)],[4002]) ).
thf(97,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(1038,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)],[97]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_2) ).
thf(1738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(460,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(3041,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)],[460]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_4) ).
thf(2354,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(67,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(907,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)],[67]) ).
thf(242,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(1849,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)],[242]) ).
thf(91,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(1023,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)],[91]) ).
thf(218,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(1702,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)],[218]) ).
thf(177,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(1485,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)],[177]) ).
thf(378,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_qc_lang1) ).
thf(2579,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice2) ).
thf(1797,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B = C )
<=> ( ( B @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_fin_topo) ).
thf(1008,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 ) ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[594]) ).
thf(478,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(3156,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)],[478]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( A @ ( E @ ( C @ ( B @ k10_relset_1 ) ) ) @ ( D @ r2_hidden ) )
<=> ? [F: $i] :
( ( D
= ( F @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) ) )
& ( A @ ( F @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( F @ r2_hidden ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_partfun2) ).
thf(876,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ? [F: $i] :
( ( D
= ( F @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) ) )
& ( A @ ( F @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( F @ r2_hidden ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ ( C @ ( B @ k10_relset_1 ) ) ) @ ( D @ r2_hidden ) ) )
& ( ( A @ ( E @ ( C @ ( B @ k10_relset_1 ) ) ) @ ( D @ r2_hidden ) )
=> ? [F: $i] :
( ( D
= ( F @ ( E @ ( C @ ( B @ k4_finseq_4 ) ) ) ) )
& ( A @ ( F @ r2_hidden ) )
& ( E @ ( C @ ( B @ k4_relset_1 ) ) @ ( F @ r2_hidden ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(516,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(3398,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)],[516]) ).
thf(345,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(2426,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)],[345]) ).
thf(453,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(2992,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)],[453]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_relat_1) ).
thf(1353,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(330,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(2357,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)],[330]) ).
thf(5,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 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( C @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F
= ( E @ ( D @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) ) )
<=> ( ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( G @ ( F @ ( B @ ( C @ k4_finseq_4 ) ) ) )
= ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) ) ) )
& ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
<=> ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( D @ ( A @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_partfun2) ).
thf(600,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 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( C @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( G @ ( F @ ( B @ ( C @ k4_finseq_4 ) ) ) )
= ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) ) ) )
& ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( D @ ( A @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) )
=> ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) )
& ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( D @ ( A @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) ) ) ) ) )
=> ( F
= ( E @ ( D @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) ) )
=> ( ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( G @ ( F @ ( B @ ( C @ k4_finseq_4 ) ) ) )
= ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) ) ) )
& ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( D @ ( A @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) )
=> ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) )
& ( ( F @ ( B @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( G @ ( D @ ( A @ ( C @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( D @ ( A @ ( C @ k4_relset_1 ) ) @ ( G @ r2_hidden ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1030,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[1029]) ).
thf(740,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(lifteq,[status(thm)],[739]) ).
thf(4143,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(rewrite,[status(thm)],[1030,740]) ).
thf(489,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ami_3) ).
thf(3224,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(496,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(3284,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)],[496]) ).
thf(522,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(3433,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)],[522]) ).
thf(386,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(2626,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(175,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(1459,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)],[175]) ).
thf(215,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(1685,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)],[215]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ v1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( ( C @ ( F @ k1_funct_1 ) )
= D )
& ( ( A @ ( F @ ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ k2_partfun1 ) ) ) )
= E ) )
=> ( ( ( E @ v2_funct_1 )
=> ( ( F @ v2_funct_1 )
| ( B @ ( D @ r2_hidden ) ) ) )
& ( ( B @ ( A @ ( E @ v2_funct_2 ) ) )
=> ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v2_funct_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_stirl2_1) ).
thf(1817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ v1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ m2_relset_1 ) ) )
& ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( ( C @ ( F @ k1_funct_1 ) )
= D )
& ( ( A @ ( F @ ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ k2_partfun1 ) ) ) )
= E ) )
=> ( ( ( E @ v2_funct_1 )
=> ( ( F @ v2_funct_1 )
| ( B @ ( D @ r2_hidden ) ) ) )
& ( ( B @ ( A @ ( E @ v2_funct_2 ) ) )
=> ( D @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( F @ v2_funct_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(277,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(2078,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)],[277]) ).
thf(542,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] :
( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
<=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
thf(3548,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] :
( ( ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(309,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(2209,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)],[309]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).
thf(844,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(395,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice2) ).
thf(2658,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(420,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(2792,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)],[420]) ).
thf(544,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(3565,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)],[544]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ r1_qmax_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) @ ( B @ k1_funct_1 ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_qmax_1) ).
thf(3401,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) @ ( B @ k1_funct_1 ) )
= C ) )
=> ( B @ ( A @ r1_qmax_1 ) ) )
& ( ( B @ ( A @ r1_qmax_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) @ ( B @ k1_funct_1 ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(454,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(2997,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)],[454]) ).
