TSTP Solution File: SEU427+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU427+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:58:58 EDT 2023
% Result : Theorem 256.17s 53.88s
% Output : Refutation 258.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1843
% Syntax : Number of formulae : 4743 (1199 unt; 302 typ; 0 def)
% Number of atoms : 18056 (4333 equ; 0 cnn)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 62455 (3343 ~;1779 |;5648 &;46111 @)
% ( 247 <=>;5327 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 590 ( 590 >; 0 *; 0 +; 0 <<)
% Number of symbols : 305 ( 302 usr; 74 con; 0-9 aty)
% Number of variables : 11188 ( 0 ^;10661 !; 527 ?;11188 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(m2_finseq_1_type,type,
m2_finseq_1: $i > $i > $o ).
thf(m2_pua2mss1_type,type,
m2_pua2mss1: $i > $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k3_funct_5_type,type,
k3_funct_5: $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_type,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k1_funcop_1_type,type,
k1_funcop_1: $i > $i ).
thf(k2_funcop_1_type,type,
k2_funcop_1: $i > $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k4_relat_1_type,type,
k4_relat_1: $i > $i ).
thf(k5_funct_5_type,type,
k5_funct_5: $i > $i ).
thf(k7_relat_1_type,type,
k7_relat_1: $i > $i > $i ).
thf(k5_funcop_1_type,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(v8_relat_2_type,type,
v8_relat_2: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(v3_relat_1_type,type,
v3_relat_1: $i > $o ).
thf(v1_finseq_1_type,type,
v1_finseq_1: $i > $o ).
thf(k3_finseq_1_type,type,
k3_finseq_1: $i > $i ).
thf(k3_funcop_1_type,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(v3_relat_2_type,type,
v3_relat_2: $i > $o ).
thf(k4_funct_5_type,type,
k4_funct_5: $i > $i ).
thf(k1_sysrel_type,type,
k1_sysrel: $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k8_relat_1_type,type,
k8_relat_1: $i > $i > $i ).
thf(k6_finseq_1_type,type,
k6_finseq_1: $i > $i ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k2_funct_4_type,type,
k2_funct_4: $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k10_funcop_1_type,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(k6_funcop_1_type,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k4_card_3_type,type,
k4_card_3: $i > $i ).
thf(k4_funcop_1_type,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(a_2_1_pua2mss1_type,type,
a_2_1_pua2mss1: $i > $i > $i ).
thf(r1_setfam_1_type,type,
r1_setfam_1: $i > $i > $o ).
thf(k1_eqrel_1_type,type,
k1_eqrel_1: $i > $i ).
thf(k4_funct_2_type,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(v2_relat_2_type,type,
v2_relat_2: $i > $o ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k4_zfmisc_1_type,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k4_mcart_1_type,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(k3_zfmisc_1_type,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(k3_mcart_1_type,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(v1_realset1_type,type,
v1_realset1: $i > $o ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(k3_setfam_1_type,type,
k3_setfam_1: $i > $i > $i ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(m3_realset1_type,type,
m3_realset1: $i > $i > $i > $o ).
thf(k4_realset1_type,type,
k4_realset1: $i > $i > $i > $i ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(k2_mcart_1_type,type,
k2_mcart_1: $i > $i ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(k5_domain_1_type,type,
k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k2_setfam_1_type,type,
k2_setfam_1: $i > $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(v6_ordinal1_type,type,
v6_ordinal1: $i > $o ).
thf(k10_pboole_type,type,
k10_pboole: $i > $i > $i ).
thf(a_3_1_pua2mss1_type,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k1_mcart_1_type,type,
k1_mcart_1: $i > $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(r2_setfam_1_type,type,
r2_setfam_1: $i > $i > $o ).
thf(k4_domain_1_type,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k10_relset_1_type,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k4_setfam_1_type,type,
k4_setfam_1: $i > $i > $i ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(k2_realset1_type,type,
k2_realset1: $i > $i > $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(a_1_0_pua2mss1_type,type,
a_1_0_pua2mss1: $i > $i ).
thf(k9_funcop_1_type,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(a_4_2_domain_1_type,type,
a_4_2_domain_1: $i > $i > $i > $i > $i ).
thf(p1_s4_domain_1_type,type,
p1_s4_domain_1: $i > $i > $i > $i > $o ).
thf(k5_xboole_0_type,type,
k5_xboole_0: $i > $i > $i ).
thf(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(m1_orders_1_type,type,
m1_orders_1: $i > $i > $o ).
thf(a_4_0_relset_2_type,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(a_3_8_domain_1_type,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(p1_s3_domain_1_type,type,
p1_s3_domain_1: $i > $i > $i > $o ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(g2_vectsp_1_type,type,
g2_vectsp_1: $i > $i > $i > $i > $i ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $i > $i ).
thf(p1_s1_domain_1_type,type,
p1_s1_domain_1: $i > $o ).
thf(k6_enumset1_type,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_type,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(a_3_0_relset_2_type,type,
a_3_0_relset_2: $i > $i > $i > $i ).
thf(k7_subset_1_type,type,
k7_subset_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(k19_mcart_1_type,type,
k19_mcart_1: $i > $i ).
thf(k3_relset_2_type,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k3_realset1_type,type,
k3_realset1: $i > $i > $i > $i ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_6_0_domain_1_type,type,
a_6_0_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s2_finset_1_type,type,
f1_s2_finset_1: $i ).
thf(p1_s2_finset_1_type,type,
p1_s2_finset_1: $i > $o ).
thf(k18_mcart_1_type,type,
k18_mcart_1: $i > $i ).
thf(a_2_3_domain_1_type,type,
a_2_3_domain_1: $i > $i > $i ).
thf(p1_s2_domain_1_type,type,
p1_s2_domain_1: $i > $i > $o ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(k3_enumset1_type,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(k2_enumset1_type,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(k7_domain_1_type,type,
k7_domain_1: $i > $i > $i > $i ).
thf(k3_domain_1_type,type,
k3_domain_1: $i > $i > $i > $i ).
thf(k9_funct_2_type,type,
k9_funct_2: $i > $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(r2_realset1_type,type,
r2_realset1: $i > $i > $i > $o ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k20_mcart_1_type,type,
k20_mcart_1: $i > $i ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k13_domain_1_type,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(g1_vectsp_1_type,type,
g1_vectsp_1: $i > $i > $i > $i ).
thf(k2_relset_2_type,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k1_enumset1_type,type,
k1_enumset1: $i > $i > $i > $i ).
thf(g1_rlvect_1_type,type,
g1_rlvect_1: $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(g3_vectsp_1_type,type,
g3_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_type,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(a_8_0_domain_1_type,type,
a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s4_funct_2_type,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_type,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_type,type,
f3_s4_funct_2: $i > $i ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k17_mcart_1_type,type,
k17_mcart_1: $i > $i ).
thf(k1_relset_2_type,type,
k1_relset_2: $i > $i > $i > $i ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_1_1_domain_1_type,type,
a_1_1_domain_1: $i > $i ).
thf(m1_ordinal1_type,type,
m1_ordinal1: $i > $i > $o ).
thf(f1_s14_funct_2_type,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_type,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_type,type,
p1_s14_funct_2: $i > $i > $o ).
thf(f1_s12_funct_2_type,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_type,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_type,type,
f2_s12_funct_2: $i ).
thf(a_3_3_domain_1_type,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s13_funct_2_type,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_type,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_type,type,
f2_s13_funct_2: $i ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(k2_domain_1_type,type,
k2_domain_1: $i > $i > $i > $i ).
thf(k9_domain_1_type,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(f1_s3_funct_2_type,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_type,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_type,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_2_0_relset_2_type,type,
a_2_0_relset_2: $i > $i > $i ).
thf(k5_enumset1_type,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_4_1_domain_1_type,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_mcart_1_type,type,
k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k14_mcart_1_type,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_0_2_domain_1_type,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_type,type,
f3_s9_domain_1: $i ).
thf(a_0_0_domain_1_type,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_type,type,
f1_s7_domain_1: $i ).
thf(k16_domain_1_type,type,
k16_domain_1: $i > $i > $i > $i > $i ).
thf(f3_s11_funct_2_type,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_type,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_type,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_type,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_type,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_type,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_type,type,
f7_s11_funct_2: $i > $i ).
thf(p1_s7_domain_1_type,type,
p1_s7_domain_1: $i > $o ).
thf(k9_relset_2_type,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(f1_s3_subset_1_type,type,
f1_s3_subset_1: $i ).
thf(p1_s3_subset_1_type,type,
p1_s3_subset_1: $i > $o ).
thf(k8_subset_1_type,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_type,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_type,type,
f2_s8_domain_1: $i ).
thf(g2_struct_0_type,type,
g2_struct_0: $i > $i > $i ).
thf(k15_domain_1_type,type,
k15_domain_1: $i > $i > $i > $i > $i ).
thf(f1_s8_domain_1_type,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_type,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_type,type,
p1_s8_domain_1: $i > $o ).
thf(k14_domain_1_type,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(f1_s1_subset_1_type,type,
f1_s1_subset_1: $i ).
thf(p1_s1_subset_1_type,type,
p1_s1_subset_1: $i > $o ).
thf(f1_s9_domain_1_type,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_type,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_type,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_type,type,
p1_s9_domain_1: $i > $i > $o ).
thf(k17_domain_1_type,type,
k17_domain_1: $i > $i > $i > $i > $i ).
thf(k7_relset_2_type,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(f1_s2_subset_1_type,type,
f1_s2_subset_1: $i ).
thf(p1_s2_subset_1_type,type,
p1_s2_subset_1: $i > $o ).
thf(f1_s4_subset_1_type,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_type,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_type,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_type,type,
f3_s4_subset_1: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk23_type,type,
sk23: $i ).
thf(sk34_type,type,
sk34: $i ).
thf(sk40_type,type,
sk40: $i > $i ).
thf(sk42_type,type,
sk42: $i ).
thf(sk62_type,type,
sk62: $i > $i ).
thf(sk161_type,type,
sk161: $i > $i ).
thf(sk164_type,type,
sk164: $i ).
thf(sk184_type,type,
sk184: $i > $i > $i ).
thf(sk275_type,type,
sk275: $i ).
thf(sk283_type,type,
sk283: $i ).
thf(sk320_type,type,
sk320: $i ).
thf(sk332_type,type,
sk332: $i ).
thf(sk401_type,type,
sk401: $i > $i > $i ).
thf(sk403_type,type,
sk403: $i > $i > $i ).
thf(sk404_type,type,
sk404: $i ).
thf(sk420_type,type,
sk420: $i ).
thf(sk421_type,type,
sk421: $i ).
thf(sk424_type,type,
sk424: $i ).
thf(sk432_type,type,
sk432: $i ).
thf(sk453_type,type,
sk453: $i ).
thf(sk462_type,type,
sk462: $i ).
thf(sk465_type,type,
sk465: $i ).
thf(sk492_type,type,
sk492: $i > $i ).
thf(sk497_type,type,
sk497: $o ).
thf(sk498_type,type,
sk498: $i ).
thf(sk500_type,type,
sk500: $o ).
thf(sk501_type,type,
sk501: $i ).
thf(sk513_type,type,
sk513: $o ).
thf(sk514_type,type,
sk514: $i ).
thf(sk522_type,type,
sk522: $i > $i ).
thf(sk527_type,type,
sk527: $i ).
thf(sk533_type,type,
sk533: $i ).
thf(sk534_type,type,
sk534: $i ).
thf(sk536_type,type,
sk536: $i ).
thf(sk544_type,type,
sk544: $o ).
thf(sk545_type,type,
sk545: $i ).
thf(sk548_type,type,
sk548: $i > $i ).
thf(sk553_type,type,
sk553: $i > $i ).
thf(sk556_type,type,
sk556: $i > $i ).
thf(sk557_type,type,
sk557: $i ).
thf(sk560_type,type,
sk560: $i ).
thf(sk564_type,type,
sk564: $i ).
thf(sk570_type,type,
sk570: $o ).
thf(sk572_type,type,
sk572: $i ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_relat_1) ).
thf(2163,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1123,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(6979,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(6172,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1479,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_subset_1) ).
thf(8475,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(778,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(5384,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(5385,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(cnf,[status(esa)],[5384]) ).
thf(793,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_domain_1) ).
thf(5437,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(36,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ A @ C )
= D )
<=> ( ( k1_funct_1 @ B @ D )
= C ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1656,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( ( k1_funct_1 @ A @ C )
= D )
=> ( ( k1_funct_1 @ B @ D )
= C ) )
& ( ( ( k1_funct_1 @ B @ D )
= C )
=> ( ( k1_funct_1 @ A @ C )
= D ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ B @ ( sk7 @ B @ A ) )
!= ( sk6 @ B @ A ) )
| ( ( k1_funct_1 @ A @ ( sk6 @ B @ A ) )
!= ( sk7 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1656]) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ B @ ( sk7 @ B @ A ) )
!= ( sk6 @ B @ A ) )
| ( ( sk7 @ B @ A )
!= ( k1_funct_1 @ A @ ( sk6 @ B @ A ) ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1662]) ).
thf(940,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_2) ).
thf(6085,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) )
& ( ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) )
=> ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(315,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
~ ( ( v1_finset_1 @ B )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
& ( v1_finset_1 @ C )
& ( ( k9_relat_1 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t195_orders_1) ).
thf(2822,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
~ ( ( v1_finset_1 @ B )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
& ( v1_finset_1 @ C )
& ( ( k9_relat_1 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_domain_1) ).
thf(7304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(16,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(1586,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1213,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_finset_1) ).
thf(7373,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(990,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(6302,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(6305,plain,
v1_xboole_0 @ sk421,
inference(cnf,[status(esa)],[6302]) ).
thf(1109,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(6906,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(6907,plain,
~ ( v1_xboole_0 @ sk465 ),
inference(cnf,[status(esa)],[6906]) ).
thf(8920,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,6907]) ).
thf(8930,plain,
sk465 != sk421,
inference(simp,[status(thm)],[8920]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(1681,plain,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1682,plain,
! [A: $i] : ( m2_finseq_1 @ ( sk8 @ A ) @ A ),
inference(cnf,[status(esa)],[1681]) ).
thf(1518,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(8642,plain,
! [A: $i,B: $i] :
( ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(8643,plain,
( ! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[8642]) ).
thf(8645,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[8643]) ).
thf(8649,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8645]) ).
thf(8650,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8649]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1543,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1546,plain,
m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[1543]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ( m2_finseq_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finseq_2) ).
thf(1557,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ( m2_finseq_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_finseq_1 @ C @ B )
| ( m2_finseq_1 @ C @ A ) ),
inference(cnf,[status(esa)],[1557]) ).
thf(8789,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m2_finseq_1 @ C @ B )
| ( m2_finseq_1 @ C @ A )
| ( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) )
!= ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1546,1558]) ).
thf(8790,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8789:[bind(A,$thf( k2_zfmisc_1 @ sk1 @ sk2 )),bind(B,$thf( sk5 )),bind(C,$thf( C ))]]) ).
thf(8794,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[8790]) ).
thf(16397,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ B @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8650,8794]) ).
thf(16427,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ~ ( m2_finseq_1 @ B @ sk5 )
| ( A != sk1 )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16397]) ).
thf(16452,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ A @ k1_xboole_0 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16427]) ).
thf(26919,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ( sk2 != k1_xboole_0 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,16452]) ).
thf(26920,plain,
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ ( sk8 @ sk5 ) @ k1_xboole_0 )
| ( sk2 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26919:[bind(A,$thf( sk5 )),bind(B,$thf( sk8 @ sk5 ))]]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(5422,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_partfun1) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[1717]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(3944,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( g2_vectsp_1 @ A @ B @ C @ D )
= ( g2_vectsp_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_vectsp_1) ).
thf(5365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( g2_vectsp_1 @ A @ B @ C @ D )
= ( g2_vectsp_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(297,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( k2_mcart_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(2744,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ! [B: $i] :
( ( ( B
= ( k2_mcart_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = D ) ) )
& ( ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = D ) )
=> ( B
= ( k2_mcart_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6355,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_2) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1320,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(7854,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(3,axiom,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_sysrel) ).
thf(1551,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1552,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
inference(cnf,[status(esa)],[1551]) ).
thf(1553,plain,
! [A: $i] :
( ( k1_tarski @ ( k4_tarski @ A @ A ) )
= ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[1552]) ).
thf(1010,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(6408,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(6410,plain,
v1_xboole_0 @ sk432,
inference(cnf,[status(esa)],[6408]) ).
thf(482,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_realset1) ).
thf(3831,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(3832,plain,
( ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) )
& ! [A: $i] : ( v1_realset1 @ ( k1_tarski @ A ) ) ),
inference(miniscope,[status(thm)],[3831]) ).
thf(3835,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[3832]) ).
thf(10480,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,3835]) ).
thf(10490,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk432 ),
inference(simp,[status(thm)],[10480]) ).
thf(11207,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk432 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10490]) ).
thf(11208,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk432 ),
inference(pattern_uni,[status(thm)],[11207:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(11211,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk432 ),
inference(simp,[status(thm)],[11208]) ).
thf(28,axiom,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
thf(1633,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(582,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(4433,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(4434,plain,
v1_xboole_0 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(1393,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(8183,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(8184,plain,
( ( k1_tarski @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8183]) ).
thf(10485,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,3835]) ).
thf(10486,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[10485:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(10495,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[10486]) ).
thf(15516,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10495]) ).
thf(15517,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[15516:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(15533,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(simp,[status(thm)],[15517]) ).
thf(24712,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,15533]) ).
thf(24713,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[24712:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(24731,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(simp,[status(thm)],[24713]) ).
thf(32735,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,24731]) ).
thf(32736,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[32735:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(32765,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[32736]) ).
thf(46907,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,32765]) ).
thf(46908,plain,
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[46907:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(46964,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,46908]) ).
thf(46998,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk275 ),
inference(simp,[status(thm)],[46964]) ).
thf(1453,axiom,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).
thf(8386,plain,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(1544,plain,
m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ sk1 ),
inference(cnf,[status(esa)],[1543]) ).
thf(8785,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m2_finseq_1 @ C @ B )
| ( m2_finseq_1 @ C @ A )
| ( ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ sk1 ) )
!= ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1544,1558]) ).
thf(8786,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ~ ( m2_finseq_1 @ A @ sk3 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8785:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(8792,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ~ ( m2_finseq_1 @ A @ sk3 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(simp,[status(thm)],[8786]) ).
thf(8823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_finseq_1 @ C @ B )
| ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ( m2_finseq_1 @ D @ sk1 )
| ( ( m2_finseq_1 @ C @ A )
!= ( m2_finseq_1 @ D @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1558,8792]) ).
thf(8824,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ( m2_finseq_1 @ B @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8823:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(8825,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 ) ),
inference(simp,[status(thm)],[8824]) ).
thf(11175,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8386,8825]) ).
thf(11179,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( a_0_1_domain_1 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f2_s8_domain_1 ) ) ),
inference(simp,[status(thm)],[11175]) ).
thf(11186,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_1_domain_1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f2_s8_domain_1 ) ) ),
inference(simp,[status(thm)],[11179]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_5) ).
thf(1765,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
| ~ ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
| ( ( k5_funct_5 @ C )
!= ( k5_funct_5 @ D ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[1765]) ).
thf(1767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_funct_5 @ C )
!= ( k5_funct_5 @ D ) )
| ( C = D )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
| ~ ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1766]) ).
thf(138,axiom,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_relat_1) ).
thf(2071,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(2072,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2071]) ).
thf(743,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(5260,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).
thf(1559,plain,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(424,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3503,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(3504,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3503]) ).
thf(3513,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( v1_funct_1 @ ( sk161 @ A ) ) ),
inference(lifteq,[status(thm)],[3504]) ).
thf(288,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2707,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(2708,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ~ ? [C: $i] :
( ( r2_hidden @ C @ B )
& ~ ? [D: $i] :
( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[2707]) ).
thf(2709,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk62 @ A ) ),
inference(cnf,[status(esa)],[2708]) ).
thf(1184,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(7270,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(7271,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( r2_hidden @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[7270]) ).
thf(7273,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[7271]) ).
thf(7276,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[7273]) ).
thf(7277,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[7276]) ).
thf(39206,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk62 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2709,7277]) ).
thf(39230,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk62 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[39206]) ).
thf(39244,plain,
! [A: $i] :
( ( sk62 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[39230]) ).
thf(49629,plain,
! [B: $i,A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( sk62 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3513,39244]) ).
thf(49630,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( sk62 @ A ) ) ),
inference(pattern_uni,[status(thm)],[49629:[bind(A,$thf( sk62 @ C )),bind(B,$thf( C ))]]) ).
thf(52049,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( sk62 @ A ) ) ),
inference(simp,[status(thm)],[49630]) ).
thf(53,axiom,
! [A: $i] :
( ( v3_relat_2 @ ( k6_partfun1 @ A ) )
& ( v8_relat_2 @ ( k6_partfun1 @ A ) )
& ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_eqrel_1) ).
thf(1732,plain,
! [A: $i] :
( ( v3_relat_2 @ ( k6_partfun1 @ A ) )
& ( v8_relat_2 @ ( k6_partfun1 @ A ) )
& ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1733,plain,
( ! [A: $i] : ( v3_relat_2 @ ( k6_partfun1 @ A ) )
& ! [A: $i] : ( v8_relat_2 @ ( k6_partfun1 @ A ) )
& ! [A: $i] : ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ! [A: $i] : ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(miniscope,[status(thm)],[1732]) ).
thf(1735,plain,
! [A: $i] : ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(cnf,[status(esa)],[1733]) ).
thf(1739,plain,
! [A: $i] : ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(simp,[status(thm)],[1735]) ).
thf(13,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(1578,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1579,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1578]) ).
thf(1580,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[1579]) ).
thf(42095,plain,
! [A: $i] : ( v1_partfun1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(rewrite,[status(thm)],[1739,1580]) ).
thf(629,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(4729,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1407,axiom,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).
thf(8231,plain,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(1545,plain,
m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ sk1 ),
inference(cnf,[status(esa)],[1543]) ).
thf(8783,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m2_finseq_1 @ C @ B )
| ( m2_finseq_1 @ C @ A )
| ( ( m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ sk1 ) )
!= ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1545,1558]) ).
thf(8784,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ~ ( m2_finseq_1 @ A @ sk4 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8783:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(8791,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ~ ( m2_finseq_1 @ A @ sk4 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(simp,[status(thm)],[8784]) ).
thf(8820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_finseq_1 @ C @ B )
| ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ( m2_finseq_1 @ D @ sk1 )
| ( ( m2_finseq_1 @ C @ A )
!= ( m2_finseq_1 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1558,8791]) ).
thf(8821,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ( m2_finseq_1 @ B @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8820:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(8822,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 ) ),
inference(simp,[status(thm)],[8821]) ).
thf(10742,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8231,8822]) ).
thf(10744,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( a_0_2_domain_1 != A )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(simp,[status(thm)],[10742]) ).
thf(10750,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_2_domain_1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(simp,[status(thm)],[10744]) ).
thf(10776,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_2_domain_1 )
| ( sk4 != f3_s9_domain_1 ) ),
inference(simp,[status(thm)],[10750]) ).
thf(26941,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk4 != f3_s9_domain_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_2_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10776]) ).
thf(26942,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_2_domain_1 ) @ sk1 )
| ( sk4 != f3_s9_domain_1 ) ),
inference(pattern_uni,[status(thm)],[26941:[bind(A,$thf( a_0_2_domain_1 )),bind(B,$thf( sk8 @ a_0_2_domain_1 ))]]) ).
thf(52,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_partfun1) ).
thf(1729,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(5950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_2) ).
thf(6651,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(416,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3434,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1489,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(8514,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(5320,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(986,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(6283,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1408,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(8232,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(8233,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk556 @ A ) ),
inference(cnf,[status(esa)],[8232]) ).
thf(15519,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10495]) ).
thf(15520,plain,
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[15519:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(15545,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8233,15520]) ).
thf(15558,plain,
! [A: $i] :
( ( sk556 @ A )
!= ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(simp,[status(thm)],[15545]) ).
thf(48863,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[3513,1545]) ).
thf(48864,plain,
( ( v1_funct_1 @ ( sk161 @ sk1 ) )
| ( m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[48863:[bind(A,$thf( sk1 ))]]) ).
thf(1486,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_2) ).
thf(8507,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(97,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( k1_funcop_1 @ ( k7_relat_1 @ A @ B ) )
= ( k7_relat_1 @ ( k1_funcop_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funcop_1) ).
thf(1899,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( k1_funcop_1 @ ( k7_relat_1 @ A @ B ) )
= ( k7_relat_1 @ ( k1_funcop_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6285,plain,
~ ( v1_xboole_0 @ sk420 ),
inference(cnf,[status(esa)],[6283]) ).
thf(1023,axiom,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(6490,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(6491,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(cnf,[status(esa)],[6490]) ).
thf(6492,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(lifteq,[status(thm)],[6491]) ).
thf(41973,plain,
! [A: $i] :
( ( ( k1_setfam_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
= A )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,6492]) ).
thf(41974,plain,
( ( k1_setfam_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[41973:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_sysrel) ).
thf(1840,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(158,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(2173,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(2175,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2173]) ).
thf(35,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_sysrel) ).
thf(1651,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1653,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1651]) ).
thf(17626,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ k1_xboole_0 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2175,1653]) ).
thf(17627,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ k1_xboole_0 ) ) @ ( k2_relat_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[17626:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(295,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2737,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(2738,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2737]) ).
thf(2740,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2738]) ).
thf(20544,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ k1_xboole_0 ) ) @ k1_xboole_0,
inference(rewrite,[status(thm)],[17627,2740]) ).
thf(665,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(4852,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(216,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2424,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(2427,plain,
v1_funct_1 @ sk42,
inference(cnf,[status(esa)],[2424]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(1982,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1217,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(7393,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(7396,plain,
( ( m1_subset_1 @ sk501 @ f1_s12_funct_2 )
| sk500 ),
inference(cnf,[status(esa)],[7393]) ).
thf(926,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(6013,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(6014,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk401 @ B @ A ) ),
inference(cnf,[status(esa)],[6013]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_5) ).
thf(1950,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
thf(5131,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1548,plain,
( ( k4_relset_2 @ ( k1_zfmisc_1 @ sk1 ) @ sk2 @ ( k6_relset_2 @ sk2 @ sk1 @ sk5 ) @ ( k3_pua2mss1 @ sk3 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1543]) ).
thf(1549,plain,
( ( k4_relset_2 @ ( k1_zfmisc_1 @ sk1 ) @ sk2 @ ( k6_relset_2 @ sk2 @ sk1 @ sk5 ) @ ( k3_pua2mss1 @ sk3 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1548]) ).
thf(195,axiom,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
thf(2320,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2321,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[2320]) ).
thf(2322,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[2321]) ).
thf(47060,plain,
! [A: $i] :
( ( ( k2_funct_1 @ k1_xboole_0 )
= ( k6_relat_1 @ A ) )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,2322]) ).
thf(47061,plain,
( ( k2_funct_1 @ k1_xboole_0 )
= ( k6_relat_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[47060:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(47344,plain,
( ( k2_funct_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[47061,2072]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_2) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1092,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ! [D: $i] :
( ( m1_eqrel_1 @ D @ B )
=> ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_pua2mss1) ).
thf(6808,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ! [D: $i] :
( ( m1_eqrel_1 @ D @ B )
=> ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(2176,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[2173]) ).
thf(901,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(5925,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(5926,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[5925]) ).
thf(5927,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[5926]) ).
thf(10499,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,5927]) ).
thf(10507,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10499]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2250,plain,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(8434,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(2622,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(5069,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1587,plain,
( ! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
inference(miniscope,[status(thm)],[1586]) ).
thf(1588,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[1587]) ).
thf(1590,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[1588]) ).
thf(1591,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(simp,[status(thm)],[1590]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_5) ).
thf(2114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1446,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(8366,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(10482,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,3835]) ).
thf(10494,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10482]) ).
thf(12428,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10494]) ).
thf(12429,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12428:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(12432,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[12429]) ).
thf(17135,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= k1_xboole_0 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12432]) ).
thf(17136,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[17135:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(17140,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[17136]) ).
thf(30003,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= k1_xboole_0 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,17140]) ).
thf(30004,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[30003:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(30018,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[30004]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4532,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(418,axiom,
! [A: $i] :
( ( v1_realset1 @ A )
<=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_realset1) ).
thf(3467,plain,
! [A: $i] :
( ( ( v1_realset1 @ A )
=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) )
& ( ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) )
=> ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(3468,plain,
( ! [A: $i] :
( ( v1_realset1 @ A )
=> ~ ( ~ ( v1_xboole_0 @ A )
& ~ ? [B: $i] :
( A
= ( k1_tarski @ B ) ) ) )
& ! [A: $i] :
( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ? [B: $i] :
( A
= ( k1_tarski @ B ) ) )
=> ( v1_realset1 @ A ) ) ),
inference(miniscope,[status(thm)],[3467]) ).
thf(3470,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[3468]) ).
thf(3473,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[3470]) ).
thf(3474,plain,
! [A: $i] : ( v1_realset1 @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[3473]) ).
thf(12422,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,3474]) ).
thf(12423,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[12422:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(12427,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[12423]) ).
thf(16890,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12427]) ).
thf(16891,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[16890:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16898,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(simp,[status(thm)],[16891]) ).
thf(429,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(3534,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1256,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(7601,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(6057,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(572,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(4368,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(4369,plain,
( ! [A: $i] : ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ! [A: $i] : ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ! [A: $i] : ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ! [A: $i] : ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
inference(miniscope,[status(thm)],[4368]) ).
thf(4373,plain,
! [A: $i] : ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[4369]) ).
thf(15472,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[4373,6285]) ).
thf(15490,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk420 ),
inference(simp,[status(thm)],[15472]) ).
thf(661,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_realset1) ).
thf(4839,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(4840,plain,
v1_realset1 @ sk320,
inference(cnf,[status(esa)],[4839]) ).
thf(692,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset1) ).
thf(5001,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(5002,plain,
~ ( v1_realset1 @ sk332 ),
inference(cnf,[status(esa)],[5001]) ).
thf(8854,plain,
( ( v1_realset1 @ sk332 )
!= ( v1_realset1 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[4840,5002]) ).
thf(8855,plain,
sk332 != sk320,
inference(simp,[status(thm)],[8854]) ).
thf(928,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(6020,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(6022,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk403 @ B @ A ) ),
inference(cnf,[status(esa)],[6020]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
thf(6587,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(7040,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(996,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6324,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(6325,plain,
v1_xboole_0 @ sk424,
inference(cnf,[status(esa)],[6324]) ).
thf(9010,plain,
( ( v1_xboole_0 @ sk424 )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[6325,6285]) ).
thf(9020,plain,
sk424 != sk420,
inference(simp,[status(thm)],[9010]) ).
thf(1326,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(7888,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(512,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k3_pua2mss1 @ A )
= ( a_1_0_pua2mss1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pua2mss1) ).
thf(4037,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k3_pua2mss1 @ A )
= ( a_1_0_pua2mss1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(24715,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,15533]) ).
thf(24716,plain,
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(pattern_uni,[status(thm)],[24715:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(24765,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,24716]) ).
thf(24772,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk424 ),
inference(simp,[status(thm)],[24765]) ).
thf(1325,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(7886,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(10484,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,3835]) ).
thf(10488,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk424 ),
inference(simp,[status(thm)],[10484]) ).
thf(10566,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk424 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10488]) ).
thf(10567,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk424 ),
inference(pattern_uni,[status(thm)],[10566:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(10568,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk424 ),
inference(simp,[status(thm)],[10567]) ).
thf(16613,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk424 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10568]) ).
thf(16614,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk424 ),
inference(pattern_uni,[status(thm)],[16613:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16620,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk424 ),
inference(simp,[status(thm)],[16614]) ).
thf(28938,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk424 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16620]) ).
thf(28939,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk424 ),
inference(pattern_uni,[status(thm)],[28938:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(28949,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk424 ),
inference(simp,[status(thm)],[28939]) ).
thf(1237,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).
thf(7477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(12421,plain,
! [A: $i] :
( ( v1_realset1 @ ( k1_tarski @ A ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[3474,5002]) ).
thf(12426,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk332 ),
inference(simp,[status(thm)],[12421]) ).
thf(168,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v2_relat_2 @ A )
=> ( v2_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_2) ).
thf(2210,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v2_relat_2 @ A )
=> ( v2_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(7940,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relset_1) ).
thf(1596,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(7083,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1118,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(6944,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_relat_1) ).
thf(3317,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1357,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(8044,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(311,axiom,
! [A: $i] : ( r1_setfam_1 @ A @ ( k2_setfam_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_setfam_1) ).
thf(2808,plain,
! [A: $i] : ( r1_setfam_1 @ A @ ( k2_setfam_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(6106,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(468,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(3762,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_relat_1) ).
thf(2381,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
= ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(6744,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
= ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1539,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(8709,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2776,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(73,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(1806,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1808,plain,
v1_relat_1 @ sk13,
inference(cnf,[status(esa)],[1806]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2659,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(5242,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1459,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(8402,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_funct_2) ).
thf(1618,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4841,plain,
~ ( v1_xboole_0 @ sk320 ),
inference(cnf,[status(esa)],[4839]) ).
thf(8804,plain,
( ( v1_xboole_0 @ sk320 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,4841]) ).
thf(8811,plain,
sk320 != sk275,
inference(simp,[status(thm)],[8804]) ).
thf(934,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(6044,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(6046,plain,
~ ( v1_xboole_0 @ sk404 ),
inference(cnf,[status(esa)],[6044]) ).
thf(9031,plain,
( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[6410,6046]) ).
thf(9045,plain,
sk432 != sk404,
inference(simp,[status(thm)],[9031]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
& ! [E: $i,F: $i,G: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_mcart_1) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
& ! [E: $i,F: $i,G: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(9,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
thf(1567,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1568,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k5_relat_1 @ A @ B )
!= A )
| ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ),
inference(cnf,[status(esa)],[1567]) ).
thf(1569,plain,
! [B: $i,A: $i] :
( ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k5_relat_1 @ A @ B )
!= A )
| ( ( k6_relat_1 @ ( k1_relat_1 @ B ) )
= B )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1568]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_2) ).
thf(1939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(279,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(2671,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(492,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
<=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(3910,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
=> ( v2_funct_1 @ A ) )
& ( ( v2_funct_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(864,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(5793,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1431,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_mcart_1) ).
thf(8315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( m2_pua2mss1 @ B @ A )
<=> ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pua2mss1) ).
thf(1725,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( m2_pua2mss1 @ B @ A )
=> ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) ) )
& ( ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) )
=> ( m2_pua2mss1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1728,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
| ~ ( v2_funct_1 @ B )
| ( m2_pua2mss1 @ B @ A ) ),
inference(cnf,[status(esa)],[1725]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_relat_1) ).
thf(3108,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1417,axiom,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(8270,plain,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(8271,plain,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[8270]) ).
thf(10481,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,3835]) ).
thf(10491,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk275 ),
inference(simp,[status(thm)],[10481]) ).
thf(11879,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk275 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10491]) ).
thf(11880,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk275 ),
inference(pattern_uni,[status(thm)],[11879:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(11883,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk275 ),
inference(simp,[status(thm)],[11880]) ).
thf(16652,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk275 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,11883]) ).
thf(16653,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk275 ),
inference(pattern_uni,[status(thm)],[16652:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16659,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk275 ),
inference(simp,[status(thm)],[16653]) ).
thf(29522,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk275 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16659]) ).
thf(29523,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk275 ),
inference(pattern_uni,[status(thm)],[29522:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(29537,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk275 ),
inference(simp,[status(thm)],[29523]) ).
thf(423,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v2_funct_1 @ k1_xboole_0 )
& ( v1_finset_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finseq_1) ).
thf(3495,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v2_funct_1 @ k1_xboole_0 )
& ( v1_finset_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(3498,plain,
v1_finset_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3495]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ A ) )
=> ( ~ ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ B ) )
=> ( ~ ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ C @ B )
& ( r2_hidden @ C @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ B ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ A ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_sysrel) ).
thf(4215,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ A ) )
=> ( ~ ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ B ) )
=> ( ~ ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ C @ B )
& ( r2_hidden @ C @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ B ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ A ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(113,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
<=> ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_2) ).
thf(1971,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v8_relat_2 @ A )
=> ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A ) )
& ( ( r1_tarski @ ( k5_relat_1 @ A @ A ) @ A )
=> ( v8_relat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(68,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(1793,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(5003,plain,
~ ( v1_xboole_0 @ sk332 ),
inference(cnf,[status(esa)],[5001]) ).
thf(8924,plain,
( ( v1_xboole_0 @ sk421 )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[6305,5003]) ).
thf(8928,plain,
sk421 != sk332,
inference(simp,[status(thm)],[8924]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(4623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(930,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(6031,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_5) ).
thf(4973,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1201,axiom,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(7340,plain,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(7341,plain,
! [A: $i] : ( m1_ordinal1 @ ( sk492 @ A ) @ A ),
inference(cnf,[status(esa)],[7340]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(5348,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(6017,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1171,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(7208,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1075,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(6729,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(6732,plain,
v1_relat_1 @ sk453,
inference(cnf,[status(esa)],[6729]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_relat_1) ).
thf(4487,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1736,plain,
! [A: $i] : ( v8_relat_2 @ ( k6_partfun1 @ A ) ),
inference(cnf,[status(esa)],[1733]) ).
thf(1740,plain,
! [A: $i] : ( v8_relat_2 @ ( k6_partfun1 @ A ) ),
inference(simp,[status(thm)],[1736]) ).
thf(12013,plain,
! [A: $i] : ( v8_relat_2 @ ( k6_relat_1 @ A ) ),
inference(rewrite,[status(thm)],[1740,1580]) ).
thf(633,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(4739,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(553,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k1_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(4279,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k1_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
<=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(4440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( A = C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(31,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_partfun1) ).
thf(1640,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4435,plain,
v1_finset_1 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(1346,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(7980,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( ( ( k2_mcart_1 @ A )
= D )
| ( ( k2_mcart_1 @ A )
= E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_mcart_1) ).
thf(6640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( ( ( k2_mcart_1 @ A )
= D )
| ( ( k2_mcart_1 @ A )
= E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
& ( A
= ( k2_xboole_0 @ C @ D ) ) )
=> ( E
= ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_sysrel) ).
thf(7793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
& ( A
= ( k2_xboole_0 @ C @ D ) ) )
=> ( E
= ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1433,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(8320,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_partfun1) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(6522,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(66,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_sysrel) ).
thf(1788,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(428,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(3530,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1794,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ ( k4_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1793]) ).
thf(64107,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk275 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4434,1794]) ).
thf(64108,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[64107:[bind(A,$thf( sk275 ))]]) ).