thf(305,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ v2_funct_1 )
=> ( ( ( ( D
= ( C @ ( E @ k1_funct_1 ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( E @ k2_funct_1 @ k1_funct_1 ) ) )
& ( E @ k2_relat_1 @ ( D @ r2_hidden ) ) ) )
& ( ( ( C
= ( D @ ( E @ k2_funct_1 @ k1_funct_1 ) ) )
& ( E @ k2_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( E @ k1_funct_1 ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_partfun2) ).
thf(2187,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ v2_funct_1 )
=> ( ( ( ( D
= ( C @ ( E @ k1_funct_1 ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( E @ k2_funct_1 @ k1_funct_1 ) ) )
& ( E @ k2_relat_1 @ ( D @ r2_hidden ) ) ) )
& ( ( ( C
= ( D @ ( E @ k2_funct_1 @ k1_funct_1 ) ) )
& ( E @ k2_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( E @ k1_funct_1 ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(3346,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(438,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(2919,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)],[438]) ).
thf(325,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(2342,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(207,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(1646,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)],[207]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(963,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(3823,plain,
( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[3821]) ).
thf(3825,plain,
( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3823]) ).
thf(341,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(2406,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)],[341]) ).
thf(111,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(1101,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)],[111]) ).
thf(506,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3336,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(270,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(2026,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)],[270]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_cat_3) ).
thf(632,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [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 @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_group_6) ).
thf(2431,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(582,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(3859,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)],[582]) ).
thf(368,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 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_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 @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_bhsp_5 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_bhsp_5) ).
thf(2526,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 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_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 @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_bhsp_5 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(1558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(78,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(961,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finseq_4) ).
thf(813,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(102,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(1062,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)],[102]) ).
thf(183,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] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).
thf(1508,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] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(512,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(3369,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)],[512]) ).
thf(3218,plain,
( ! [A: $i] : ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ! [A: $i] : ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[3217]) ).
thf(3219,plain,
! [B: $i,A: $i] :
( ( k1_xboole_0 @ ( B @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3218]) ).
thf(3220,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3219]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(731,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(504,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(3331,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(393,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(2648,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)],[393]) ).
thf(72,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun2) ).
thf(929,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setwiseo) ).
thf(2576,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(304,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(2183,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)],[304]) ).
thf(3989,plain,
( ( ( sk158 @ v1_xboole_0 )
!= ( sk96 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1636,2508]) ).
thf(3990,plain,
( ( sk158 @ v1_xboole_0 )
!= ( sk96 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[3989]) ).
thf(3993,plain,
sk158 != sk96,
inference(simp,[status(thm)],[3990]) ).
thf(288,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 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_2) ).
thf(2120,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 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D
= ( C @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) )
<=> ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_partfun2) ).
thf(832,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( D
= ( C @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) ) )
& ( E @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) ) )
=> ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(322,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ k4_tarski ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ k1_funct_1 ) )
= ( H @ ( F @ ( D @ ( C @ k8_funct_2 ) ) ) @ ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_funct_3) ).
thf(2315,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ k4_tarski ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ k1_funct_1 ) )
= ( H @ ( F @ ( D @ ( C @ k8_funct_2 ) ) ) @ ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(411,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(2739,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)],[411]) ).
thf(483,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(3181,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)],[483]) ).
thf(566,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(3694,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)],[566]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ ( C @ k2_funct_1 @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_7) ).
thf(667,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ ( C @ k2_funct_1 @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(153,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 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_4) ).
thf(1294,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 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(313,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 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_4) ).
thf(2230,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 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(157,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(1309,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)],[157]) ).
thf(437,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(2917,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)],[437]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_funcop_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_4) ).
thf(2623,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_funcop_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(23,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(716,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).
thf(1161,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) ) )
& ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_glib_002) ).
thf(2142,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(332,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(2374,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)],[332]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_jordan1k) ).
thf(752,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_card_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_card_4) ).
thf(1774,plain,
! [A: $i] :
( ( ( A @ k1_card_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_card_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(149,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(1280,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)],[149]) ).
thf(585,axiom,
( ( ! [A: $i] :
( ( f1_s20_scheme1 @ ( A @ m1_subset_1 ) )
=> ~ ( ~ ( A @ p4_s20_scheme1 )
& ~ ( A @ p3_s20_scheme1 )
& ~ ( A @ p2_s20_scheme1 )
& ~ ( A @ p1_s20_scheme1 ) ) )
& ! [A: $i] :
( ( f1_s20_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p3_s20_scheme1 ) )
& ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p2_s20_scheme1 ) )
& ~ ( ( A @ p3_s20_scheme1 )
& ( A @ p2_s20_scheme1 ) )
& ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) )
& ~ ( ( A @ p3_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) )
& ~ ( ( A @ p2_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s20_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p4_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f6_s20_scheme1 ) ) )
& ( ( B @ p3_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f5_s20_scheme1 ) ) )
& ( ( B @ p2_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f4_s20_scheme1 ) ) )
& ( ( B @ p1_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f3_s20_scheme1 ) ) ) ) )
& ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s20_scheme1) ).