thf(64345,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk275 ) )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[64108,4841]) ).
thf(64355,plain,
( ( k4_relat_1 @ sk275 )
!= sk320 ),
inference(simp,[status(thm)],[64345]) ).
thf(871,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(5814,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(10764,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk501 @ f1_s12_funct_2 )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7396,8822]) ).
thf(10765,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk501 != A )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s12_funct_2 ) ),
inference(simp,[status(thm)],[10764]) ).
thf(10775,plain,
! [A: $i] :
( sk500
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk501 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s12_funct_2 ) ),
inference(simp,[status(thm)],[10765]) ).
thf(543,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(4234,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(38,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(1671,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(8732,plain,
( ( v1_xboole_0 @ sk332 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,5003]) ).
thf(8733,plain,
sk332 != k1_xboole_0,
inference(simp,[status(thm)],[8732]) ).
thf(473,axiom,
! [A: $i] : ( r1_setfam_1 @ ( k4_setfam_1 @ A @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_setfam_1) ).
thf(3794,plain,
! [A: $i] : ( r1_setfam_1 @ ( k4_setfam_1 @ A @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_finseq_2) ).
thf(1607,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1608,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ F @ B )
| ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ),
inference(cnf,[status(esa)],[1607]) ).
thf(619,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k7_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(4633,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k7_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
& ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
& ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k7_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1084,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(6764,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) )
=> ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1655,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1651]) ).
thf(64100,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6410,1794]) ).
thf(64101,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[64100:[bind(A,$thf( sk432 ))]]) ).
thf(64272,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk465 ) ),
inference(paramod_ordered,[status(thm)],[64101,6907]) ).
thf(64302,plain,
( ( k4_relat_1 @ sk432 )
!= sk465 ),
inference(simp,[status(thm)],[64272]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(3429,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(7203,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1495,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f2_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f3_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(8551,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f2_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f2_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f3_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f3_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(6911,plain,
v1_relat_1 @ sk465,
inference(cnf,[status(esa)],[6906]) ).
thf(18481,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk465 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6911,1655]) ).
thf(18482,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk465 ) ) @ ( k2_relat_1 @ sk465 ),
inference(pattern_uni,[status(thm)],[18481:[bind(A,$thf( sk465 ))]]) ).
thf(1279,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(7697,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1278,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(7695,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(7405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(5755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(10762,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk501 @ f1_s12_funct_2 )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7396,8825]) ).
thf(10768,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk501 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s12_funct_2 ) ),
inference(simp,[status(thm)],[10762]) ).
thf(10772,plain,
! [A: $i] :
( sk500
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk501 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s12_funct_2 ) ),
inference(simp,[status(thm)],[10768]) ).
thf(370,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(3135,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(3942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(8745,plain,
( ( v1_xboole_0 @ sk420 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,6285]) ).
thf(8747,plain,
sk420 != k1_xboole_0,
inference(simp,[status(thm)],[8745]) ).
thf(1442,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(8353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(1482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k17_domain_1 @ A @ B @ C @ D )
= ( k20_mcart_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k17_domain_1) ).
thf(8490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k17_domain_1 @ A @ B @ C @ D )
= ( k20_mcart_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1491,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(8519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k2_tarski @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_mssubfam) ).
thf(6089,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k2_tarski @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k5_relset_2 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
thf(2933,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( C
= ( k5_relset_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) )
=> ( C
= ( k5_relset_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(7669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1074,axiom,
! [A: $i] : ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_eqrel_1) ).
thf(6727,plain,
! [A: $i] : ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_relat_1) ).
thf(2141,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(742,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(5257,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1425,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( r2_hidden @ B @ A )
<=> ( p1_s3_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1) ).
thf(8298,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( ( r2_hidden @ B @ A )
=> ( p1_s3_subset_1 @ B ) )
& ( ( p1_s3_subset_1 @ B )
=> ( r2_hidden @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funcop_1) ).
thf(5146,plain,
! [A: $i,B: $i,C: $i] :
( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1337,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(7949,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(90,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_1 @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t184_relat_1) ).
thf(1872,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_1 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) ) )
& ( ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(514,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(4058,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(2428,plain,
v1_relat_1 @ sk42,
inference(cnf,[status(esa)],[2424]) ).
thf(17608,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk42 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2428,1653]) ).
thf(17609,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk42 ) ) @ ( k2_relat_1 @ sk42 ),
inference(pattern_uni,[status(thm)],[17608:[bind(A,$thf( sk42 ))]]) ).
thf(480,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(3826,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1222,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_realset1) ).
thf(7422,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_partfun1) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ C ) @ B )
| ( C
= ( k3_partfun1 @ C @ A @ B ) ) ),
inference(cnf,[status(esa)],[1759]) ).
thf(1761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_partfun1 @ C @ A @ B )
= C )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ),
inference(lifteq,[status(thm)],[1760]) ).
thf(13955,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[8233,5003]) ).
thf(13960,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk332 ),
inference(simp,[status(thm)],[13955]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funct_1) ).
thf(3121,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(7188,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k2_xboole_0 @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_setfam_1) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k2_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k2_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k2_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k2_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1789,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[1788]) ).
thf(61567,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk42 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2428,1789]) ).
thf(61568,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk42 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk42 ) ),
inference(pattern_uni,[status(thm)],[61567:[bind(A,$thf( sk42 ))]]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(6117,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_5) ).
thf(1954,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1292,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(7748,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(1315,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(7841,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(7842,plain,
v1_relat_1 @ sk534,
inference(cnf,[status(esa)],[7841]) ).
thf(1652,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1651]) ).
thf(17284,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk534 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7842,1652]) ).
thf(17285,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk534 ) ) @ ( k1_relat_1 @ sk534 ),
inference(pattern_uni,[status(thm)],[17284:[bind(A,$thf( sk534 ))]]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_mcart_1) ).
thf(5412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(2575,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ B )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
& ( v2_funct_1 @ D ) )
=> ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pua2mss1) ).
thf(3370,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ B )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
& ( v2_funct_1 @ D ) )
=> ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( A
= ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_mcart_1) ).
thf(7018,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( A
= ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3350,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(1497,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(8578,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(5921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1414,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(8246,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(8247,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( v1_funct_2 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(cnf,[status(esa)],[8246]) ).
thf(8256,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( v1_funct_2 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[8247]) ).
thf(141,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k2_funct_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2082,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k2_funct_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(50,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_relat_1 @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_funct_1) ).
thf(1721,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v3_relat_1 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1724,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( sk10 @ A ) @ ( k1_relat_1 @ A ) )
| ( v3_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1721]) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( B = k1_xboole_0 )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(cnf,[status(esa)],[1618]) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(lifteq,[status(thm)],[1620]) ).
thf(1136,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_setfam_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_setfam_1) ).
thf(7028,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_setfam_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(954,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(6138,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(55,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_relat_1 @ A )
<=> ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_pboole) ).
thf(1746,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v3_relat_1 @ A )
=> ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(360,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
<=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(3103,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ A ) )
& ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(975,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(6236,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(4792,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1329,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(7897,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(7899,plain,
v1_xboole_0 @ sk536,
inference(cnf,[status(esa)],[7897]) ).
thf(10479,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,3835]) ).
thf(10492,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk536 ),
inference(simp,[status(thm)],[10479]) ).
thf(12042,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk536 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10492]) ).
thf(12043,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk536 ),
inference(pattern_uni,[status(thm)],[12042:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(12046,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk536 ),
inference(simp,[status(thm)],[12043]) ).
thf(16863,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk536 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12046]) ).
thf(16864,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk536 ),
inference(pattern_uni,[status(thm)],[16863:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16868,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk536 ),
inference(simp,[status(thm)],[16864]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(2972,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(5977,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(6909,plain,
v1_finseq_1 @ sk465,
inference(cnf,[status(esa)],[6906]) ).
thf(24758,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,24716]) ).
thf(24776,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24758]) ).
thf(49167,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3513,24776]) ).
thf(49168,plain,
v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(pattern_uni,[status(thm)],[49167:[bind(A,$thf( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ))]]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(1914,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(13952,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8233,3835]) ).
thf(13965,plain,
! [B: $i,A: $i] :
( ( sk556 @ A )
!= ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[13952]) ).
thf(1265,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(7637,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(983,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(6268,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(2548,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_funct_2 @ A @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_funct_2 @ A @ B ) )
& ( ( k4_funct_5 @ C )
= ( k4_funct_5 @ D ) ) )
=> ( ( A = k1_xboole_0 )
| ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_5) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_funct_2 @ A @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_funct_2 @ A @ B ) )
& ( ( k4_funct_5 @ C )
= ( k4_funct_5 @ D ) ) )
=> ( ( A = k1_xboole_0 )
| ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(391,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(3312,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(3313,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[3312]) ).
thf(3314,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[3313]) ).
thf(40217,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,3314]) ).
thf(40238,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk536 ),
inference(simp,[status(thm)],[40217]) ).
thf(3502,plain,
v1_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3495]) ).
thf(903,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5933,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(5934,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[5933]) ).
thf(5935,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[5934]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_sysrel) ).
thf(1741,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1743,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
!= k1_xboole_0 )
| ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[1741]) ).
thf(1745,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
!= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) )
= ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) )
| ~ ( v1_relat_1 @ B ) ),
inference(lifteq,[status(thm)],[1743]) ).
thf(42809,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
!= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ A )
= ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) )
| ~ ( v1_relat_1 @ B ) ),
inference(rewrite,[status(thm)],[1745,1591]) ).
thf(808,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(5517,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(5518,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[5517]) ).
thf(1106,axiom,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(6872,plain,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(6623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1288,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( m1_ordinal1 @ C @ A )
=> ( m1_ordinal1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
thf(7734,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( m1_ordinal1 @ C @ A )
=> ( m1_ordinal1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(7235,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1286,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(7729,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
= k1_xboole_0 )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_sysrel) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
= k1_xboole_0 )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(101,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v8_relat_2 @ A )
& ( v8_relat_2 @ B ) )
=> ( v8_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_relat_2) ).
thf(1935,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v8_relat_2 @ A )
& ( v8_relat_2 @ B ) )
=> ( v8_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(7904,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(7905,plain,
( ! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(miniscope,[status(thm)],[7904]) ).
thf(7906,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(cnf,[status(esa)],[7905]) ).
thf(7914,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(lifteq,[status(thm)],[7906]) ).
thf(7915,plain,
! [A: $i] : ( r2_hidden @ A @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[7914]) ).
thf(42630,plain,
! [A: $i] :
( ( r2_hidden @ A @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,7915]) ).
thf(42631,plain,
r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[42630:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(1689,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( B
!= ( k6_relat_1 @ A ) )
| ~ ( r2_hidden @ C @ A )
| ( ( k1_funct_1 @ B @ C )
= C ) ),
inference(cnf,[status(esa)],[1689]) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k6_relat_1 @ A ) )
| ( ( k1_funct_1 @ B @ C )
= C )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( r2_hidden @ C @ A ) ),
inference(lifteq,[status(thm)],[1690]) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ~ ( v1_relat_1 @ ( k6_relat_1 @ A ) )
| ~ ( v1_funct_1 @ ( k6_relat_1 @ A ) )
| ~ ( r2_hidden @ B @ A ) ),
inference(simp,[status(thm)],[1694]) ).
thf(37,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(1669,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1670,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1669]) ).
thf(82,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(1843,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1844,plain,
( ! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(miniscope,[status(thm)],[1843]) ).
thf(1845,plain,
! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1844]) ).
thf(1847,plain,
! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ),
inference(simp,[status(thm)],[1845]) ).
thf(29361,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ~ $true
| ~ $true
| ~ ( r2_hidden @ B @ A ) ),
inference(rewrite,[status(thm)],[1695,1670,1847]) ).
thf(29362,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ~ ( r2_hidden @ B @ A ) ),
inference(simp,[status(thm)],[29361]) ).
thf(42666,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ( ( r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( r2_hidden @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42631,29362]) ).
thf(42667,plain,
( ( k1_funct_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[42666:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(650,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_realset1) ).
thf(4803,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(4124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(34,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_funct_5 @ A ) )
& ( v1_funct_1 @ ( k4_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_5) ).
thf(1648,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_funct_5 @ A ) )
& ( v1_funct_1 @ ( k4_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1650,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_funct_1 @ ( k4_funct_5 @ A ) ) ),
inference(cnf,[status(esa)],[1648]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ B @ ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_setfam_1) ).
thf(5723,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ B @ ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
thf(1643,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ B )
| ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[1643]) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1644]) ).
thf(1654,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1651]) ).
thf(17842,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk13 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1654]) ).
thf(17843,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk13 ) ) @ ( k1_relat_1 @ sk13 ),
inference(pattern_uni,[status(thm)],[17842:[bind(A,$thf( sk13 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5301,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(478,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(3809,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1528,axiom,
! [A: $i] :
( ( r1_setfam_1 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_setfam_1) ).
thf(8678,plain,
! [A: $i] :
( ( r1_setfam_1 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(6306,plain,
v1_relat_1 @ sk421,
inference(cnf,[status(esa)],[6302]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(4607,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1352,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(8025,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(638,axiom,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(4760,plain,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_mcart_1 @ A @ B @ C )
= ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_mcart_1) ).
thf(4963,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_mcart_1 @ A @ B @ C )
= ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1294,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_xboole_1) ).
thf(7761,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(2819,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(746,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(5269,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1050,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_pua2mss1) ).
thf(6608,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1410,axiom,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).
thf(8237,plain,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(11142,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8237,8822]) ).
thf(11145,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( a_0_0_domain_1 != A )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(simp,[status(thm)],[11142]) ).
thf(11151,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_0_domain_1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(simp,[status(thm)],[11145]) ).
thf(614,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(4610,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(1142,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(7043,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(7178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1404,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(8224,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(596,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(4508,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(4511,plain,
v1_relat_1 @ sk283,
inference(cnf,[status(esa)],[4508]) ).
thf(1214,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(7379,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(7382,plain,
( ( m1_subset_1 @ sk498 @ f1_s14_funct_2 )
| sk497 ),
inference(cnf,[status(esa)],[7379]) ).
thf(10575,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk498 @ f1_s14_funct_2 )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7382,8822]) ).
thf(10578,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk498 != A )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s14_funct_2 ) ),
inference(simp,[status(thm)],[10575]) ).
thf(10584,plain,
! [A: $i] :
( sk497
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk498 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s14_funct_2 ) ),
inference(simp,[status(thm)],[10578]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(5352,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(5797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1503,axiom,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(8603,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(7390,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(337,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_partfun1) ).
thf(2957,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1391,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(8178,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t183_relat_1) ).
thf(1791,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[1791]) ).
thf(579,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4422,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(730,axiom,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(5188,plain,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(183,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(2272,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(2274,plain,
v3_relat_1 @ sk34,
inference(cnf,[status(esa)],[2272]) ).
thf(43543,plain,
! [B: $i,A: $i] :
( ( ( sk556 @ A )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8184,13965]) ).
thf(43544,plain,
! [A: $i] :
( ( sk556 @ A )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[43543:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1449,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(8374,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1290,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(7739,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(7740,plain,
( ~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ! [A: $i,B: $i] : ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
inference(miniscope,[status(thm)],[7739]) ).
thf(7741,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k2_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[7740]) ).
thf(7743,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k2_tarski @ A @ B ) ),
inference(simp,[status(thm)],[7741]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(5765,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(4439,plain,
v2_funct_1 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(1179,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(7241,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ A ) )
& ( ~ ( r2_hidden @ B @ A )
=> ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
<=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_pua2mss1) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) )
=> ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1302,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(7790,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
<=> ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_mcart_1) ).
thf(3221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) ) )
& ( ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) )
=> ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(32738,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,24731]) ).
thf(32739,plain,
~ ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[32738:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(32792,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,32739]) ).
thf(32807,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[32792]) ).
thf(49573,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3513,32807]) ).
thf(49574,plain,
v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[49573:[bind(A,$thf( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ))]]) ).
thf(32786,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,32739]) ).
thf(32811,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk275 ),
inference(simp,[status(thm)],[32786]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_relat_1) ).
thf(4743,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
=> ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
<=> ( ( k2_relat_1 @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(3275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
=> ( ( k2_relat_1 @ C )
= B ) )
& ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(6034,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1467,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(8426,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(892,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_domain_1) ).
thf(5883,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1035,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(6538,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(679,axiom,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(4956,plain,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(365,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v2_relat_2 @ A )
=> ( v2_relat_2 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_2) ).
thf(3116,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v2_relat_2 @ A )
=> ( v2_relat_2 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1218,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(7401,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(6274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(5284,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3689,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(17856,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk283 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4511,1654]) ).
thf(17857,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk283 ) ) @ ( k1_relat_1 @ sk283 ),
inference(pattern_uni,[status(thm)],[17856:[bind(A,$thf( sk283 ))]]) ).
thf(398,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3342,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(298,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funcop_1) ).
thf(2755,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(4224,plain,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
<=> ~ ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(6878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1072,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(6723,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(17597,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk421 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6306,1653]) ).
thf(17598,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk421 ) ) @ ( k2_relat_1 @ sk421 ),
inference(pattern_uni,[status(thm)],[17597:[bind(A,$thf( sk421 ))]]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(7528,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(6423,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(6749,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(8301,plain,
m1_subset_1 @ sk560 @ ( k1_zfmisc_1 @ f1_s3_subset_1 ),
inference(cnf,[status(esa)],[8298]) ).
thf(11160,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk560 @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8301,8822]) ).
thf(11161,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk560 != A )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(simp,[status(thm)],[11160]) ).
thf(11168,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk560 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(simp,[status(thm)],[11161]) ).
thf(23568,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk560 )
| ( sk4 != f1_s3_subset_1 ) ),
inference(simp,[status(thm)],[11168]) ).
thf(26933,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk4 != f1_s3_subset_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk560 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,23568]) ).
thf(26934,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk560 ) @ sk1 )
| ( sk4 != f1_s3_subset_1 ) ),
inference(pattern_uni,[status(thm)],[26933:[bind(A,$thf( sk560 )),bind(B,$thf( sk8 @ sk560 ))]]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(5274,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(2425,plain,
v1_xboole_0 @ sk42,
inference(cnf,[status(esa)],[2424]) ).
thf(621,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(4669,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(4670,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(miniscope,[status(thm)],[4669]) ).
thf(4671,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(cnf,[status(esa)],[4670]) ).
thf(40255,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,4671]) ).
thf(40266,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk42 ),
inference(simp,[status(thm)],[40255]) ).
thf(620,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_orders_1) ).
thf(4654,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1003,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(6350,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1297,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(7771,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(3125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ D )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ A ) ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_sysrel) ).
thf(1826,plain,
! [A: $i,B: $i] :
( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(105,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pboole) ).
thf(1944,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1947,plain,
v1_relat_1 @ sk23,
inference(cnf,[status(esa)],[1944]) ).
thf(17612,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk23 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1947,1653]) ).
thf(17613,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk23 ) ) @ ( k2_relat_1 @ sk23 ),
inference(pattern_uni,[status(thm)],[17612:[bind(A,$thf( sk23 ))]]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_2) ).
thf(2682,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(17269,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk453 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6732,1652]) ).
thf(17270,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk453 ) ) @ ( k1_relat_1 @ sk453 ),
inference(pattern_uni,[status(thm)],[17269:[bind(A,$thf( sk453 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_partfun1) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
inference(cnf,[status(esa)],[1575]) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C )
| ~ ( m2_relset_1 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1576]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(6713,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
<=> ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).
thf(5640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
=> ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) ) )
& ( ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) )
=> ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(5712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(6519,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_5) ).
thf(1992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(7000,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ~ ( r2_hidden @ D @ C ) )
& ( ~ ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(401,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(3352,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(3353,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(cnf,[status(esa)],[3352]) ).
thf(145,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(2126,plain,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_1) ).
thf(3803,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_sysrel) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(879,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(5836,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(8867,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1546,8822]) ).
thf(8871,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk5 != A )
| ( ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( k1_zfmisc_1 @ sk4 ) ) ),
inference(simp,[status(thm)],[8867]) ).
thf(8880,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( k1_zfmisc_1 @ sk4 ) ) ),
inference(simp,[status(thm)],[8871]) ).
thf(200,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ A )
= ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(2356,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ A )
= ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( m1_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(5461,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( m1_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( m1_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1131,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(7011,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(13956,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8233,5927]) ).
thf(13961,plain,
! [B: $i,A: $i] :
( ( sk556 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[13956]) ).
thf(1027,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(6502,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_sysrel) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(4437,plain,
v1_relat_1 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(17883,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk275 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4437,1654]) ).
thf(17884,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk275 ) ) @ ( k1_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[17883:[bind(A,$thf( sk275 ))]]) ).
thf(8249,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( v1_funct_1 @ sk557 ) ),
inference(cnf,[status(esa)],[8246]) ).
thf(8257,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( v1_funct_1 @ sk557 ) ),
inference(lifteq,[status(thm)],[8249]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(5744,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_relat_1) ).
thf(2691,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1323,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(7862,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(6010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1374,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(8121,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_mcart_1) ).
thf(6240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(359,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(3099,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_partfun1) ).
thf(1798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
| ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C )
| ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ),
inference(cnf,[status(esa)],[1798]) ).
thf(1800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
| ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ),
inference(lifteq,[status(thm)],[1799]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setfam_1) ).
thf(5338,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1360,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(8054,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(568,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4353,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_mcart_1) ).
thf(5866,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k1_relset_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).
thf(8389,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k1_relset_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_pua2mss1) ).
thf(2403,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(5521,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
=> ( r1_tarski @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(40224,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,3314]) ).
thf(40234,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk42 ),
inference(simp,[status(thm)],[40224]) ).
thf(3834,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[3832]) ).
thf(3837,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[3834]) ).
thf(12484,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,3837]) ).
thf(12485,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[12484:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(12488,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[12485]) ).
thf(17148,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12488]) ).
thf(17149,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[17148:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(17155,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(simp,[status(thm)],[17149]) ).
thf(28975,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,17155]) ).
thf(28976,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[28975:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(28989,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(simp,[status(thm)],[28976]) ).
thf(31041,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,28989]) ).
thf(31042,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[31041:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(31051,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[31042]) ).
thf(36001,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,31051]) ).
thf(36002,plain,
v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[36001:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
thf(1702,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k2_relat_1 @ B )
!= ( k1_relat_1 @ A ) )
| ( ( k5_relat_1 @ B @ A )
!= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1702]) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( ( k2_relat_1 @ B )
!= ( k1_relat_1 @ A ) )
| ( ( k5_relat_1 @ B @ A )
!= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1703]) ).
thf(28581,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16898]) ).
thf(28582,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[28581:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(28591,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ),
inference(simp,[status(thm)],[28582]) ).
thf(30085,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,28591]) ).
thf(30086,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[30085:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(30096,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[30086]) ).
thf(35095,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,30096]) ).
thf(35096,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35095:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(35118,plain,
! [A: $i] : ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[35096]) ).
thf(43836,plain,
! [A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,35118]) ).
thf(43837,plain,
v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[43836:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(44459,plain,
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[43837,5002]) ).
thf(44486,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= sk332 ),
inference(simp,[status(thm)],[44459]) ).
thf(1306,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
thf(7803,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ C )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(7843,plain,
~ ( v1_xboole_0 @ sk534 ),
inference(cnf,[status(esa)],[7841]) ).
thf(8816,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,7843]) ).
thf(8819,plain,
sk534 != sk42,
inference(simp,[status(thm)],[8816]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).
thf(5193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) )
=> ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(8556,plain,
( sk570
| ( m1_subset_1 @ sk572 @ f1_s4_subset_1 )
| ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(cnf,[status(esa)],[8551]) ).
thf(8571,plain,
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk570
| ( m1_subset_1 @ sk572 @ f1_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[8556]) ).
thf(1478,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_subset_1) ).
thf(8468,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ E )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_eqrel_1) ).
thf(1609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v8_relat_2 @ E )
& ( v1_partfun1 @ E @ A @ A )
& ( m2_relset_1 @ E @ A @ A ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ E )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(829,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(5622,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(5323,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( k1_funcop_1 @ ( k2_funcop_1 @ A @ ( k4_tarski @ B @ C ) ) )
= ( k2_funcop_1 @ A @ ( k4_tarski @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funcop_1) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( k1_funcop_1 @ ( k2_funcop_1 @ A @ ( k4_tarski @ B @ C ) ) )
= ( k2_funcop_1 @ A @ ( k4_tarski @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ( k1_funcop_1 @ ( k2_funcop_1 @ A @ ( k4_tarski @ B @ C ) ) )
= ( k2_funcop_1 @ A @ ( k4_tarski @ C @ B ) ) ),
inference(cnf,[status(esa)],[1570]) ).
thf(1572,plain,
! [C: $i,B: $i,A: $i] :
( ( k1_funcop_1 @ ( k2_funcop_1 @ A @ ( k4_tarski @ B @ C ) ) )
= ( k2_funcop_1 @ A @ ( k4_tarski @ C @ B ) ) ),
inference(lifteq,[status(thm)],[1571]) ).
thf(1409,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(8235,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(1115,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(6936,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(50727,plain,
! [B: $i,A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k6_relat_1 @ ( k1_tarski @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[3513,12432]) ).
thf(50728,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[50727:[bind(A,$thf( k6_relat_1 @ ( k1_tarski @ D ) )),bind(B,$thf( D ))]]) ).
thf(52292,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ),
inference(simp,[status(thm)],[50728]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(7857,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(701,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(5052,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(623,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(4675,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(17587,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk13 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1653]) ).
thf(17588,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk13 ) ) @ ( k2_relat_1 @ sk13 ),
inference(pattern_uni,[status(thm)],[17587:[bind(A,$thf( sk13 ))]]) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[1741]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
!= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) )
= ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) )
| ~ ( v1_relat_1 @ B ) ),
inference(lifteq,[status(thm)],[1742]) ).
thf(1589,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[1587]) ).
thf(1592,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[1589]) ).
thf(42385,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
!= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ A )
= ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) )
| ~ ( v1_relat_1 @ B ) ),
inference(rewrite,[status(thm)],[1744,1592]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(7436,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(883,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(5850,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(5851,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(cnf,[status(esa)],[5850]) ).
thf(451,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(3657,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(29931,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk536 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16868]) ).
thf(29932,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk536 ),
inference(pattern_uni,[status(thm)],[29931:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(29943,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk536 ),
inference(simp,[status(thm)],[29932]) ).
thf(1507,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(8615,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_relat_1) ).
thf(3951,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(15060,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk332 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12426]) ).
thf(15061,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk332 ),
inference(pattern_uni,[status(thm)],[15060:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(15065,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk332 ),
inference(simp,[status(thm)],[15061]) ).
thf(17174,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk332 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,15065]) ).
thf(17175,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk332 ),
inference(pattern_uni,[status(thm)],[17174:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(17181,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk332 ),
inference(simp,[status(thm)],[17175]) ).
thf(64273,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[64101,5003]) ).
thf(64295,plain,
( ( k4_relat_1 @ sk432 )
!= sk332 ),
inference(simp,[status(thm)],[64273]) ).
thf(461,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_partfun1) ).
thf(3708,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(60,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_5) ).
thf(1768,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1769,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ~ ? [B: $i,C: $i] : ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[1768]) ).
thf(1771,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( k4_tarski @ ( sk11 @ A ) @ ( sk12 @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( k3_funct_5 @ A )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1769]) ).
thf(1773,plain,
! [A: $i] :
( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( k4_tarski @ ( sk11 @ A ) @ ( sk12 @ A ) ) @ ( k1_relat_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1771]) ).
thf(9035,plain,
( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[6410,4841]) ).
thf(9039,plain,
sk432 != sk320,
inference(simp,[status(thm)],[9035]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_relat_1) ).
thf(5076,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1376,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(8126,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(110,axiom,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_5) ).
thf(1960,plain,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1961,plain,
( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1960]) ).
thf(1963,plain,
( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1961]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(3557,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1354,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(8031,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(8037,plain,
( ( m1_subset_1 @ sk545 @ f1_s3_funct_2 )
| sk544 ),
inference(cnf,[status(esa)],[8031]) ).
thf(35999,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,31051]) ).
thf(36000,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35999:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(36025,plain,
! [A: $i] : ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[36000]) ).
thf(44626,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,36025]) ).
thf(44627,plain,
v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[44626:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(6025,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( r1_tarski @ ( k2_tarski @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1076,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(6734,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(376,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3229,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(3230,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3229]) ).
thf(3231,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3230]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_partfun1) ).
thf(4302,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
thf(3866,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(5617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_2) ).
thf(7112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1239,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(7500,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_mcart_1) ).
thf(7309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(3533,plain,
v1_relat_1 @ sk164,
inference(cnf,[status(esa)],[3530]) ).
thf(18478,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk164 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3533,1655]) ).
thf(18479,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk164 ) ) @ ( k2_relat_1 @ sk164 ),
inference(pattern_uni,[status(thm)],[18478:[bind(A,$thf( sk164 ))]]) ).
thf(1423,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(8293,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(5974,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1946,plain,
v3_relat_1 @ sk23,
inference(cnf,[status(esa)],[1944]) ).
thf(1396,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
thf(8190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(6840,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1328,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(7894,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(712,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_sysrel) ).
thf(5084,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(5861,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(5856,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1521,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( k3_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_realset1) ).
thf(8659,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( k3_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(122,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_relat_1) ).
thf(2007,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(5682,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1371,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(8109,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_xboole_0 @ A @ B )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_sysrel) ).
thf(2237,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_xboole_0 @ A @ B )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(687,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(4988,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(5264,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(10728,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk424 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10488]) ).
thf(10729,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk424 ),
inference(pattern_uni,[status(thm)],[10728:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1152,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(7107,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k17_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
= A )
& ( ( k18_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
= B )
& ( ( k19_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
= D )
& ( ( k20_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_mcart_1) ).
thf(7144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k17_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
= A )
& ( ( k18_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
= B )
& ( ( k19_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
= D )
& ( ( k20_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ C @ A ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ D ) ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k4_funct_5 @ C ) ) )
& ( ( k1_funct_1 @ ( k4_funct_5 @ C ) @ ( k4_tarski @ A @ B ) )
= ( k1_funct_1 @ D @ B ) )
& ( r2_hidden @ ( k1_funct_1 @ D @ B ) @ ( k2_relat_1 @ ( k4_funct_5 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_5) ).
thf(1707,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ C @ A ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ D ) ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k4_funct_5 @ C ) ) )
& ( ( k1_funct_1 @ ( k4_funct_5 @ C ) @ ( k4_tarski @ A @ B ) )
= ( k1_funct_1 @ D @ B ) )
& ( r2_hidden @ ( k1_funct_1 @ D @ B ) @ ( k2_relat_1 @ ( k4_funct_5 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ( D
!= ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
| ( ( k1_funct_1 @ ( k4_funct_5 @ C ) @ ( k4_tarski @ A @ B ) )
= ( k1_funct_1 @ D @ B ) ) ),
inference(cnf,[status(esa)],[1707]) ).
thf(1713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( k1_funct_1 @ C @ A ) )
| ( ( k1_funct_1 @ ( k4_funct_5 @ C ) @ ( k4_tarski @ A @ B ) )
= ( k1_funct_1 @ D @ B ) )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) ) ),
inference(lifteq,[status(thm)],[1709]) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_funct_1 @ ( k1_funct_1 @ C @ A ) @ B )
= ( k1_funct_1 @ ( k4_funct_5 @ C ) @ ( k4_tarski @ A @ B ) ) )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( v1_funct_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(simp,[status(thm)],[1713]) ).
thf(1463,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_subset_1) ).
thf(8416,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(465,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(3724,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1276,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(7674,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(7676,plain,
v1_relat_1 @ sk527,
inference(cnf,[status(esa)],[7674]) ).
thf(17634,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk527 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7676,1653]) ).
thf(17635,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk527 ) ) @ ( k2_relat_1 @ sk527 ),
inference(pattern_uni,[status(thm)],[17634:[bind(A,$thf( sk527 ))]]) ).
thf(30087,plain,
! [A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,28591]) ).
thf(30088,plain,
v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(pattern_uni,[status(thm)],[30087:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(30943,plain,
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[30088,5002]) ).
thf(30962,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk332 ),
inference(simp,[status(thm)],[30943]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(4600,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1342,axiom,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(7969,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(26915,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s14_funct_2 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk498 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10584]) ).
thf(26916,plain,
( sk497
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk498 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s14_funct_2 ) ),
inference(pattern_uni,[status(thm)],[26915:[bind(A,$thf( sk498 )),bind(B,$thf( sk8 @ sk498 ))]]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_finseq_2) ).
thf(1626,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1628,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_finseq_1 @ D )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ F @ A )
| ~ ( m2_finseq_1 @ G @ B )
| ( ( k3_finseq_1 @ F )
!= ( k3_finseq_1 @ G ) )
| ( D
!= ( k3_funcop_1 @ E @ F @ G ) )
| ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) ) ),
inference(cnf,[status(esa)],[1626]) ).
thf(1631,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ F )
!= ( k3_finseq_1 @ G ) )
| ( D
!= ( k3_funcop_1 @ E @ F @ G ) )
| ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_finseq_1 @ D )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ F @ A )
| ~ ( m2_finseq_1 @ G @ B ) ),
inference(lifteq,[status(thm)],[1628]) ).
thf(1632,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ E )
!= ( k3_finseq_1 @ F ) )
| ( ( k3_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) )
= ( k3_finseq_1 @ E ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_funct_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ E @ A )
| ~ ( m2_finseq_1 @ F @ B ) ),
inference(simp,[status(thm)],[1631]) ).
thf(1512,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(8627,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(26937,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,8792]) ).
thf(26938,plain,
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk3 )
| ( m2_finseq_1 @ ( sk8 @ sk3 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26937:[bind(A,$thf( sk3 )),bind(B,$thf( sk8 @ sk3 ))]]) ).
thf(8925,plain,
( ( v1_xboole_0 @ sk421 )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[6305,4841]) ).
thf(8934,plain,
sk421 != sk320,
inference(simp,[status(thm)],[8925]) ).
thf(1151,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(7104,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_relat_1) ).
thf(2451,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(6135,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(6733,plain,
~ ( v1_xboole_0 @ sk453 ),
inference(cnf,[status(esa)],[6729]) ).
thf(8927,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,6733]) ).
thf(8929,plain,
sk453 != sk421,
inference(simp,[status(thm)],[8927]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(7537,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(527,axiom,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(4147,plain,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_sysrel) ).
thf(3525,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(10487,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,3835]) ).
thf(10489,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk421 ),
inference(simp,[status(thm)],[10487]) ).
thf(10753,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk421 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10489]) ).
thf(10754,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk421 ),
inference(pattern_uni,[status(thm)],[10753:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(10757,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk421 ),
inference(simp,[status(thm)],[10754]) ).
thf(35097,plain,
! [A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,30096]) ).
thf(35098,plain,
v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35097:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(627,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(4724,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1277,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_orders_1) ).
thf(7677,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(699,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(5032,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_finset_1) ).
thf(7532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(15543,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,15520]) ).
thf(15554,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk536 ),
inference(simp,[status(thm)],[15543]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k3_domain_1 @ A @ B @ C )
= ( k2_mcart_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_domain_1) ).
thf(6054,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k3_domain_1 @ A @ B @ C )
= ( k2_mcart_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_5) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_2) ).
thf(4134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(39,axiom,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_1) ).
thf(1676,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1677,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(cnf,[status(esa)],[1676]) ).
thf(25458,plain,
! [A: $i] :
( ( m2_relset_1 @ k1_xboole_0 @ A @ A )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,1677]) ).
thf(25459,plain,
m2_relset_1 @ k1_xboole_0 @ k1_xboole_0 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[25458:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(25516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C )
| ( ( m2_relset_1 @ k1_xboole_0 @ k1_xboole_0 @ k1_xboole_0 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25459,1577]) ).
thf(25517,plain,
( ( k5_relat_1 @ k1_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[25516:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(25584,plain,
( ( k5_relat_1 @ k1_xboole_0 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[25517,2072]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(5805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(669,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(4871,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_2) ).
thf(2555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( ( k15_domain_1 @ A @ B @ C @ D )
= ( k18_mcart_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_domain_1) ).
thf(8511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( ( k15_domain_1 @ A @ B @ C @ D )
= ( k18_mcart_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(649,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(4798,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(493,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(3918,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(3919,plain,
( ! [A: $i] :
( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ! [A: $i] :
( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[3918]) ).
thf(3920,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3919]) ).
thf(3922,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3920]) ).
thf(3923,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3922]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_sysrel) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17861,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk534 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7842,1654]) ).
thf(17862,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk534 ) ) @ ( k1_relat_1 @ sk534 ),
inference(pattern_uni,[status(thm)],[17861:[bind(A,$thf( sk534 ))]]) ).
thf(1159,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(7139,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(8749,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,6733]) ).
thf(8751,plain,
sk453 != k1_xboole_0,
inference(simp,[status(thm)],[8749]) ).
thf(49337,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk453 ) ),
inference(paramod_ordered,[status(thm)],[3513,8751]) ).
thf(49338,plain,
v1_funct_1 @ ( sk161 @ sk453 ),
inference(pattern_uni,[status(thm)],[49337:[bind(A,$thf( sk453 ))]]) ).
thf(645,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(4783,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2073,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1523,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(8664,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(4162,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(5834,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(4842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(161,axiom,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(2189,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(2190,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[2189]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_partfun1) ).
thf(4307,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(657,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(4825,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1359,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(8050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(2964,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_rlvect_1 @ A @ B @ C )
= ( g1_rlvect_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_rlvect_1) ).
thf(6591,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_rlvect_1 @ A @ B @ C )
= ( g1_rlvect_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(4751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) )
=> ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(11157,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk560 @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8301,8825]) ).
thf(11163,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk560 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(simp,[status(thm)],[11157]) ).
thf(11169,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk560 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(simp,[status(thm)],[11163]) ).
thf(24828,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk560 )
| ( sk3 != f1_s3_subset_1 ) ),
inference(simp,[status(thm)],[11169]) ).
thf(26973,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk3 != f1_s3_subset_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk560 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,24828]) ).
thf(26974,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk560 ) @ sk1 )
| ( sk3 != f1_s3_subset_1 ) ),
inference(pattern_uni,[status(thm)],[26973:[bind(A,$thf( sk560 )),bind(B,$thf( sk8 @ sk560 ))]]) ).
thf(1419,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(8274,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(15487,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[4373,4841]) ).
thf(15494,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk320 ),
inference(simp,[status(thm)],[15487]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_partfun1) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1139,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7036,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1060,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(6648,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(5773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(356,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(3068,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(542,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ( ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_mcart_1) ).
thf(4230,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ( ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(8841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_finseq_1 @ C @ B )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ D @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( ( m2_finseq_1 @ C @ A )
!= ( m2_finseq_1 @ D @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1558,8794]) ).