thf(3907,plain,
( ( ! [A: $i] :
( ( f1_s20_scheme1 @ ( A @ m1_subset_1 ) )
=> ~ ( ~ ( A @ p4_s20_scheme1 )
& ~ ( A @ p3_s20_scheme1 )
& ~ ( A @ p2_s20_scheme1 )
& ~ ( A @ p1_s20_scheme1 ) ) )
& ! [A: $i] :
( ( f1_s20_scheme1 @ ( A @ m1_subset_1 ) )
=> ( ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p3_s20_scheme1 ) )
& ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p2_s20_scheme1 ) )
& ~ ( ( A @ p3_s20_scheme1 )
& ( A @ p2_s20_scheme1 ) )
& ~ ( ( A @ p4_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) )
& ~ ( ( A @ p3_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) )
& ~ ( ( A @ p2_s20_scheme1 )
& ( A @ p1_s20_scheme1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s20_scheme1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p4_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f6_s20_scheme1 ) ) )
& ( ( B @ p3_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f5_s20_scheme1 ) ) )
& ( ( B @ p2_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f4_s20_scheme1 ) ) )
& ( ( B @ p1_s20_scheme1 )
=> ( ( B @ ( A @ ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ k8_funct_2 ) ) ) )
= ( B @ f3_s20_scheme1 ) ) ) ) )
& ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ ( A @ m2_relset_1 ) ) )
& ( f2_s20_scheme1 @ ( f1_s20_scheme1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ? [C: $i] :
( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_euler_1) ).
thf(967,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ? [C: $i] :
( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(314,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(2233,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)],[314]) ).
thf(169,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( C = B ) )
& ( A
!= ( B @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_hahnban) ).
thf(1395,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( C = B ) )
& ( A
!= ( B @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(469,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(3100,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)],[469]) ).
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 ) )
=> ( ( ( 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(1593,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)],[197]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_ami_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k8_funct_2 ) ) ) )
!= k1_xboole_0 )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_ami_1) ).
thf(2951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k8_funct_2 ) ) ) )
!= k1_xboole_0 )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_ami_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_ami_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( E @ ( D @ ( C @ ( B @ k8_funct_2 ) ) ) )
!= k1_xboole_0 )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(536,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] :
~ ( ( ( E @ ( C @ k1_funct_1 ) )
= D )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_4) ).
thf(3521,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] :
~ ( ( ( E @ ( C @ k1_funct_1 ) )
= D )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(532,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(3496,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)],[532]) ).
thf(415,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2768,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(526,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(3469,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)],[526]) ).
thf(558,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(3658,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)],[558]) ).
thf(317,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(2258,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)],[317]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2736,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(264,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(2008,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)],[264]) ).
thf(156,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(1303,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)],[156]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_tarski ) )
=> ( D
= ( C @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( C @ k4_tarski ) @ k1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_partfun2) ).
thf(790,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_tarski ) )
=> ( D
= ( C @ ( D @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( C @ k4_tarski ) @ k1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(244,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(1859,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)],[244]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_oposet_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_oposet_1) ).
thf(3277,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_oposet_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(543,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).
thf(3558,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( C @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_triang_1) ).
thf(807,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( C @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(412,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(2746,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)],[412]) ).
thf(10,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(664,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)],[10]) ).
thf(1891,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1890]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(696,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(397,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(2668,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)],[397]) ).
thf(581,axiom,
( ( ( f4_s1_rlvect_4 != f5_s1_rlvect_4 )
& ( f3_s1_rlvect_4 != f5_s1_rlvect_4 )
& ( f3_s1_rlvect_4 != f4_s1_rlvect_4 ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_rlvect_4 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
!= ( B @ f9_s1_rlvect_4 ) )
& ( B != f5_s1_rlvect_4 )
& ( B != f4_s1_rlvect_4 )
& ( B != f3_s1_rlvect_4 ) ) )
& ( ( f5_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f8_s1_rlvect_4 )
& ( ( f4_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f7_s1_rlvect_4 )
& ( ( f3_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f6_s1_rlvect_4 )
& ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_rlvect_4) ).