thf(8842,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk5 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8841:[bind(A,$thf( sk5 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(8847,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk5 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[8842]) ).
thf(9555,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( ( m1_subset_1 @ sk4 @ ( k1_zfmisc_1 @ sk1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1545,8847]) ).
thf(9590,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk4 != A )
| ( ( k1_zfmisc_1 @ sk5 )
!= ( k1_zfmisc_1 @ sk1 ) ) ),
inference(simp,[status(thm)],[9555]) ).
thf(9616,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ A @ sk4 )
| ( ( k1_zfmisc_1 @ sk5 )
!= ( k1_zfmisc_1 @ sk1 ) ) ),
inference(simp,[status(thm)],[9590]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_relat_1) ).
thf(4033,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1259,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(7613,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(5401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(185,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_sysrel) ).
thf(2281,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_2) ).
thf(6110,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(230,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(2483,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1737,plain,
! [A: $i] : ( v3_relat_2 @ ( k6_partfun1 @ A ) ),
inference(cnf,[status(esa)],[1733]) ).
thf(11876,plain,
! [A: $i] : ( v3_relat_2 @ ( k6_relat_1 @ A ) ),
inference(rewrite,[status(thm)],[1737,1580]) ).
thf(8814,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,7843]) ).
thf(8817,plain,
sk534 != sk275,
inference(simp,[status(thm)],[8814]) ).
thf(9445,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[7899,4841]) ).
thf(9452,plain,
sk536 != sk320,
inference(simp,[status(thm)],[9445]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(6947,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(11139,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8237,8825]) ).
thf(11143,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( a_0_0_domain_1 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(simp,[status(thm)],[11139]) ).
thf(11150,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_0_domain_1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(simp,[status(thm)],[11143]) ).
thf(18097,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_0_domain_1 )
| ( sk3 != f1_s7_domain_1 ) ),
inference(simp,[status(thm)],[11150]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_partfun1) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(26925,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk560 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11168]) ).
thf(26926,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk560 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[26925:[bind(A,$thf( sk560 )),bind(B,$thf( sk8 @ sk560 ))]]) ).
thf(1619,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( A != k1_xboole_0 )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(cnf,[status(esa)],[1618]) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(lifteq,[status(thm)],[1619]) ).
thf(1622,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ k1_xboole_0 @ A )
| ~ ( m2_relset_1 @ B @ k1_xboole_0 @ A )
| ( v1_partfun1 @ ( k3_partfun1 @ B @ k1_xboole_0 @ A ) @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[1621]) ).
thf(1002,axiom,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k2_xboole_0 @ A @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k2_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_setfam_1) ).
thf(6347,plain,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k2_xboole_0 @ A @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k2_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_relat_1) ).
thf(4996,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(5296,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_mcart_1) ).
thf(4040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
& ( ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(121,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_sysrel) ).
thf(2002,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(467,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3740,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(3741,plain,
~ ? [A: $i,B: $i] :
( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[3740]) ).
thf(3743,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( B
= ( k1_relat_1 @ ( sk184 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[3741]) ).
thf(3755,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k1_relat_1 @ ( sk184 @ B @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[3743]) ).
thf(3756,plain,
! [A: $i] :
( ( k1_relat_1 @ ( sk184 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3755]) ).
thf(503,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(3955,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(6991,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(6992,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[6991]) ).
thf(6993,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[6992]) ).
thf(42031,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,6993]) ).
thf(42052,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk432 ),
inference(simp,[status(thm)],[42031]) ).
thf(32803,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,32739]) ).
thf(32806,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk424 ),
inference(simp,[status(thm)],[32803]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(187,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2286,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1311,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(7830,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(957,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(6156,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1598,plain,
! [B: $i,A: $i] :
( ~ ( m2_relset_1 @ B @ A @ A )
| ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(cnf,[status(esa)],[1596]) ).
thf(1600,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ~ ( m2_relset_1 @ B @ A @ A ) ),
inference(lifteq,[status(thm)],[1598]) ).
thf(720,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(5137,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(4379,plain,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(49339,plain,
! [B: $i,A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3513,10494]) ).
thf(49340,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[49339:[bind(A,$thf( k1_tarski @ C )),bind(B,$thf( C ))]]) ).
thf(51989,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[49340]) ).
thf(437,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_partfun1) ).
thf(3559,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(5819,plain,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1366,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(8094,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(153,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ A )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_sysrel) ).
thf(2154,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ A )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(5824,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(6103,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(5328,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(4211,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(10483,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,3835]) ).
thf(10493,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk42 ),
inference(simp,[status(thm)],[10483]) ).
thf(12305,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk42 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10493]) ).
thf(12306,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk42 ),
inference(pattern_uni,[status(thm)],[12305:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(9012,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,7843]) ).
thf(9024,plain,
sk534 != sk424,
inference(simp,[status(thm)],[9012]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2586,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_2) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4065,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(843,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(5695,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(7,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_5) ).
thf(1562,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1564,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ),
inference(cnf,[status(esa)],[1562]) ).
thf(8739,plain,
( ( v1_xboole_0 @ sk332 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,5003]) ).
thf(8742,plain,
sk332 != sk42,
inference(simp,[status(thm)],[8739]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2762,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(8421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(5298,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(1604,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1322,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(7859,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(5968,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(3679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(5174,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(911,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(5961,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1182,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(7254,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(8170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(64098,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7899,1794]) ).
thf(64099,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[64098:[bind(A,$thf( sk536 ))]]) ).
thf(64217,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk453 ) ),
inference(paramod_ordered,[status(thm)],[64099,6733]) ).
thf(64227,plain,
( ( k4_relat_1 @ sk536 )
!= sk453 ),
inference(simp,[status(thm)],[64217]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(5406,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_funct_1) ).
thf(3591,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1299,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k2_domain_1 @ A @ B @ C )
= ( k1_mcart_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_domain_1) ).
thf(7782,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k2_domain_1 @ A @ B @ C )
= ( k1_mcart_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2204,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(7471,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(61572,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk534 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7842,1789]) ).
thf(61573,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk534 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk534 ) ),
inference(pattern_uni,[status(thm)],[61572:[bind(A,$thf( sk534 ))]]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_2) ).
thf(4589,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1517,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(8640,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(227,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_partfun1) ).
thf(2473,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1358,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m3_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_realset1) ).
thf(8046,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m3_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(438,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(3567,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( A
!= ( k1_mcart_1 @ A ) )
& ( A
!= ( k2_mcart_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_mcart_1) ).
thf(7022,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( A
!= ( k1_mcart_1 @ A ) )
& ( A
!= ( k2_mcart_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1426,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relset_2) ).
thf(8302,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(6015,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk401 @ B @ A ) ),
inference(cnf,[status(esa)],[6013]) ).
thf(463,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(3720,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(6731,plain,
v1_funct_1 @ sk453,
inference(cnf,[status(esa)],[6729]) ).
thf(16639,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk432 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,11211]) ).
thf(16640,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk432 ),
inference(pattern_uni,[status(thm)],[16639:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16644,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk432 ),
inference(simp,[status(thm)],[16640]) ).
thf(29486,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk432 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16644]) ).
thf(29487,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk432 ),
inference(pattern_uni,[status(thm)],[29486:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(29499,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk432 ),
inference(simp,[status(thm)],[29487]) ).
thf(1413,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(8243,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(507,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(3984,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(3265,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(6047,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(10498,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,5927]) ).
thf(10506,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk275 ),
inference(simp,[status(thm)],[10498]) ).
thf(1309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
<=> ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_mcart_1) ).
thf(7814,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
=> ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 ) )
& ( ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 )
=> ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(3531,plain,
v2_funct_1 @ sk164,
inference(cnf,[status(esa)],[3530]) ).
thf(1452,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).
thf(8382,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k4_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k1_setfam_1 @ ( k4_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_setfam_1) ).
thf(5443,plain,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k4_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k1_setfam_1 @ ( k4_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(7217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1547,plain,
( ( k8_relset_2 @ sk1 @ sk2 @ ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( k8_relset_2 @ sk1 @ sk2 @ sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[1543]) ).
thf(1550,plain,
( ( k8_relset_2 @ sk1 @ sk2 @ ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( k8_relset_2 @ sk1 @ sk2 @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[1547]) ).
thf(8736,plain,
( ( sk1 != sk1 )
| ( sk2 != sk2 )
| ( ( k4_subset_1 @ sk1 @ sk3 @ sk4 )
!= sk4 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[1550]) ).
thf(8737,plain,
( ( k4_subset_1 @ sk1 @ sk3 @ sk4 )
!= sk4 ),
inference(simp,[status(thm)],[8736]) ).
thf(51644,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( sk4 != k1_xboole_0 )
| ( A
!= ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3513,8737]) ).
thf(51645,plain,
( ( v1_funct_1 @ ( sk161 @ ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) ) )
| ( sk4 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[51644:[bind(A,$thf( k4_subset_1 @ sk1 @ sk3 @ sk4 ))]]) ).
thf(61291,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( v1_funct_1 @ ( sk161 @ ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) ) )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[3513,51645]) ).
thf(61292,plain,
( ( v1_funct_1 @ ( sk161 @ sk4 ) )
| ( v1_funct_1 @ ( sk161 @ ( k4_subset_1 @ sk1 @ sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[61291:[bind(A,$thf( sk4 ))]]) ).
thf(12424,plain,
! [A: $i] :
( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,3474]) ).
thf(12425,plain,
v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12424:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1335,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(7937,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(1457,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(8397,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_relat_1) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( r2_tarski @ A @ B )
<=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( D = F )
<=> ( E = G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).
thf(3995,plain,
! [A: $i,B: $i] :
( ( ( r2_tarski @ A @ B )
=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) )
=> ( r2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1208,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(7357,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
& ( v2_funct_1 @ C ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_2) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
& ( v2_funct_1 @ C ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ B @ A )
| ~ ( m2_relset_1 @ D @ B @ A )
| ( ( k2_relat_1 @ C )
!= B )
| ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
!= ( k6_partfun1 @ A ) )
| ~ ( v2_funct_1 @ C )
| ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ),
inference(cnf,[status(esa)],[1611]) ).
thf(1613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k2_relat_1 @ C )
!= B )
| ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
!= ( k6_partfun1 @ A ) )
| ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ B @ A )
| ~ ( m2_relset_1 @ D @ B @ A )
| ~ ( v2_funct_1 @ C ) ),
inference(lifteq,[status(thm)],[1612]) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_partfun1 @ A @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ B ) @ A @ B @ C )
!= ( k6_partfun1 @ A ) )
| ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ B )
= k1_xboole_0 )
| ( C
= ( k2_funct_1 @ B ) )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ A @ ( k2_relat_1 @ B ) )
| ~ ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_relat_1 @ B ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_relat_1 @ B ) @ A )
| ~ ( v2_funct_1 @ B ) ),
inference(simp,[status(thm)],[1613]) ).
thf(12068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_partfun1 @ A @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ B ) @ A @ B @ C )
!= ( k6_relat_1 @ A ) )
| ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ B )
= k1_xboole_0 )
| ( C
= ( k2_funct_1 @ B ) )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ A @ ( k2_relat_1 @ B ) )
| ~ ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_relat_1 @ B ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_relat_1 @ B ) @ A )
| ~ ( v2_funct_1 @ B ) ),
inference(rewrite,[status(thm)],[1614,1580]) ).
thf(6307,plain,
v1_funct_1 @ sk421,
inference(cnf,[status(esa)],[6302]) ).
thf(189,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_funct_5) ).
thf(2296,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(3054,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(2641,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_1) ).
thf(5519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(6741,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(2496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(4312,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(9033,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,6907]) ).
thf(9041,plain,
sk465 != sk432,
inference(simp,[status(thm)],[9033]) ).
thf(1524,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(8668,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(9034,plain,
( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[6410,5003]) ).
thf(9043,plain,
sk432 != sk332,
inference(simp,[status(thm)],[9034]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_mcart_1) ).
thf(2773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(7900,plain,
v1_relat_1 @ sk536,
inference(cnf,[status(esa)],[7897]) ).
thf(17641,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk536 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7900,1653]) ).
thf(17642,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk536 ) ) @ ( k2_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[17641:[bind(A,$thf( sk536 ))]]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_sysrel) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1635]) ).
thf(716,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(5122,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1540,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(8712,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ D ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_mcart_1) ).
thf(7439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ D ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1723,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ ( sk10 @ A ) ) )
| ( v3_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1721]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(5734,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) )
=> ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(6605,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(2606,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r1_tarski @ ( k4_card_3 @ C ) @ ( k4_card_3 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pua2mss1) ).
thf(2015,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r1_tarski @ ( k4_card_3 @ C ) @ ( k4_card_3 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(181,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_sysrel) ).
thf(2264,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(42030,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,6993]) ).
thf(42051,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk536 ),
inference(simp,[status(thm)],[42030]) ).
thf(950,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(6120,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(6121,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[6120]) ).
thf(6122,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[6121]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(5630,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).
thf(2805,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(199,axiom,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(2354,plain,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(2355,plain,
! [A: $i] : ( m2_pua2mss1 @ ( sk40 @ A ) @ A ),
inference(cnf,[status(esa)],[2354]) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ~ ( m2_pua2mss1 @ B @ A )
| ( v1_funct_1 @ B ) ),
inference(cnf,[status(esa)],[1559]) ).
thf(38291,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_funct_1 @ C )
| ( ( m2_pua2mss1 @ ( sk40 @ A ) @ A )
!= ( m2_pua2mss1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2355,1561]) ).
thf(38292,plain,
! [A: $i] : ( v1_funct_1 @ ( sk40 @ A ) ),
inference(pattern_uni,[status(thm)],[38291:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk40 @ D ))]]) ).
thf(38295,plain,
! [A: $i] : ( v1_funct_1 @ ( sk40 @ A ) ),
inference(simp,[status(thm)],[38292]) ).
thf(40246,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,4671]) ).
thf(40262,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk536 ),
inference(simp,[status(thm)],[40246]) ).
thf(1364,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(8090,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(8091,plain,
! [A: $i] : ( m1_eqrel_1 @ ( sk548 @ A ) @ A ),
inference(cnf,[status(esa)],[8090]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_finseq_2) ).
thf(2596,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1435,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(8329,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(577,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k5_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(4397,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k5_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1310,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(7827,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(7353,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(982,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
=> ( ( m1_orders_1 @ B @ A )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_orders_1) ).
thf(6264,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
=> ( ( ( m1_orders_1 @ B @ A )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) )
=> ( m1_orders_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(51590,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A
!= ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3513,1546]) ).
thf(51591,plain,
( ( v1_funct_1 @ ( sk161 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[51590:[bind(A,$thf( k2_zfmisc_1 @ sk1 @ sk2 ))]]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(5512,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(18470,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk275 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4437,1655]) ).
thf(18471,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk275 ) ) @ ( k2_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[18470:[bind(A,$thf( sk275 ))]]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k3_relset_2 @ A @ B @ C @ D )
= ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relset_2) ).
thf(5455,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k3_relset_2 @ A @ B @ C @ D )
= ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(24766,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,24716]) ).
thf(24775,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk421 ),
inference(simp,[status(thm)],[24766]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(6565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(341,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(2969,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(565,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4344,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(30039,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk332 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,17181]) ).
thf(30040,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk332 ),
inference(pattern_uni,[status(thm)],[30039:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(30054,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk332 ),
inference(simp,[status(thm)],[30040]) ).
thf(3742,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk184 @ B @ A ) ) ),
inference(cnf,[status(esa)],[3741]) ).
thf(3751,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk184 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[3742]) ).
thf(3752,plain,
! [A: $i] : ( v1_funct_1 @ ( sk184 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[3751]) ).
thf(1436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_domain_1) ).
thf(8334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(535,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
= ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t189_relat_1) ).
thf(4204,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
= ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(64178,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[64099,6285]) ).
thf(64230,plain,
( ( k4_relat_1 @ sk536 )
!= sk420 ),
inference(simp,[status(thm)],[64178]) ).
thf(439,axiom,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_5) ).
thf(3570,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(3571,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3570]) ).
thf(3572,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3571]) ).
thf(17193,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[3572,8184]) ).
thf(1266,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(7640,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_5) ).
thf(4493,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_partfun1) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(3816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1348,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( r1_tarski @ ( k2_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) @ ( k1_setfam_1 @ ( k2_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_setfam_1) ).
thf(7984,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( r1_tarski @ ( k2_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) @ ( k1_setfam_1 @ ( k2_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(6496,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(5396,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(962,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_domain_1) ).
thf(6178,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_partfun1) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( ( k3_zfmisc_1 @ A @ B @ C )
= k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_mcart_1) ).
thf(5843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( ( k3_zfmisc_1 @ A @ B @ C )
= k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(7301,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1338,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(7957,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(8744,plain,
( ( v1_xboole_0 @ sk420 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,6285]) ).
thf(8746,plain,
sk420 != sk42,
inference(simp,[status(thm)],[8744]) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ~ ( m2_pua2mss1 @ B @ A )
| ( v1_relat_1 @ B ) ),
inference(cnf,[status(esa)],[1559]) ).
thf(1510,axiom,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_setfam_1) ).
thf(8623,plain,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1307,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(7806,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(7807,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[7806]) ).
thf(7808,plain,
~ ( v1_xboole_0 @ sk533 ),
inference(cnf,[status(esa)],[7807]) ).
thf(9446,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[7899,7808]) ).
thf(9455,plain,
sk536 != sk533,
inference(simp,[status(thm)],[9446]) ).
thf(65,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_1 @ A )
<=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_relat_1) ).
thf(1785,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_1 @ A )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) )
& ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1786,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v3_relat_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(59326,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v3_relat_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(rewrite,[status(thm)],[1786,8184]) ).
thf(698,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( k1_mcart_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(5021,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ! [B: $i] :
( ( ( B
= ( k1_mcart_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = C ) ) )
& ( ! [C: $i,D: $i] :
( ( A
= ( k4_tarski @ C @ D ) )
=> ( B = C ) )
=> ( B
= ( k1_mcart_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(4746,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(6096,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1296,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k1_tarski @ C ) )
=> ( ( k8_setfam_1 @ A @ B )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(7767,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k1_tarski @ C ) )
=> ( ( k8_setfam_1 @ A @ B )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(5769,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(384,axiom,
! [A: $i,B: $i] : ( r2_setfam_1 @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_setfam_1) ).
thf(3270,plain,
! [A: $i] : ( r2_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(3271,plain,
! [A: $i] : ( r2_setfam_1 @ A @ A ),
inference(cnf,[status(esa)],[3270]) ).
thf(504,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(3958,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1178,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(7237,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(6303,plain,
v1_finset_1 @ sk421,
inference(cnf,[status(esa)],[6302]) ).
thf(8803,plain,
( ( v1_xboole_0 @ sk420 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,6285]) ).
thf(8810,plain,
sk420 != sk275,
inference(simp,[status(thm)],[8803]) ).
thf(1345,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(7977,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_relat_1) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(8251,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk557 @ f4_s11_funct_2 )
= f6_s11_funct_2 ) ),
inference(cnf,[status(esa)],[8246]) ).
thf(8255,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk557 @ f4_s11_funct_2 )
= f6_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[8251]) ).
thf(891,axiom,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(5879,plain,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(10755,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk421 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10489]) ).
thf(10756,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk421 ),
inference(pattern_uni,[status(thm)],[10755:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(918,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k4_funcop_1 @ E @ ( k6_finseq_1 @ A ) @ D )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_finseq_2) ).