thf(3843,plain,
( ( ( f4_s1_rlvect_4 != f5_s1_rlvect_4 )
& ( f3_s1_rlvect_4 != f5_s1_rlvect_4 )
& ( f3_s1_rlvect_4 != f4_s1_rlvect_4 ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_rlvect_4 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
!= ( B @ f9_s1_rlvect_4 ) )
& ( B != f5_s1_rlvect_4 )
& ( B != f4_s1_rlvect_4 )
& ( B != f3_s1_rlvect_4 ) ) )
& ( ( f5_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f8_s1_rlvect_4 )
& ( ( f4_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f7_s1_rlvect_4 )
& ( ( f3_s1_rlvect_4 @ ( A @ ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ k8_funct_2 ) ) ) )
= f6_s1_rlvect_4 )
& ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_rlvect_4 @ ( f1_s1_rlvect_4 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1610,plain,
sk94 @ v1_finset_1,
inference(cnfConj,[status(thm)],[1608]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ~ ( ( D
= ( F @ ( E @ k1_funct_1 ) ) )
& ( A @ ( F @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) ) )
& ( A @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_partfun2) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ~ ( ( D
= ( F @ ( E @ k1_funct_1 ) ) )
& ( A @ ( F @ r2_hidden ) )
& ( E @ ( B @ ( C @ k4_relset_1 ) ) @ ( F @ r2_hidden ) ) ) )
& ( A @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(501,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(3309,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)],[501]) ).
thf(477,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(3145,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)],[477]) ).
thf(306,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(2201,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)],[306]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finseq_4) ).
thf(801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k4_finseq_4 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(4022,plain,
( ( ( sk222 @ v1_finset_1 )
!= ( sk94 @ v1_finset_1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1610,3134]) ).
thf(4023,plain,
( ( sk222 @ v1_finset_1 )
!= ( sk94 @ v1_finset_1 ) ),
inference(simp,[status(thm)],[4022]) ).
thf(4024,plain,
sk222 != sk94,
inference(simp,[status(thm)],[4023]) ).
thf(274,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(2070,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)],[274]) ).
thf(65,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun2) ).
thf(897,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setwiseo) ).
thf(1410,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( A
= ( E @ ( D @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( D @ ( B @ ( C @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_partfun2) ).
thf(767,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ? [E: $i] :
( ( A
= ( E @ ( D @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( D @ ( B @ ( C @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( E @ m1_subset_1 ) ) )
=> ( D @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( A
= ( E @ ( D @ ( B @ ( C @ k4_finseq_4 ) ) ) ) )
& ( D @ ( B @ ( C @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(448,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(2961,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)],[448]) ).
thf(151,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(1288,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)],[151]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ k1_card_1 )
= ( D @ k1_card_1 ) )
& ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_5) ).
thf(1710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ k1_card_1 )
= ( D @ k1_card_1 ) )
& ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(132,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
<=> ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tmap_1) ).
thf(1197,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r1_tarski ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r1_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(2091,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_finset_1 )
=> ( B @ k1_card_1 @ ( A @ k1_tarski @ k1_card_1 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_card_fil) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_finset_1 )
=> ( B @ k1_card_1 @ ( A @ k1_tarski @ k1_card_1 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(62,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(886,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)],[62]) ).
thf(227,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_orders_1) ).
thf(1742,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(109,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(1093,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)],[109]) ).
thf(146,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(1261,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)],[146]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( B @ m1_relset_1 ) ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_armstrng) ).
thf(1152,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( B @ m1_relset_1 ) ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
| ~ ( C @ ( A @ ( E @ m1_relset_1 ) ) )
| ~ ( C @ ( A @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( B @ ( A @ ( D @ m1_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[594]) ).
thf(196,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(1582,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)],[196]) ).
thf(180,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(1500,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] : ( B @ k1_tarski @ ( C @ ( B @ ( A @ k2_funcop_1 ) @ k9_relat_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_borsuk_1) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] : ( B @ k1_tarski @ ( C @ ( B @ ( A @ k2_funcop_1 ) @ k9_relat_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(249,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(1880,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)],[249]) ).
thf(576,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(3812,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)],[576]) ).
thf(291,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(2138,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)],[291]) ).
thf(297,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(2159,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)],[297]) ).
thf(511,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(3362,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)],[511]) ).
thf(185,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(1532,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)],[185]) ).
thf(426,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(2847,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)],[426]) ).
thf(550,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(3605,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)],[550]) ).
thf(358,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(2485,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)],[358]) ).
thf(586,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ k2_oposet_1 ) @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_oposet_1) ).
thf(3939,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( A @ k2_oposet_1 ) @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_borsuk_3) ).
thf(1505,plain,
! [A: $i,B: $i] :
( ( A @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow15) ).
thf(2270,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(528,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(3474,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)],[528]) ).
thf(413,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(2754,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)],[413]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) )
<=> ( ( C @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_partfun2) ).
thf(1320,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( C @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ r2_hidden ) )
& ( E @ ( D @ ( E @ ( B @ ( A @ k4_finseq_4 ) ) ) @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(551,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(3626,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)],[551]) ).
thf(129,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(1184,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)],[129]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(1565,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(271,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(2059,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)],[271]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( C @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_partit_2) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( C @ ( C @ ( B @ ( A @ r1_partit_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(328,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(2351,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)],[328]) ).
thf(459,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(3035,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)],[459]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_2) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(324,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(2321,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)],[324]) ).
thf(74,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
<=> ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( D @ ( A @ ( B @ k4_relset_1 ) ) @ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun2) ).
thf(940,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( D @ ( A @ ( B @ k4_relset_1 ) ) @ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( ( D @ ( C @ r1_tarski ) )
=> ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ ( A @ ( B @ k4_finseq_4 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k4_finseq_4 ) ) ) ) ) ) )
& ( D @ ( A @ ( B @ k4_relset_1 ) ) @ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ r1_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(487,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 @ k2_monoid_0 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_monoid_0) ).
thf(3212,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 @ k2_monoid_0 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(499,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(3299,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)],[499]) ).
thf(268,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boolmark) ).
thf(2018,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k2_funcop_1 ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_t_0topsp) ).
thf(2866,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(246,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(1870,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)],[246]) ).
thf(562,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(3669,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)],[562]) ).
thf(7789,plain,
$false,
inference(e,[status(thm)],[2163,2822,809,2094,3053,3666,3830,1083,2559,1549,1110,1369,1190,2072,3661,3477,1031,1211,762,1005,2908,1808,3509,2590,741,1205,2854,677,597,861,2117,1596,2495,2381,2671,2676,2014,2686,3648,3135,1867,1233,1327,3826,1761,1954,1078,3217,3530,3338,2933,1872,2712,2627,698,3629,2348,3994,2491,1576,2010,1650,2082,1366,2136,2531,973,3088,1529,2067,2825,2819,1803,1228,1482,3597,3820,3204,3425,3275,2444,3280,3043,1660,1298,702,3485,1832,2897,949,2571,1800,638,1892,2552,1609,1347,3902,2520,1815,3268,1922,2691,1704,1890,2989,1963,2456,2222,1489,924,3431,1632,3163,2925,1960,2105,1811,2451,2236,3527,3702,2880,1682,1136,2508,687,3068,2281,1215,692,734,1447,3676,2242,1697,3492,2523,1072,2424,2979,1943,1201,3011,3720,793,1915,3265,2646,2061,1636,1057,3679,894,746,1021,3867,820,3134,1619,2528,2396,3471,1274,2441,1042,952,1217,598,2147,3307,3166,847,1602,1920,852,3349,2179,1159,3535,1027,682,1291,1888,3718,3600,1457,757,2345,3033,3408,1740,842,1402,1360,1541,2100,2946,650,1953,3381,1498,1878,593,3941,2638,3105,3467,3784,874,1143,2115,1096,2509,3704,1138,2724,1567,2460,3000,3210,1700,590,2666,970,706,2023,3326,669,3728,901,1075,997,3654,1249,1539,3059,2387,654,2851,1932,2566,1852,3109,2272,2140,3126,2681,2581,2465,3540,721,3834,2203,1086,2761,3173,3999,2402,1616,888,3807,3824,2634,765,1054,1663,2089,2144,2729,1146,2391,2585,2941,856,3289,1301,965,750,1251,2413,2556,1103,1927,3985,1154,2727,1389,2525,2489,2393,1652,2568,3458,1124,1226,2134,4000,3187,2970,3319,3636,2938,1795,1701,2161,1503,936,2220,3726,3646,3651,3663,1107,3594,3700,804,3416,704,2474,1224,1356,1635,2935,1733,2166,1090,979,2361,2679,1282,1722,3384,1571,863,1209,3352,2151,2229,2084,3238,2774,3287,3683,3515,2943,737,2856,3500,3138,2378,3066,3586,1667,811,2632,858,816,3073,2780,726,2446,1325,915,3583,2278,2974,1952,1112,2785,2593,1029,2835,1044,2620,1015,1176,2967,3178,2207,922,1805,685,1171,2770,2075,2418,2212,959,2506,1562,1034,3031,2107,2318,1420,927,2503,2449,2684,1340,3455,1018,754,2899,1181,1551,2927,2629,776,3391,1770,2863,1025,2012,2588,3129,739,2175,1780,1267,2882,3988,2513,1611,1156,2831,2689,3080,1716,1188,840,2429,3544,1658,1220,1637,3334,4003,1038,1738,3041,2354,907,1849,1023,1702,1485,2579,1797,1008,595,3156,876,3398,2426,2992,1353,2357,600,4143,3224,3284,3433,2626,1459,1685,1817,2078,3548,2209,844,2658,2792,3565,3401,2997,2187,3346,2919,2342,1646,588,963,3825,2406,1101,3336,2026,632,2431,3859,2526,1558,961,813,1062,1508,3369,3220,731,3331,2648,929,2576,2183,1607,3993,2120,832,2315,2739,3181,3694,667,1294,2230,1309,2917,2623,716,1161,2142,2374,752,1774,1280,3907,967,2233,1395,3100,1593,2951,3521,3496,2768,3469,3658,2258,2736,2008,1303,3132,790,1859,3277,3558,807,2746,664,1891,696,2668,3843,1610,2651,3309,3145,2201,801,4024,2070,897,1410,767,2961,1288,1710,1197,2091,2404,886,1742,1093,1261,1152,596,1582,1500,1925,1880,3812,2138,2159,3362,1532,2847,3605,2485,3939,1713,1505,2270,3474,2754,1320,3626,1184,1565,2059,2453,2351,3200,592,3035,2177,2321,940,3212,3299,2018,2866,1870,3669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU444+4 : 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
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 10:01:13 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.82/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 15.11/10.87 % [INFO] Parsing done (9832ms).