thf(5983,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k4_funcop_1 @ E @ ( k6_finseq_1 @ A ) @ D )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(4140,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_relat_1) ).
thf(4849,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1448,axiom,
! [A: $i] :
( ( k1_eqrel_1 @ A )
= ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_eqrel_1) ).
thf(8371,plain,
! [A: $i] :
( ( k1_eqrel_1 @ A )
= ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(5465,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1253,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(7576,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(606,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(4585,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(2433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_partfun1) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(2565,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(8815,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,7843]) ).
thf(8818,plain,
sk534 != k1_xboole_0,
inference(simp,[status(thm)],[8815]) ).
thf(51928,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk534 ) ),
inference(paramod_ordered,[status(thm)],[3513,8818]) ).
thf(51929,plain,
v1_funct_1 @ ( sk161 @ sk534 ),
inference(pattern_uni,[status(thm)],[51928:[bind(A,$thf( sk534 ))]]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(6427,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_mcart_1) ).
thf(2663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_domain_1) ).
thf(7449,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) )
=> ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(689,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(4994,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_sysrel) ).
thf(4947,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(46962,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,46908]) ).
thf(47002,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk432 ),
inference(simp,[status(thm)],[46962]) ).
thf(841,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5690,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(17605,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk283 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4511,1653]) ).
thf(17606,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk283 ) ) @ ( k2_relat_1 @ sk283 ),
inference(pattern_uni,[status(thm)],[17605:[bind(A,$thf( sk283 ))]]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
& ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_sysrel) ).
thf(1888,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
& ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(605,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(4553,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(7503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_setfam_1) ).
thf(6708,plain,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(4776,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v2_funct_1 @ C )
| ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ),
inference(cnf,[status(esa)],[1686]) ).
thf(137,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2068,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ~ ( v3_relat_1 @ ( k7_relat_1 @ B @ A ) )
& ( v3_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t190_relat_1) ).
thf(1624,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ~ ( v3_relat_1 @ ( k7_relat_1 @ B @ A ) )
& ( v3_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1334,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(7934,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(12303,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk42 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10493]) ).
thf(12304,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk42 ),
inference(pattern_uni,[status(thm)],[12303:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(12307,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
!= sk42 ),
inference(simp,[status(thm)],[12304]) ).
thf(16876,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk42 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,12307]) ).
thf(16877,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk42 ),
inference(pattern_uni,[status(thm)],[16876:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16883,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk42 ),
inference(simp,[status(thm)],[16877]) ).
thf(29967,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk42 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16883]) ).
thf(29968,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk42 ),
inference(pattern_uni,[status(thm)],[29967:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(29981,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk42 ),
inference(simp,[status(thm)],[29968]) ).
thf(886,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_orders_1) ).
thf(5858,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(7891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1405,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(8226,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(2739,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2737]) ).
thf(2741,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2739]) ).
thf(1422,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(8287,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(64347,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk275 ) )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[64108,7808]) ).
thf(64350,plain,
( ( k4_relat_1 @ sk275 )
!= sk533 ),
inference(simp,[status(thm)],[64347]) ).
thf(1634,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1633]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_partfun1) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5936,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(170,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_sysrel) ).
thf(2228,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( v3_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v8_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v1_partfun1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A )
& ( m2_relset_1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_eqrel_1) ).
thf(3931,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( v3_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v8_relat_2 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) )
& ( v1_partfun1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A )
& ( m2_relset_1 @ ( k6_setfam_1 @ ( k2_zfmisc_1 @ A @ A ) @ B ) @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(350,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ D @ C ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_orders_1) ).
thf(3033,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ D @ C ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t163_relat_1) ).
thf(1573,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_finseq_2) ).
thf(3799,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_relat_1) ).
thf(5066,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1383,axiom,
! [A: $i,B: $i] : ( r1_setfam_1 @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_setfam_1) ).
thf(8155,plain,
! [A: $i] : ( r1_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_2) ).
thf(4063,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(2653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_partfun1) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).
thf(3060,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) ) )
& ( ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(16892,plain,
! [A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,12427]) ).
thf(16893,plain,
v1_realset1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16892:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(46972,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,46908]) ).
thf(46992,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk42 ),
inference(simp,[status(thm)],[46972]) ).
thf(15550,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,15520]) ).
thf(15559,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk424 ),
inference(simp,[status(thm)],[15550]) ).
thf(1411,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(8238,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(7540,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_relat_1) ).
thf(4808,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_1) ).
thf(5313,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
=> ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(1089,axiom,
! [A: $i,B: $i] :
( ( ( k3_zfmisc_1 @ A @ A @ A )
= ( k3_zfmisc_1 @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_mcart_1) ).
thf(6795,plain,
! [A: $i,B: $i] :
( ( ( k3_zfmisc_1 @ A @ A @ A )
= ( k3_zfmisc_1 @ B @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(175,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
thf(2245,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(830,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(5624,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(5625,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[5624]) ).
thf(5626,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[5625]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(7281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
=> ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(5904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1473,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_1_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(8446,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_1_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_1_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
thf(6677,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(16908,plain,
( ( v1_realset1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[16893,5002]) ).
thf(16910,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk332 ),
inference(simp,[status(thm)],[16908]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ A @ B @ C )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(5609,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ A @ B @ C )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(17313,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk527 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7676,1652]) ).
thf(17314,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk527 ) ) @ ( k1_relat_1 @ sk527 ),
inference(pattern_uni,[status(thm)],[17313:[bind(A,$thf( sk527 ))]]) ).
thf(42037,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,6993]) ).
thf(42045,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk42 ),
inference(simp,[status(thm)],[42037]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_partfun1) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(2515,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(380,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_relat_1) ).
thf(3254,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(944,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(6101,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(84,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(1851,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1770,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( k4_tarski @ ( sk11 @ A ) @ ( sk12 @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1769]) ).
thf(1772,plain,
! [A: $i] :
( ( ( k5_funct_5 @ A )
= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( k4_tarski @ ( sk11 @ A ) @ ( sk12 @ A ) ) @ ( k1_relat_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1770]) ).
thf(333,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(2946,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(2990,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(8252,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( m2_relset_1 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(cnf,[status(esa)],[8246]) ).
thf(8253,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( m2_relset_1 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[8252]) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
inference(cnf,[status(esa)],[1762]) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C )
| ~ ( m2_relset_1 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1763]) ).
thf(44720,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C )
| ( ( m2_relset_1 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8253,1764]) ).
thf(44721,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k5_relat_1 @ ( k6_relat_1 @ f1_s11_funct_2 ) @ sk557 )
= sk557 ) ),
inference(pattern_uni,[status(thm)],[44720:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk557 ))]]) ).
thf(1117,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v3_relat_2 @ A )
& ( v3_relat_2 @ B ) )
=> ( ( v3_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v3_relat_2 @ ( k3_xboole_0 @ A @ B ) )
& ( v3_relat_2 @ ( k4_xboole_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_relat_2) ).
thf(6940,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v3_relat_2 @ A )
& ( v3_relat_2 @ B ) )
=> ( ( v3_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v3_relat_2 @ ( k3_xboole_0 @ A @ B ) )
& ( v3_relat_2 @ ( k4_xboole_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1339,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(7960,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(7961,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[7960]) ).
thf(7962,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[7961]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(6153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(4512,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(282,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_partfun1) ).
thf(2685,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(5006,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(8558,plain,
( sk570
| ( r2_hidden @ sk572 @ f3_s4_subset_1 )
| ( p1_s4_subset_1 @ sk572 )
| ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(cnf,[status(esa)],[8551]) ).
thf(8562,plain,
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk570
| ( r2_hidden @ sk572 @ f3_s4_subset_1 )
| ( p1_s4_subset_1 @ sk572 ) ),
inference(lifteq,[status(thm)],[8558]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4248,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(826,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(5615,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(6195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(8282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(201,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_relat_1) ).
thf(2359,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1438,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(8339,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(6603,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1787,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
| ( v3_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(60521,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( v3_relat_1 @ A ) ),
inference(rewrite,[status(thm)],[1787,8184]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(5635,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(6459,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(4789,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
thf(1856,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(24764,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4373,24716]) ).
thf(24771,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(simp,[status(thm)],[24764]) ).
thf(1314,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
<=> ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(7838,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
=> ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(8923,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,7843]) ).
thf(8931,plain,
sk534 != sk421,
inference(simp,[status(thm)],[8923]) ).
thf(1356,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(8041,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(8619,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(2509,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1350,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(8014,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(3518,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(8774,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,7808]) ).
thf(8776,plain,
sk533 != k1_xboole_0,
inference(simp,[status(thm)],[8774]) ).
thf(50739,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk533 ) ),
inference(paramod_ordered,[status(thm)],[3513,8776]) ).
thf(50740,plain,
v1_funct_1 @ ( sk161 @ sk533 ),
inference(pattern_uni,[status(thm)],[50739:[bind(A,$thf( sk533 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(1878,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_2) ).
thf(2631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(4930,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_finseq_2) ).
thf(1719,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(4227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1395,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_domain_1) ).
thf(8187,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1515,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
thf(8636,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(5811,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1006,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(6360,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(1121,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(6958,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relset_2) ).
thf(8429,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_sysrel) ).
thf(5081,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1496,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
<=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_2) ).
thf(8572,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1522,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_mcart_1) ).
thf(8662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(735,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(5233,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( ( ( k2_mcart_1 @ A )
= C )
| ( ( k2_mcart_1 @ A )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_mcart_1) ).
thf(7809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( ( ( k2_mcart_1 @ A )
= C )
| ( ( k2_mcart_1 @ A )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(5687,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1379,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(8138,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(803,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(5475,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(40230,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,3314]) ).
thf(40237,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk421 ),
inference(simp,[status(thm)],[40230]) ).
thf(7898,plain,
v1_funct_1 @ sk536,
inference(cnf,[status(esa)],[7897]) ).
thf(196,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k1_funcop_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ! [D: $i,E: $i] :
( ( ( k1_funct_1 @ A @ C )
= ( k4_tarski @ D @ E ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k4_tarski @ E @ D ) ) )
& ~ ( ( ( k1_funct_1 @ A @ C )
!= ( k1_funct_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k1_funct_1 @ A @ C )
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funcop_1) ).
thf(2323,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k1_funcop_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ! [D: $i,E: $i] :
( ( ( k1_funct_1 @ A @ C )
= ( k4_tarski @ D @ E ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k4_tarski @ E @ D ) ) )
& ~ ( ( ( k1_funct_1 @ A @ C )
!= ( k1_funct_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k1_funct_1 @ A @ C )
!= ( k4_tarski @ D @ E ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ! [D: $i,E: $i] :
( ( ( k1_funct_1 @ A @ C )
= ( k4_tarski @ D @ E ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k4_tarski @ E @ D ) ) )
& ~ ( ( ( k1_funct_1 @ A @ C )
!= ( k1_funct_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k1_funct_1 @ A @ C )
!= ( k4_tarski @ D @ E ) ) ) ) ) )
=> ( B
= ( k1_funcop_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(6304,plain,
v2_funct_1 @ sk421,
inference(cnf,[status(esa)],[6302]) ).
thf(15483,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk534 ) ),
inference(paramod_ordered,[status(thm)],[4373,7843]) ).
thf(15495,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk534 ),
inference(simp,[status(thm)],[15483]) ).
thf(9062,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ sk3 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ C @ sk1 )
| ( ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( m2_finseq_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8794,8825]) ).
thf(9063,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ sk3 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9062:[bind(A,$thf( A )),bind(B,$thf( k2_zfmisc_1 @ sk1 @ sk2 )),bind(C,$thf( A ))]]) ).
thf(9085,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk3 )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ sk3 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(simp,[status(thm)],[9063]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(2978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_2) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(12044,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk536 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10492]) ).
thf(12045,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk536 ),
inference(pattern_uni,[status(thm)],[12044:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(989,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(6299,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_sysrel) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1150,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(7101,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(4333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(6862,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(64180,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[64099,6046]) ).
thf(64235,plain,
( ( k4_relat_1 @ sk536 )
!= sk404 ),
inference(simp,[status(thm)],[64180]) ).
thf(1537,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(8704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(64138,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk421 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6305,1794]) ).
thf(64139,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk421 ),
inference(pattern_uni,[status(thm)],[64138:[bind(A,$thf( sk421 ))]]) ).
thf(1513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(8631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(17889,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk527 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7676,1654]) ).
thf(17890,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk527 ) ) @ ( k1_relat_1 @ sk527 ),
inference(pattern_uni,[status(thm)],[17889:[bind(A,$thf( sk527 ))]]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(6175,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1962,plain,
( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1960]) ).
thf(1964,plain,
( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1962]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_sysrel) ).
thf(1942,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(5915,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(485,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ( ( A
!= ( k1_mcart_1 @ A ) )
& ( A
!= ( k2_mcart_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_mcart_1) ).
thf(3846,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( k4_tarski @ B @ C ) )
=> ( ( A
!= ( k1_mcart_1 @ A ) )
& ( A
!= ( k2_mcart_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(8938,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[8880]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(5181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(2275,plain,
v1_relat_1 @ sk34,
inference(cnf,[status(esa)],[2272]) ).
thf(17618,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk34 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2275,1653]) ).
thf(17619,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk34 ) ) @ ( k2_relat_1 @ sk34 ),
inference(pattern_uni,[status(thm)],[17618:[bind(A,$thf( sk34 ))]]) ).
thf(1284,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
& ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_pboole) ).
thf(7717,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
& ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(6720,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(29371,plain,
! [B: $i,A: $i] :
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk570
| ( p1_s4_subset_1 @ sk572 )
| ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B )
| ( ( r2_hidden @ sk572 @ f3_s4_subset_1 )
!= ( r2_hidden @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8562,29362]) ).
thf(29372,plain,
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk570
| ( p1_s4_subset_1 @ sk572 )
| ( ( k1_funct_1 @ ( k6_relat_1 @ f3_s4_subset_1 ) @ sk572 )
= sk572 ) ),
inference(pattern_uni,[status(thm)],[29371:[bind(A,$thf( f3_s4_subset_1 )),bind(B,$thf( sk572 ))]]) ).
thf(1317,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_domain_1) ).
thf(7846,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1347,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_2) ).
thf(7981,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(8644,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[8643]) ).
thf(8647,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8644]) ).
thf(8648,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8647]) ).
thf(16315,plain,
! [A: $i] :
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
!= ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8648,1546]) ).
thf(16332,plain,
! [A: $i] :
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( sk1 != k1_xboole_0 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[16315]) ).
thf(16348,plain,
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16332]) ).
thf(357,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3094,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(17894,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk465 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6911,1654]) ).
thf(17895,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk465 ) ) @ ( k1_relat_1 @ sk465 ),
inference(pattern_uni,[status(thm)],[17894:[bind(A,$thf( sk465 ))]]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_mcart_1) ).
thf(5992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1485,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_relset_2) ).
thf(8499,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) )
& ( ( ( k3_pua2mss1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(8500,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) )
& ! [A: $i] :
( ( ( k3_pua2mss1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[8499]) ).
thf(8502,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[8500]) ).
thf(8505,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8502]) ).
thf(8506,plain,
( ( k3_pua2mss1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8505]) ).
thf(10527,plain,
( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ sk1 ) @ sk2 @ ( k6_relset_2 @ sk2 @ sk1 @ sk5 ) @ k1_xboole_0 )
= k1_xboole_0 )
| ( ( k3_pua2mss1 @ sk3 )
!= ( k3_pua2mss1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[8506,1549]) ).
thf(10528,plain,
( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ sk1 ) @ sk2 @ ( k6_relset_2 @ sk2 @ sk1 @ sk5 ) @ k1_xboole_0 )
= k1_xboole_0 )
| ( sk3 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10527]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(3714,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(6363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1196,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(7318,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(8740,plain,
( ( v1_xboole_0 @ sk320 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,4841]) ).
thf(8743,plain,
sk320 != sk42,
inference(simp,[status(thm)],[8740]) ).
thf(1531,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(8687,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(163,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(2196,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_sysrel) ).
thf(2240,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(13954,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk465 ) ),
inference(paramod_ordered,[status(thm)],[8233,6907]) ).
thf(13964,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk465 ),
inference(simp,[status(thm)],[13954]) ).
thf(1377,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(8132,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(6630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(102,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_sysrel @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_sysrel) ).
thf(1937,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_sysrel @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(7930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1238,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(7480,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(7059,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(447,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3643,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(6945,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[6944]) ).
thf(6946,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[6945]) ).
thf(64206,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk465 ) ),
inference(paramod_ordered,[status(thm)],[64099,6907]) ).
thf(64220,plain,
( ( k4_relat_1 @ sk536 )
!= sk465 ),
inference(simp,[status(thm)],[64206]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_partfun1) ).
thf(2666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(6625,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(10739,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8231,8825]) ).
thf(10747,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( a_0_2_domain_1 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(simp,[status(thm)],[10739]) ).
thf(10752,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_2_domain_1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(simp,[status(thm)],[10747]) ).
thf(51648,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( ( k4_subset_1 @ sk1 @ k1_xboole_0 @ sk4 )
!= sk4 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[3513,8737]) ).
thf(51649,plain,
( ( v1_funct_1 @ ( sk161 @ sk3 ) )
| ( ( k4_subset_1 @ sk1 @ k1_xboole_0 @ sk4 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[51648:[bind(A,$thf( sk3 ))]]) ).
thf(654,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(4814,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(984,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(6271,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1243,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_domain_1) ).
thf(7523,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_1) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(2965,plain,
( ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ! [A: $i,B: $i] : ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[2964]) ).
thf(2966,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ),
inference(cnf,[status(esa)],[2965]) ).
thf(2968,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ),
inference(simp,[status(thm)],[2966]) ).
thf(46986,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,46908]) ).
thf(46988,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk421 ),
inference(simp,[status(thm)],[46986]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_mcart_1) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(719,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(5134,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1532,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(8690,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(4934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(703,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(5058,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(32804,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,32739]) ).
thf(32810,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk421 ),
inference(simp,[status(thm)],[32804]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_relat_1) ).
thf(4347,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k4_xboole_0 @ A @ ( k1_setfam_1 @ B ) )
= ( k3_tarski @ ( k4_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_setfam_1) ).
thf(5317,plain,
! [A: $i,B: $i] :
( ( B != k1_xboole_0 )
=> ( ( k4_xboole_0 @ A @ ( k1_setfam_1 @ B ) )
= ( k3_tarski @ ( k4_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_sysrel) ).
thf(1774,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
| ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ),
inference(cnf,[status(esa)],[1774]) ).
thf(663,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ ( k1_funcop_1 @ D ) @ E )
= ( k4_tarski @ ( k2_mcart_1 @ ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) @ ( k1_mcart_1 @ ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_funcop_1) ).
thf(4846,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ ( k1_funcop_1 @ D ) @ E )
= ( k4_tarski @ ( k2_mcart_1 @ ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) @ ( k1_mcart_1 @ ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( k3_zfmisc_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).
thf(8458,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( k3_zfmisc_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1526,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(8673,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(1402,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(8219,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(40247,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,4671]) ).
thf(40265,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk432 ),
inference(simp,[status(thm)],[40247]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_relat_1) ).
thf(5149,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1434,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(8326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(6032,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(cnf,[status(esa)],[6031]) ).
thf(6033,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(lifteq,[status(thm)],[6032]) ).
thf(1233,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
<=> ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(7463,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1132,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(7014,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( D
= ( k5_partfun1 @ A @ B @ C ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ D )
<=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_partfun1) ).