% 15.24/10.98 % [INFO] Running in sequential loop mode.
% 15.69/11.35 % [INFO] eprover registered as external prover.
% 15.69/11.36 % [INFO] Scanning for conjecture ...
% 24.23/17.80 % [INFO] Found a conjecture (or negated_conjecture) and 71137 axioms. Running axiom selection ...
% 37.44/30.40 % [INFO] Axiom selection finished. Selected 585 axioms (removed 70552 axioms).
% 39.04/31.22 % [INFO] Problem is first-order (TPTP FOF).
% 39.04/31.29 % [INFO] Type checking passed.
% 39.34/31.30 % [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 ...
% 86.85/47.38 % External prover 'e' found a proof!
% 86.85/47.38 % [INFO] Killing All external provers ...
% 86.85/47.38 % Time passed: 46844ms (effective reasoning time: 36402ms)
% 86.85/47.38 % 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)>
% 86.85/47.38 % Axioms used in derivation (585): t119_funct_2, t1_jordan1d, t2_jordan1k, t5_fraenkel, t62_partfun1, dt_k4_finseq_4, dt_k1_bhsp_5, rc2_lopclset, t38_funct_4, t51_partfun1, redefinition_m2_relset_1, t13_zfmisc_1, t30_funct_2, t10_lattice2, t68_partfun2, t177_orders_1, t14_cqc_the1, t75_partfun2, t1_card_fil, t15_setwiseo, cc2_finset_1, fc1_zfmisc_1, d1_tarski, t25_relset_1, t66_funct_2, t66_partfun1, t14_finset_1, t53_subset_1, d1_partit_2, dt_k8_cohsp_1, t67_stirl2_1, t35_subset_1, t135_zfmisc_1, dt_k6_relset_1, t105_zfmisc_1, t1_funct_4, fc4_yellow_3, t27_funct_2, dt_k1_oposet_1, t2_collsp, t20_funct_2, t13_cqc_the1, t35_partfun2, t3_xboole_1, t1_jordan1k, dt_k4_relset_1, d1_funct_5, rc4_finset_1, t57_funcop_1, t47_relset_1, t1_boole, t7_subset_1, t2_realset1, t32_funct_2, fc1_xboole_0, t4_jordan1k, t113_xboole_1, t111_zfmisc_1, t64_funct_5, t41_partfun2, t53_funct_2, t6_funct_4, t37_funct_4, t4_ordinal1, s12_funct_2, t1_subset, t10_partfun1, t16_funct_2, t113_zfmisc_1, t7_lattice2, dt_k4_graphsp, rc1_topgen_3, t56_partfun1, t8_subset_1, reflexivity_r1_partit_2, t1_group_6, t59_partfun1, t158_partfun1, d2_oposet_1, t9_lattice2, fc4_subset_1, s20_scheme1, dt_k3_funct_2, t168_funct_2, t16_fraenkel, t7_funct_2, t78_funct_3, dt_k9_relset_1, t13_funcop_1, t6_xboole_1, t41_funct_2, t67_partfun2, d5_xboole_0, t54_relset_2, t32_topgen_2, t54_partfun1, t81_zfmisc_1, t9_measure1, t146_funct_2, t16_setwiseo, t96_zfmisc_1, t166_funct_2, t148_partfun1, t19_finset_1, t1_boolmark, t35_zfmisc_1, t117_zfmisc_1, t1_qc_lang1, t15_funct_5, t1_gate_1, s1_monoid_1, fc2_borsuk_3, t43_zfmisc_1, t65_partfun1, t44_funct_2, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, t10_armstrng, t95_zfmisc_1, t15_relset_1, s11_scheme1, t99_zfmisc_1, t49_funct_2, t45_zfmisc_1, t5_funct_7, t1_yellow_3, t162_partfun1, cc1_sgraph1, t80_finseq_4, t50_funct_2, t26_funct_2, s19_scheme1, t41_zfmisc_1, t12_funct_5, d7_partfun1, dt_k2_oposet_1, t49_zfmisc_1, t55_relset_2, t29_partfun1, t70_partfun1, t130_funct_2, t35_topgen_3, t9_xboole_1, dt_m2_relset_1, t18_finset_1, t10_partfun2, redefinition_k2_funct_2, t30_card_1, t36_subset_1, t176_partfun1, t62_funct_2, t115_zfmisc_1, t152_funct_2, t65_funct_2, t2_borsuk_5, t129_zfmisc_1, involutiveness_k3_subset_1, dt_m2_realset1, t22_funcop_1, t64_funct_2, t80_funct_3, t25_funct_2, fc2_xboole_0, involutiveness_k6_relset_1, t12_euler_1, t175_partfun1, t172_relat_1, d1_xboole_0, t34_partfun1, t138_zfmisc_1, t96_funct_3, d2_funcop_1, s13_scheme1, t130_zfmisc_1, t46_funct_2, t31_finset_1, t154_funct_2, t48_funct_2, t20_hilbert3, t156_funct_2, t18_funct_5, t30_finset_1, t3_jordan1k, t108_zfmisc_1, t165_funct_2, t27_relset_1, t60_partfun1, t118_funct_2, t14_relset_1, existence_m1_realset1, t16_relset_1, t39_funct_4, t46_zfmisc_1, t31_partfun1, t6_boole, t4_funct_5, dt_k6_subset_1, t47_funct_2, t79_funct_3, t52_relset_1, t118_zfmisc_1, t8_funct_2, t164_funct_2, fc2_funct_2, rc2_subset_1, fc9_finset_1, t1_xboole_1, t26_relset_1, t64_partfun1, t77_funct_2, t5_functor0, rc2_waybel_7, t68_partfun1, t32_partfun1, t5_subset, t1_yellow_8, t66_funct_5, t6_partfun2, t42_partfun2, t81_finseq_4, commutativity_k2_xboole_0, t128_zfmisc_1, t39_partfun1, t5_altcat_1, t6_lattice2, t63_funct_5, cc1_yellow15, t1_zfmisc_1, t46_partfun1, t16_partfun2, fc2_subset_1, t45_funct_2, t1_kurato_2, dt_k8_funct_2, t94_zfmisc_1, s1_abcmiz_0, d2_realset1, t53_relset_2, t150_relat_1, existence_m1_relset_1, t79_zfmisc_1, t12_lattice2, t18_setwiseo, t24_finset_1, t28_partfun1, t40_funct_2, t102_zfmisc_1, t2_tarski, rc1_hahnban, t13_setwiseo, t2_zfmisc_1, d6_realset1, dt_k1_partfun1, t167_funct_2, t53_partfun1, t11_funct_2, t1_tmap_1, t142_funct_2, t82_funct_2, t25_borsuk_1, t1_setlim_1, t52_subset_1, t5_ordinal1, fc1_glib_002, t4_cat_1, dt_k16_funct_3, dt_k9_relset_2, fc3_xboole_0, d2_xboole_0, cc1_funct_2, d4_tarski, t42_relset_2, t49_card_1, t4_subset, s2_seq_1, t176_orders_1, cc1_sf_mastr, t61_partfun1, dt_k14_funct_3, s1_rlvect_4, t25_finset_1, t148_funct_2, t51_funct_2, existence_m2_realset1, dt_k5_bhsp_5, dt_k1_polynom1, t36_partfun2, t17_funct_2, d4_partfun1, t11_funct_5, t132_funct_2, redefinition_k10_relset_1, s1_relset_1, t139_zfmisc_1, t32_lopclset, t16_lattice2, t7_boole, cc1_funct_1, t24_partfun2, t17_funct_5, s11_funct_2, t78_partfun2, d1_cat_3, t3_ordinal1, t9_domain_1, t1_t_0topsp, d2_subset_1, fc1_subset_1, t33_zfmisc_1, t13_finset_1, t3_yellow15, t5_setwiseo, t6_funct_5, t29_fin_topo, t49_partfun1, t9_funct_2, t158_funct_2, t51_relset_2, fc1_yellow_3, t22_finset_1, t91_orders_1, dt_k2_partfun1, t17_partfun2, t69_partfun1, t7_ordinal1, t31_funct_2, rc1_subset_1, t36_mcart_2, t149_funct_2, t6_fraenkel, t1_heyting1, t4_subset_1, t19_funct_2, t7_finseqop, t2_t_0topsp, d2_funct_5, t70_funct_4, t60_funct_2, t6_setwiseo, fraenkel_a_3_0_ami_1, dt_k2_monoid_0, t113_funct_2, t71_partfun1, t12_setwiseo, cc1_triang_1, t159_funct_2, t116_zfmisc_1, t14_funct_2, t155_funct_2, t4_isocat_2, d3_funct_2, t3_partfun2, t120_zfmisc_1, t21_funcop_1, t169_partfun1, t2_gate_1, t22_relset_1, t10_funct_5, t52_relset_2, existence_m1_subset_1, t41_funct_4, s2_lmod_7, t8_relset_1, t4_relset_1, dt_k4_funct_2, t31_subset_1, t3_subset, t55_subset_1, t79_funct_2, t136_funct_2, t6_borsuk_1, d2_zfmisc_1, t27_card_1, fc3_yellow_3, t106_zfmisc_1, dt_k2_funct_2, t44_zfmisc_1, t5_funct_5, fc1_finset_1, t5_lattice2, t92_zfmisc_1, t73_funct_2, t8_setwiseo, t14_xboole_1, t44_setfam_1, t1_cat_3, t17_relset_1, t20_cohsp_1, t99_partfun1, t107_zfmisc_1, t22_armstrng, t121_funct_2, t58_partfun1, d1_zfmisc_1, t15_xboole_1, t43_funct_2, t1_card_4, existence_m2_relset_1, t4_funct_7, t116_funct_2, t3_funct_7, t19_funct_5, t79_partfun2, t114_zfmisc_1, t31_zfmisc_1, t22_finseq_4, t100_zfmisc_1, t61_card_3, cc3_finsub_1, t40_waybel26, t2_msualg_9, t73_partfun1, t9_partfun2, t13_funct_5, fc1_heyting3, t6_funct_2, t168_partfun1, t46_partfun2, t51_subset_1, rc1_triang_1, t14_setwiseo, d3_tarski, t74_partfun1, cc6_funct_2, t13_xboole_1, t19_setwiseo, t17_subset_1, reflexivity_r1_tarski, t84_funct_3, t8_xboole_1, t8_realset1, t58_funcop_1, t6_relset_1, d1_relset_1, t39_zfmisc_1, d1_realset1, t131_funct_2, t119_zfmisc_1, dt_k12_turing_1, t40_subset_1, t6_zfmisc_1, t27_finsub_1, t143_funct_2, t19_hilbert3, t18_funct_2, t56_setfam_1, t9_necklace, rc2_setwiseo, t1_realset1, fc2_yellow_3, t9_mcart_1, t1_partfun1, d6_qmax_1, t34_funct_2, redefinition_r1_partit_2, dt_k10_relset_1, t81_card_2, t121_zfmisc_1, t10_subset_1, t21_fin_topo, t68_stirl2_1, t2_xboole_1, t57_partfun1, t4_xboole_1, d1_funct_2, t3_lattice4, rc3_finset_1, redefinition_k14_funct_3, t66_partfun2, t73_partfun2, t151_funct_2, redefinition_v1_yellow18, t7_funct_4, t19_ami_3, t45_partfun1, t12_funct_2, t28_finsub_1, t40_funct_4, t35_partfun1, dt_k11_cohsp_1, t26_finsub_1, t44_partfun2, t54_subset_1, rc1_finset_1, t2_tmap_1, cc1_finset_1, t3_hahnban, t8_boole, rc1_xboole_0, fc1_waybel_2, t11_xboole_1, t23_finset_1, redefinition_k8_funct_2, t35_relset_1, d1_orders_1, t34_zfmisc_1, t80_zfmisc_1, t68_card_2, t24_zfmisc_1, t1_functor0, t2_subset, t38_funct_2, t14_funcop_1, d11_turing_1, t37_zfmisc_1, t23_finsub_1, t20_funcop_1, t109_zfmisc_1, t25_finsub_1, t175_orders_1, t65_partfun2, rc1_card_5, dt_m1_orders_1, t120_funct_2, redefinition_k3_funct_2, fc3_pscomp_1, t59_funct_2, t12_xboole_1, t22_funct_3, t34_finsub_1, t85_funct_2, t30_finsub_1, d1_oposet_1, t134_zfmisc_1, t68_funct_5, rc1_setwiseo, d1_funct_1, cc1_card_5, t4_partfun2, t40_partfun2, d10_xboole_0, t7_xboole_1, t115_funct_2, idempotence_k2_xboole_0, t32_finsub_1, t48_subset_1, dt_k6_cohsp_1, t50_subset_1, t2_grcat_1, t5_xboole_1, t145_funct_2, t27_partfun1, t67_partfun1, t6_ordinal1, cc2_armstrng, cc5_funct_2, fc1_borsuk_3, t5_funct_4, t49_subset_1, t7_tarski, t2_funct_7, t47_card_1, t22_funct_2, t14_funct_3, fc14_finset_1, t17_funct_3, t36_relset_1, t83_funct_3, fc1_amistd_1, t143_partfun1, t72_funcop_1, rc2_xboole_0, t38_partfun1, existence_m1_orders_1, t67_funct_2, t26_partfun1, t64_partfun2, t174_partfun1, s14_scheme1, t112_zfmisc_1, t61_funct_2, t172_partfun1, t30_partfun1, t5_jct_misc, antisymmetry_r2_hidden, t7_hilbert3, t10_xboole_1, t28_funct_2, dt_k3_subset_1, fc1_funct_2, fc4_topgen_3, t14_lattice2, t63_subset_1, t112_partfun1
% 86.85/47.38 % No. of inferences in proof: 1239
% 86.85/47.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 46844 ms resp. 36402 ms w/o parsing
% 90.12/48.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.12/48.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------