thf(4068,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( D
= ( k5_partfun1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) ) )
& ( ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) )
=> ( D
= ( k5_partfun1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1129,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(6997,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(6998,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[6997]) ).
thf(6999,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[6998]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_mcart_1) ).
thf(7966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3770,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1461,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_subset_1) ).
thf(8410,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ A @ ( sk6 @ B @ A ) )
= ( sk7 @ B @ A ) )
| ( ( k1_funct_1 @ B @ ( sk7 @ B @ A ) )
= ( sk6 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1656]) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( sk7 @ B @ A )
= ( k1_funct_1 @ A @ ( sk6 @ B @ A ) ) )
| ( ( k1_funct_1 @ B @ ( sk7 @ B @ A ) )
= ( sk6 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1657]) ).
thf(114,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
<=> ( A
= ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_2) ).
thf(1974,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_2 @ A )
=> ( A
= ( k4_relat_1 @ A ) ) )
& ( ( A
= ( k4_relat_1 @ A ) )
=> ( v3_relat_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(6433,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) )
& ( ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) )
=> ( m1_eqrel_1 @ B @ A ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( m1_eqrel_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(6475,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(6876,plain,
v1_funct_1 @ sk462,
inference(cnf,[status(esa)],[6872]) ).
thf(9443,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk465 ) ),
inference(paramod_ordered,[status(thm)],[7899,6907]) ).
thf(9448,plain,
sk536 != sk465,
inference(simp,[status(thm)],[9443]) ).
thf(15551,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,15520]) ).
thf(15560,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk421 ),
inference(simp,[status(thm)],[15551]) ).
thf(61529,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk13 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1789]) ).
thf(61530,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk13 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk13 ) ),
inference(pattern_uni,[status(thm)],[61529:[bind(A,$thf( sk13 ))]]) ).
thf(56,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_finseq_1) ).
thf(1754,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1755,plain,
( ! [A: $i] : ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ! [A: $i] : ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
inference(miniscope,[status(thm)],[1754]) ).
thf(1757,plain,
! [A: $i] : ( v1_xboole_0 @ ( k6_finseq_1 @ A ) ),
inference(cnf,[status(esa)],[1755]) ).
thf(12023,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
!= ( v1_xboole_0 @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1757,3835]) ).
thf(12033,plain,
! [B: $i,A: $i] :
( ( k6_finseq_1 @ A )
!= ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[12023]) ).
thf(8604,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[8603]) ).
thf(8605,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8604]) ).
thf(43486,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[12033,8605]) ).
thf(446,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(3628,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) )
& ( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(923,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_setfam_1 @ ( k4_setfam_1 @ A @ B ) ) @ ( k4_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_setfam_1) ).
thf(6005,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_setfam_1 @ ( k4_setfam_1 @ A @ B ) ) @ ( k4_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(5305,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(6908,plain,
v1_finset_1 @ sk465,
inference(cnf,[status(esa)],[6906]) ).
thf(1474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(8455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(6465,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(8773,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,7808]) ).
thf(8775,plain,
sk533 != sk42,
inference(simp,[status(thm)],[8773]) ).
thf(323,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2862,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(31043,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,28989]) ).
thf(31044,plain,
v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(pattern_uni,[status(thm)],[31043:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ~ ( m2_relset_1 @ B @ A @ A )
| ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ),
inference(cnf,[status(esa)],[1596]) ).
thf(1599,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
| ~ ( m2_relset_1 @ B @ A @ A ) ),
inference(lifteq,[status(thm)],[1597]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(6418,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(867,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(5801,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1720,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ E @ A )
| ~ ( m2_finseq_1 @ F @ B )
| ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ),
inference(cnf,[status(esa)],[1719]) ).
thf(822,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5603,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(18451,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk534 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7842,1655]) ).
thf(18452,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk534 ) ) @ ( k2_relat_1 @ sk534 ),
inference(pattern_uni,[status(thm)],[18451:[bind(A,$thf( sk534 ))]]) ).
thf(115,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_relat_1) ).
thf(1979,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(8142,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) )
& ( ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) )
=> ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(40229,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,3314]) ).
thf(40233,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk424 ),
inference(simp,[status(thm)],[40229]) ).
thf(1261,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(7624,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1200,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(7333,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(971,axiom,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(6224,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(6988,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(12027,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1757,5927]) ).
thf(12038,plain,
! [B: $i,A: $i] :
( ( k6_finseq_1 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[12027]) ).
thf(43501,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[12038,8605]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(5245,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_sysrel) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(8921,plain,
( ( v1_xboole_0 @ sk421 )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[6305,6285]) ).
thf(8935,plain,
sk421 != sk420,
inference(simp,[status(thm)],[8921]) ).
thf(16626,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk421 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,10757]) ).
thf(16627,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk421 ),
inference(pattern_uni,[status(thm)],[16626:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(16632,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) )
!= sk421 ),
inference(simp,[status(thm)],[16627]) ).
thf(29450,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk421 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,16632]) ).
thf(29451,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk421 ),
inference(pattern_uni,[status(thm)],[29450:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(29461,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) )
!= sk421 ),
inference(simp,[status(thm)],[29451]) ).
thf(602,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(4535,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(5310,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(17292,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk23 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1947,1652]) ).
thf(17293,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk23 ) ) @ ( k1_relat_1 @ sk23 ),
inference(pattern_uni,[status(thm)],[17292:[bind(A,$thf( sk23 ))]]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ~ ( r1_xboole_0 @ A @ E )
& ~ ( r1_xboole_0 @ B @ F )
& ~ ( r1_xboole_0 @ C @ G )
& ~ ( r1_xboole_0 @ D @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_mcart_1) ).
thf(2702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ~ ( r1_xboole_0 @ A @ E )
& ~ ( r1_xboole_0 @ B @ F )
& ~ ( r1_xboole_0 @ C @ G )
& ~ ( r1_xboole_0 @ D @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(25661,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_1_domain_1 )
| ( sk3 != f2_s8_domain_1 ) ),
inference(simp,[status(thm)],[11186]) ).
thf(26957,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk3 != f2_s8_domain_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_1_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,25661]) ).
thf(26958,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_1_domain_1 ) @ sk1 )
| ( sk3 != f2_s8_domain_1 ) ),
inference(pattern_uni,[status(thm)],[26957:[bind(A,$thf( a_0_1_domain_1 )),bind(B,$thf( sk8 @ a_0_1_domain_1 ))]]) ).
thf(912,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_orders_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(5964,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_orders_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(339,axiom,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_relat_1) ).
thf(2961,plain,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(2962,plain,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2961]) ).
thf(2963,plain,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2962]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(7646,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(1272,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) )
=> ( ! [D: $i,E: $i] :
( A
!= ( k4_tarski @ D @ E ) )
| ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_mcart_1) ).
thf(7661,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) )
=> ( ! [D: $i,E: $i] :
( A
!= ( k4_tarski @ D @ E ) )
| ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(8839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
| ( m2_finseq_1 @ D @ B )
| ( ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( m2_finseq_1 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8794,1558]) ).
thf(8840,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ B ) )
| ( m2_finseq_1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[8839:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( k2_zfmisc_1 @ sk1 @ sk2 )),bind(D,$thf( A ))]]) ).
thf(8846,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ B ) )
| ( m2_finseq_1 @ A @ B ) ),
inference(simp,[status(thm)],[8840]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k4_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2634,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= A ) )
& ( ( ( k4_xboole_0 @ A @ B )
= A )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(6409,plain,
v1_relat_1 @ sk432,
inference(cnf,[status(esa)],[6408]) ).
thf(62,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_5) ).
thf(1777,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1778,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
inference(cnf,[status(esa)],[1777]) ).
thf(1779,plain,
! [A: $i] :
( ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1778]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(7052,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(48567,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk332 ) ),
inference(paramod_ordered,[status(thm)],[3513,8733]) ).
thf(48568,plain,
v1_funct_1 @ ( sk161 @ sk332 ),
inference(pattern_uni,[status(thm)],[48567:[bind(A,$thf( sk332 ))]]) ).
thf(7718,plain,
( ! [A: $i,B: $i] : ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
& ! [A: $i,B: $i] : ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
& ! [A: $i,B: $i] : ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
inference(miniscope,[status(thm)],[7717]) ).
thf(7721,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( k10_pboole @ A @ B ) ),
inference(cnf,[status(esa)],[7718]) ).
thf(26931,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk3 != f1_s7_domain_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_0_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,18097]) ).
thf(26932,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_0_domain_1 ) @ sk1 )
| ( sk3 != f1_s7_domain_1 ) ),
inference(pattern_uni,[status(thm)],[26931:[bind(A,$thf( a_0_0_domain_1 )),bind(B,$thf( sk8 @ a_0_0_domain_1 ))]]) ).
thf(15488,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[4373,7808]) ).
thf(15499,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk533 ),
inference(simp,[status(thm)],[15488]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_finseq_2) ).
thf(2043,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(49855,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[3513,16348]) ).
thf(49856,plain,
( ( v1_funct_1 @ ( sk161 @ sk1 ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[49855:[bind(A,$thf( sk1 ))]]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(7614,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[7613]) ).
thf(7618,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk522 @ A ) ),
inference(cnf,[status(esa)],[7614]) ).
thf(42146,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk522 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7618,7277]) ).
thf(42171,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk522 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[42146]) ).
thf(42185,plain,
! [A: $i] :
( ( sk522 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[42171]) ).
thf(1103,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(6859,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(9036,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,7808]) ).
thf(9044,plain,
sk533 != sk432,
inference(simp,[status(thm)],[9036]) ).
thf(1563,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_relat_1 @ ( k3_funct_5 @ A ) ) ),
inference(cnf,[status(esa)],[1562]) ).
thf(1069,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(6716,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(133,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_relat_1) ).
thf(2057,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ( D
!= ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
| ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(cnf,[status(esa)],[1707]) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( k1_funct_1 @ C @ A ) )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
| ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(lifteq,[status(thm)],[1708]) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( v1_funct_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_funct_1 @ C @ A ) ) )
| ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1220,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relset_1) ).
thf(7414,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(16306,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ B @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
!= ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8648,8794]) ).
thf(16324,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ~ ( m2_finseq_1 @ B @ sk5 )
| ( sk1 != k1_xboole_0 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[16306]) ).
thf(16341,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ A @ k1_xboole_0 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16324]) ).
thf(26985,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,16341]) ).
thf(26986,plain,
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ ( sk8 @ sk5 ) @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26985:[bind(A,$thf( sk5 )),bind(B,$thf( sk8 @ sk5 ))]]) ).
thf(1747,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v3_relat_1 @ A )
| ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1746]) ).
thf(1750,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v3_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[1747]) ).
thf(43136,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v3_relat_1 @ A ) ),
inference(rewrite,[status(thm)],[1750,8184]) ).
thf(10501,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,5927]) ).
thf(10503,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk424 ),
inference(simp,[status(thm)],[10501]) ).
thf(788,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(5419,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(15547,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,15520]) ).
thf(15552,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15547]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
<=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(4448,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) )
& ( ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( ( k2_mcart_1 @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_mcart_1) ).
thf(6756,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( ( k2_mcart_1 @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1660,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( r2_hidden @ ( sk7 @ B @ A ) @ ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1656]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( r2_hidden @ ( sk7 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(lifteq,[status(thm)],[1660]) ).
thf(1505,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relset_2) ).
thf(8609,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(6610,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1450,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(8378,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
thf(2645,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_2) ).
thf(6038,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(13957,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[8233,4841]) ).
thf(13968,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk320 ),
inference(simp,[status(thm)],[13957]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(3841,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1343,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(7972,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(1105,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(6869,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(881,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(5840,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(18461,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk34 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2275,1655]) ).
thf(18462,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk34 ) ) @ ( k2_relat_1 @ sk34 ),
inference(pattern_uni,[status(thm)],[18461:[bind(A,$thf( sk34 ))]]) ).
thf(1057,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_domain_1) ).
thf(6637,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_5) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ( ( k1_relat_1 @ C )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k1_relat_1 @ D )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k3_funct_5 @ C )
!= ( k3_funct_5 @ D ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[1678]) ).
thf(1680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k1_relat_1 @ D )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k3_funct_5 @ C )
!= ( k3_funct_5 @ D ) )
| ( C = D )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D ) ),
inference(lifteq,[status(thm)],[1679]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(5359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) )
& ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(4438,plain,
v1_funct_1 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(1542,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(8728,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(8769,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,6907]) ).
thf(8771,plain,
sk465 != sk42,
inference(simp,[status(thm)],[8769]) ).
thf(902,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(5928,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(585,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(4453,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1046,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(6598,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(8806,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,6733]) ).
thf(8807,plain,
sk453 != sk275,
inference(simp,[status(thm)],[8806]) ).
thf(144,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_sysrel) ).
thf(2121,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v3_relat_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(2144,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v3_relat_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( m2_pua2mss1 @ B @ A )
| ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A ) ),
inference(cnf,[status(esa)],[1725]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(6314,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(9030,plain,
( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[6410,6285]) ).
thf(9040,plain,
sk432 != sk420,
inference(simp,[status(thm)],[9030]) ).
thf(213,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(2413,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(51646,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( ( k4_subset_1 @ k1_xboole_0 @ sk3 @ sk4 )
!= sk4 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[3513,8737]) ).
thf(51647,plain,
( ( v1_funct_1 @ ( sk161 @ sk1 ) )
| ( ( k4_subset_1 @ k1_xboole_0 @ sk3 @ sk4 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[51646:[bind(A,$thf( sk1 ))]]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(7046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_sysrel) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(811,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(5524,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_domain_1 @ A @ B @ C @ D )
= ( k1_enumset1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).
thf(6507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_domain_1 @ A @ B @ C @ D )
= ( k1_enumset1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ E )
& ( r2_hidden @ E @ B ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_pua2mss1) ).
thf(5808,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ E )
& ( r2_hidden @ E @ B ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(26909,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s12_funct_2 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk501 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10775]) ).
thf(26910,plain,
( sk500
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk501 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= f1_s12_funct_2 ) ),
inference(pattern_uni,[status(thm)],[26909:[bind(A,$thf( sk501 )),bind(B,$thf( sk8 @ sk501 ))]]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(3358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(126,axiom,
! [A: $i] :
( ( v3_relat_2 @ ( k1_eqrel_1 @ A ) )
& ( v8_relat_2 @ ( k1_eqrel_1 @ A ) )
& ( v1_partfun1 @ ( k1_eqrel_1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_eqrel_1) ).
thf(2028,plain,
! [A: $i] :
( ( v3_relat_2 @ ( k1_eqrel_1 @ A ) )
& ( v8_relat_2 @ ( k1_eqrel_1 @ A ) )
& ( v1_partfun1 @ ( k1_eqrel_1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(2029,plain,
( ! [A: $i] : ( v3_relat_2 @ ( k1_eqrel_1 @ A ) )
& ! [A: $i] : ( v8_relat_2 @ ( k1_eqrel_1 @ A ) )
& ! [A: $i] : ( v1_partfun1 @ ( k1_eqrel_1 @ A ) @ A @ A )
& ! [A: $i] : ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ) ),
inference(miniscope,[status(thm)],[2028]) ).
thf(2033,plain,
! [A: $i] : ( v3_relat_2 @ ( k1_eqrel_1 @ A ) ),
inference(cnf,[status(esa)],[2029]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(5762,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(177,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2253,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(489,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(3871,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(4594,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1231,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
thf(7459,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1398,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(8195,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(381,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(3257,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_relat_1) ).
thf(2717,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(6699,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(9553,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ sk1 ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1544,8847]) ).
thf(9591,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk3 != A )
| ( ( k1_zfmisc_1 @ sk5 )
!= ( k1_zfmisc_1 @ sk1 ) ) ),
inference(simp,[status(thm)],[9553]) ).
thf(9617,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ A @ sk3 )
| ( ( k1_zfmisc_1 @ sk5 )
!= ( k1_zfmisc_1 @ sk1 ) ) ),
inference(simp,[status(thm)],[9591]) ).
thf(10030,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ A @ sk3 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[9617]) ).
thf(17298,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk34 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2275,1652]) ).
thf(17299,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk34 ) ) @ ( k1_relat_1 @ sk34 ),
inference(pattern_uni,[status(thm)],[17298:[bind(A,$thf( sk34 ))]]) ).
thf(17320,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk536 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7900,1652]) ).
thf(17321,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk536 ) ) @ ( k1_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[17320:[bind(A,$thf( sk536 ))]]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(5230,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(42096,plain,
! [A: $i] :
( ( v1_partfun1 @ k1_xboole_0 @ A @ A )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,42095]) ).
thf(42097,plain,
v1_partfun1 @ k1_xboole_0 @ k1_xboole_0 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[42096:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(5048,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1481,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_2_domain_1 )
<=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(8480,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_2_domain_1 )
=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) )
& ( ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) )
=> ( r2_hidden @ A @ a_0_2_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(9015,plain,
( ( v1_xboole_0 @ sk424 )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[6325,4841]) ).
thf(9021,plain,
sk424 != sk320,
inference(simp,[status(thm)],[9015]) ).
thf(46961,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,46908]) ).
thf(46997,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk536 ),
inference(simp,[status(thm)],[46961]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(6243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(8591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(6001,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_2) ).
thf(3738,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3375,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_5) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ( ( k1_relat_1 @ C )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k1_relat_1 @ D )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k5_funct_5 @ C )
!= ( k5_funct_5 @ D ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[1593]) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k1_relat_1 @ D )
!= ( k2_zfmisc_1 @ A @ B ) )
| ( ( k5_funct_5 @ C )
!= ( k5_funct_5 @ D ) )
| ( C = D )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D ) ),
inference(lifteq,[status(thm)],[1594]) ).
thf(294,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( k4_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_realset1) ).
thf(2734,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( k4_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
<=> ( B
= ( k2_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(6228,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
=> ( B
= ( k2_subset_1 @ A ) ) )
& ( ( B
= ( k2_subset_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(363,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3111,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(7785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(7118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(454,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(3686,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1429,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(8311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(9444,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[7899,5003]) ).
thf(9451,plain,
sk536 != sk332,
inference(simp,[status(thm)],[9444]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_msualg_1) ).
thf(3696,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(5715,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(5758,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_mcart_1) ).
thf(4365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( ( v3_relat_2 @ D )
& ( v8_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_eqrel_1) ).
thf(1833,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ? [C: $i] :
( ( v3_relat_2 @ C )
& ( v8_relat_2 @ C )
& ( v1_partfun1 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( ( v3_relat_2 @ D )
& ( v8_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pua2mss1) ).
thf(1884,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(5923,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_mcart_1) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_setfam_1) ).
thf(5612,plain,
! [A: $i,B: $i] :
( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1387,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(8167,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_5) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(64129,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk424 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6325,1794]) ).
thf(64130,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk424 ),
inference(pattern_uni,[status(thm)],[64129:[bind(A,$thf( sk424 ))]]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_partfun1) ).
thf(3536,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_mcart_1) ).
thf(6140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1281,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_realset1) ).
thf(7709,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3372,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(974,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_orders_1) ).
thf(6234,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( k2_realset1 @ A @ B @ C )
= ( k1_realset1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(7833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( k2_realset1 @ A @ B @ C )
= ( k1_realset1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(691,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ D @ C )
= ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_2) ).
thf(4998,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ D @ C )
= ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1283,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(7714,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(552,axiom,
! [A: $i] :
( ( v1_funct_1 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(4268,plain,
! [A: $i] :
( ( ( v1_funct_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) )
=> ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(6493,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1415,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_0_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(8259,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_0_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_5) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(3925,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(2859,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(24,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funcop_1 @ ( k1_funcop_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k1_funcop_1) ).
thf(1615,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funcop_1 @ ( k1_funcop_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_funct_2 @ A @ B ) )
| ~ ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_funct_2 @ A @ B ) )
| ( ( k4_funct_5 @ C )
!= ( k4_funct_5 @ D ) )
| ( A = k1_xboole_0 )
| ( C = D ) ),
inference(cnf,[status(esa)],[1782]) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_funct_5 @ C )
!= ( k4_funct_5 @ D ) )
| ( A = k1_xboole_0 )
| ( C = D )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_funct_2 @ A @ B ) )
| ~ ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_funct_2 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1783]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(6510,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(947,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(6108,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ D @ B )
& ( m1_eqrel_1 @ E @ C ) )
=> ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).
thf(6949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ D @ B )
& ( m1_eqrel_1 @ E @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) ) )
& ( ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) )
=> ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(992,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(6312,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_mcart_1) ).
thf(7736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1176,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(7233,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(17279,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk283 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4511,1652]) ).
thf(17280,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk283 ) ) @ ( k1_relat_1 @ sk283 ),
inference(pattern_uni,[status(thm)],[17279:[bind(A,$thf( sk283 ))]]) ).
thf(274,axiom,
! [A: $i] : ( r1_setfam_1 @ ( k3_setfam_1 @ A @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_setfam_1) ).
thf(2657,plain,
! [A: $i] : ( r1_setfam_1 @ ( k3_setfam_1 @ A @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(4159,plain,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1498,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(8580,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(558,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_relat_1) ).
thf(4309,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(9017,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,6733]) ).
thf(9025,plain,
sk453 != sk424,
inference(simp,[status(thm)],[9017]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(5627,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(8800,plain,
( ( v1_xboole_0 @ sk404 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,6046]) ).
thf(8809,plain,
sk404 != sk275,
inference(simp,[status(thm)],[8800]) ).
thf(280,axiom,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(2674,plain,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1375,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(8124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1530,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k7_setfam_1 @ A @ B )
= ( k7_setfam_1 @ A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(8684,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k7_setfam_1 @ A @ B )
= ( k7_setfam_1 @ A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_mcart_1) ).
thf(5831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_funct_1) ).
thf(4605,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(890,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(5876,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1795,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1793]) ).
thf(1693,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= A )
| ( ( k1_funct_1 @ B @ ( sk9 @ B @ A ) )
!= ( sk9 @ B @ A ) )
| ( B
= ( k6_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1689]) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= A )
| ( ( k1_funct_1 @ B @ ( sk9 @ B @ A ) )
!= ( sk9 @ B @ A ) )
| ( B
= ( k6_relat_1 @ A ) )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1693]) ).
thf(1701,plain,
! [A: $i] :
( ( ( k1_funct_1 @ A @ ( sk9 @ A @ ( k1_relat_1 @ A ) ) )
!= ( sk9 @ A @ ( k1_relat_1 @ A ) ) )
| ( ( k6_relat_1 @ ( k1_relat_1 @ A ) )
= A )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(simp,[status(thm)],[1700]) ).
thf(209,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_sysrel) ).
thf(2398,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1365,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(8092,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_partfun1) ).
thf(5350,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1163,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
!= ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(7180,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
!= ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1340,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(7963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(3404,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(3868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(5745,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[5744]) ).
thf(5747,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[5745]) ).
thf(5751,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(lifteq,[status(thm)],[5747]) ).
thf(5752,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(simp,[status(thm)],[5751]) ).
thf(40261,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,4671]) ).
thf(40263,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk421 ),
inference(simp,[status(thm)],[40261]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5799,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(18476,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk527 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7676,1655]) ).
thf(18477,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk527 ) ) @ ( k2_relat_1 @ sk527 ),
inference(pattern_uni,[status(thm)],[18476:[bind(A,$thf( sk527 ))]]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
<=> ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_relat_1) ).
thf(2134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
=> ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
& ( ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1140,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7038,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(2959,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(5535,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(3796,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(48529,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk420 ) ),
inference(paramod_ordered,[status(thm)],[3513,8747]) ).
thf(48530,plain,
v1_funct_1 @ ( sk161 @ sk420 ),
inference(pattern_uni,[status(thm)],[48529:[bind(A,$thf( sk420 ))]]) ).
thf(1247,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(7534,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_xboole_1) ).
thf(6334,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(8387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(1451,axiom,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(8380,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(8381,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(cnf,[status(esa)],[8380]) ).
thf(1502,axiom,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_5) ).
thf(8601,plain,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(5427,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_mcart_1) ).
thf(3773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) )
& ( ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(8770,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,6907]) ).
thf(8772,plain,
sk465 != k1_xboole_0,
inference(simp,[status(thm)],[8770]) ).
thf(50893,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk465 ) ),
inference(paramod_ordered,[status(thm)],[3513,8772]) ).
thf(50894,plain,
v1_funct_1 @ ( sk161 @ sk465 ),
inference(pattern_uni,[status(thm)],[50893:[bind(A,$thf( sk465 ))]]) ).
thf(1370,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_domain_1) ).
thf(8107,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(64281,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[64101,7808]) ).
thf(64304,plain,
( ( k4_relat_1 @ sk432 )
!= sk533 ),
inference(simp,[status(thm)],[64281]) ).
thf(366,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(3118,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1494,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(8549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3051,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
thf(2308,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(4837,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(3646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(519,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(4112,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(18483,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk536 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7900,1655]) ).
thf(18484,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk536 ) ) @ ( k2_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[18483:[bind(A,$thf( sk536 ))]]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(5331,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_finseq_2) ).
thf(1865,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(622,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_relat_1) ).
thf(4672,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(4822,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(8359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(8624,plain,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[8623]) ).
thf(444,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3594,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(120,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 )
& ( ( k5_relat_1 @ B @ A )
= B )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ B )
= B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_sysrel) ).
thf(1997,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 )
& ( ( k5_relat_1 @ B @ A )
= B )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ B )
= B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(639,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(4764,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_relat_1) ).
thf(3123,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1332,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
<=> ( B
= ( k1_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(7924,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
=> ( B
= ( k1_subset_1 @ A ) ) )
& ( ( B
= ( k1_subset_1 @ A ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1305,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(7800,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(132,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
=> ( v8_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_relat_2) ).
thf(2055,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v8_relat_2 @ A )
=> ( v8_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1204,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(7347,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3700,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_subset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(4060,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C ) )
=> ( ( B = k1_xboole_0 )
| ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
= ( k6_partfun1 @ A ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
= ( k6_partfun1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_2) ).
thf(2166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C ) )
=> ( ( B = k1_xboole_0 )
| ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
= ( k6_partfun1 @ A ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
= ( k6_partfun1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1400,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(8212,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_partfun1) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(6123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(17610,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk534 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7842,1653]) ).
thf(17611,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk534 ) ) @ ( k2_relat_1 @ sk534 ),
inference(pattern_uni,[status(thm)],[17610:[bind(A,$thf( sk534 ))]]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(7658,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(30,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_funcop_1 @ A ) )
& ( v1_funct_1 @ ( k1_funcop_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funcop_1) ).
thf(1637,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_funcop_1 @ A ) )
& ( v1_funct_1 @ ( k1_funcop_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1638,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_relat_1 @ ( k1_funcop_1 @ A ) ) ),
inference(cnf,[status(esa)],[1637]) ).
thf(1195,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_orders_1) ).
thf(7315,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_relat_1) ).
thf(4245,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(10502,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,5927]) ).
thf(10505,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk421 ),
inference(simp,[status(thm)],[10502]) ).
thf(18430,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk13 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1655]) ).
thf(18431,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk13 ) ) @ ( k2_relat_1 @ sk13 ),
inference(pattern_uni,[status(thm)],[18430:[bind(A,$thf( sk13 ))]]) ).
thf(1673,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v2_funct_1 @ A )
| ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[1671]) ).
thf(1675,plain,
! [A: $i] :
( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1673]) ).
thf(9070,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1546,8825]) ).
thf(9082,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk5 != A )
| ( ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( k1_zfmisc_1 @ sk3 ) ) ),
inference(simp,[status(thm)],[9070]) ).
thf(9097,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( k1_zfmisc_1 @ sk3 ) ) ),
inference(simp,[status(thm)],[9082]) ).
thf(9318,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[9097]) ).
thf(26983,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk3 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,9318]) ).
thf(26984,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk5 ) @ sk1 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[26983:[bind(A,$thf( sk5 )),bind(B,$thf( sk8 @ sk5 ))]]) ).
thf(3532,plain,
v1_funct_1 @ sk164,
inference(cnf,[status(esa)],[3530]) ).
thf(17859,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk42 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2428,1654]) ).
thf(17860,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk42 ) ) @ ( k1_relat_1 @ sk42 ),
inference(pattern_uni,[status(thm)],[17859:[bind(A,$thf( sk42 ))]]) ).
thf(1021,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v2_relat_2 @ A )
& ( v2_relat_2 @ B ) )
=> ( ( v2_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v2_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_2) ).
thf(6478,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( v2_relat_2 @ A )
& ( v2_relat_2 @ B ) )
=> ( ( v2_relat_2 @ ( k2_xboole_0 @ A @ B ) )
& ( v2_relat_2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(15473,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[4373,6046]) ).
thf(15492,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk404 ),
inference(simp,[status(thm)],[15473]) ).
thf(1111,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
<=> ( v1_finset_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(6920,plain,
! [A: $i] :
( ( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
=> ( v1_finset_1 @ ( k3_tarski @ A ) ) )
& ( ( v1_finset_1 @ ( k3_tarski @ A ) )
=> ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2284,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(6340,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_relat_1) ).
thf(2839,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(332,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(2944,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(2945,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(cnf,[status(esa)],[2944]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(5381,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_domain_1) ).
thf(8419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(2521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(5071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(17891,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk164 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3533,1654]) ).
thf(17892,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk164 ) ) @ ( k1_relat_1 @ sk164 ),
inference(pattern_uni,[status(thm)],[17891:[bind(A,$thf( sk164 ))]]) ).
thf(722,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(5143,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(7594,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
=> ~ ( r2_hidden @ A @ B ) )
& ( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(7514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(991,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(6308,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(379,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(3251,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2151,plain,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1267,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(7643,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(9441,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[7899,6046]) ).
thf(9454,plain,
sk536 != sk404,
inference(simp,[status(thm)],[9441]) ).
thf(762,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
<=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(5325,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1378,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(8135,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1574,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[1573]) ).
thf(658,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_relat_1) ).
thf(4828,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(28583,plain,
! [A: $i] :
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,16898]) ).
thf(28584,plain,
v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[28583:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(28867,plain,
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[28584,5002]) ).
thf(28877,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk332 ),
inference(simp,[status(thm)],[28867]) ).
thf(11877,plain,
! [A: $i] :
( ( v3_relat_2 @ k1_xboole_0 )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,11876]) ).
thf(11878,plain,
v3_relat_2 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[11877:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(6197,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1258,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finset_1) ).
thf(7607,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1533,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(8693,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(1602,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ),
inference(cnf,[status(esa)],[1601]) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ),
inference(lifteq,[status(thm)],[1602]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(6321,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2299,plain,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1476,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_2) ).
thf(8461,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) )
& ( ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(3106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(8250,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk557 @ f3_s11_funct_2 )
= f5_s11_funct_2 ) ),
inference(cnf,[status(esa)],[8246]) ).
thf(8254,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk557 @ f3_s11_funct_2 )
= f5_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[8250]) ).
thf(1722,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v3_relat_1 @ A )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
| ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1721]) ).
thf(1199,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_subset_1 @ A )
= ( a_1_1_domain_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_domain_1) ).
thf(7330,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_subset_1 @ A )
= ( a_1_1_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(651,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( k1_realset1 @ A @ B )
= ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_realset1) ).
thf(4805,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( k1_realset1 @ A @ B )
= ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1430,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k2_domain_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_domain_1) ).
thf(8313,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k2_domain_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(2669,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(4213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_2) ).
thf(7360,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1170,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_relset_2) ).
thf(7206,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_2) ).
thf(3197,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(46985,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,46908]) ).
thf(47003,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk424 ),
inference(simp,[status(thm)],[46985]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ D )
= ( k1_funcop_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_funcop_1) ).
thf(1801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ D )
= ( k1_funcop_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(714,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(5093,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(988,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(6289,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(2802,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(3500,plain,
v2_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3495]) ).
thf(964,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( r2_realset1 @ A @ B @ C )
<=> ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_realset1) ).
thf(6184,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( r2_realset1 @ A @ B @ C )
=> ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) )
& ( ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) )
=> ( r2_realset1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(4370,plain,
! [A: $i] : ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[4369]) ).
thf(4374,plain,
! [A: $i] : ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[4370]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(5972,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(7501,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[7500]) ).
thf(7502,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[7501]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k9_relat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_relat_1) ).
thf(4773,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k9_relat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(26993,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_2_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10750]) ).
thf(26994,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_2_domain_1 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(pattern_uni,[status(thm)],[26993:[bind(A,$thf( a_0_2_domain_1 )),bind(B,$thf( sk8 @ a_0_2_domain_1 ))]]) ).
thf(4509,plain,
v1_finseq_1 @ sk283,
inference(cnf,[status(esa)],[4508]) ).
thf(1287,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(7731,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(5267,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(6216,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(12014,plain,
! [A: $i] :
( ( v8_relat_2 @ k1_xboole_0 )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,12013]) ).
thf(12015,plain,
v8_relat_2 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[12014:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( r2_hidden @ ( sk6 @ B @ A ) @ ( k1_relat_1 @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1656]) ).
thf(1667,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( r2_hidden @ ( sk6 @ B @ A ) @ ( k1_relat_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1661]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5552,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(32783,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,32739]) ).
thf(32813,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk536 ),
inference(simp,[status(thm)],[32783]) ).
thf(15489,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk453 ) ),
inference(paramod_ordered,[status(thm)],[4373,6733]) ).
thf(15497,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk453 ),
inference(simp,[status(thm)],[15489]) ).
thf(182,axiom,
! [A: $i] :
( ( v3_relat_2 @ ( k6_relat_1 @ A ) )
& ( v8_relat_2 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_2) ).
thf(2267,plain,
! [A: $i] :
( ( v3_relat_2 @ ( k6_relat_1 @ A ) )
& ( v8_relat_2 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_funct_1) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
& ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(7186,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
& ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_orders_1) ).
thf(2553,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(8926,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,7808]) ).
thf(8932,plain,
sk533 != sk421,
inference(simp,[status(thm)],[8926]) ).
thf(9037,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,6733]) ).
thf(9042,plain,
sk453 != sk432,
inference(simp,[status(thm)],[9037]) ).
thf(8734,plain,
( ( v1_xboole_0 @ sk404 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,6046]) ).
thf(8735,plain,
sk404 != k1_xboole_0,
inference(simp,[status(thm)],[8734]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(5816,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(17636,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk164 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3533,1653]) ).
thf(17637,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk164 ) ) @ ( k2_relat_1 @ sk164 ),
inference(pattern_uni,[status(thm)],[17636:[bind(A,$thf( sk164 ))]]) ).
thf(603,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(4541,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(64279,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[64101,4841]) ).
thf(64300,plain,
( ( k4_relat_1 @ sk432 )
!= sk320 ),
inference(simp,[status(thm)],[64279]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(2742,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1514,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(8633,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1280,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ~ ( ( r2_hidden @ A @ B )
<=> ( r2_hidden @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(7699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
=> ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) ) )
& ( ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) )
=> ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(50052,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3513,15552]) ).
thf(50053,plain,
v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[50052:[bind(A,$thf( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ))]]) ).
thf(64213,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk320 ) ),
inference(paramod_ordered,[status(thm)],[64099,4841]) ).
thf(64221,plain,
( ( k4_relat_1 @ sk536 )
!= sk320 ),
inference(simp,[status(thm)],[64213]) ).
thf(8156,plain,
! [A: $i] : ( r1_setfam_1 @ A @ A ),
inference(cnf,[status(esa)],[8155]) ).
thf(265,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(2625,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(7292,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(142,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(2111,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1369,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(8103,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1100,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(6849,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(1627,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_finseq_1 @ D )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ F @ A )
| ~ ( m2_finseq_1 @ G @ B )
| ( ( k3_finseq_1 @ F )
!= ( k3_finseq_1 @ G ) )
| ( D
!= ( k3_funcop_1 @ E @ F @ G ) )
| ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ),
inference(cnf,[status(esa)],[1626]) ).
thf(1629,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ F )
!= ( k3_finseq_1 @ G ) )
| ( D
!= ( k3_funcop_1 @ E @ F @ G ) )
| ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_finseq_1 @ D )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ F @ A )
| ~ ( m2_finseq_1 @ G @ B ) ),
inference(lifteq,[status(thm)],[1627]) ).
thf(1630,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ E )
!= ( k3_finseq_1 @ F ) )
| ( ( k3_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) )
= ( k3_finseq_1 @ F ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ( v1_xboole_0 @ C )
| ~ ( v1_relat_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_funct_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
| ~ ( m2_finseq_1 @ E @ A )
| ~ ( m2_finseq_1 @ F @ B ) ),
inference(simp,[status(thm)],[1629]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(7566,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_domain_1) ).
thf(8517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(655,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(4818,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(180,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(2261,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[1729]) ).
thf(1731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1730]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(6725,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(8748,plain,
( ( v1_xboole_0 @ sk453 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,6733]) ).
thf(8750,plain,
sk453 != sk42,
inference(simp,[status(thm)],[8748]) ).
thf(46971,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,46908]) ).
thf(47000,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[46971]) ).
thf(50951,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3513,47000]) ).
thf(50952,plain,
v1_funct_1 @ ( sk161 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[50951:[bind(A,$thf( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ))]]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_relat_1) ).
thf(1862,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(6645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(6747,plain,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(212,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funcop_1) ).
thf(2410,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1298,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(7778,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(257,axiom,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_relat_1) ).
thf(2591,plain,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(2592,plain,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2591]) ).
thf(2593,plain,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2592]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(5656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) )
& ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_1) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) )
& ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1324,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( C
= ( k7_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ C )
<=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(7869,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( C
= ( k7_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(7675,plain,
v1_funct_1 @ sk527,
inference(cnf,[status(esa)],[7674]) ).
thf(8469,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) )
& ! [B: $i] :
( ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ),
inference(miniscope,[status(thm)],[8468]) ).
thf(8473,plain,
m1_subset_1 @ sk564 @ ( k1_zfmisc_1 @ f1_s1_subset_1 ),
inference(cnf,[status(esa)],[8469]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(4726,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(2251,plain,
! [B: $i,A: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2250]) ).
thf(2252,plain,
! [B: $i,A: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2251]) ).
thf(1519,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(8652,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_2) ).
thf(6568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(61593,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk432 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6409,1789]) ).
thf(61594,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk432 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk432 ) ),
inference(pattern_uni,[status(thm)],[61593:[bind(A,$thf( sk432 ))]]) ).
thf(320,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(2842,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(880,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5838,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1462,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_setfam_1 @ A @ B )
= ( k1_setfam_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(8413,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_setfam_1 @ A @ B )
= ( k1_setfam_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(1330,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(7901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v2_funct_1 @ C )
| ( v1_funct_1 @ ( k2_funct_1 @ C ) ) ),
inference(cnf,[status(esa)],[1686]) ).
thf(38285,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ C )
| ( ( m2_pua2mss1 @ ( sk40 @ A ) @ A )
!= ( m2_pua2mss1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2355,1560]) ).
thf(38286,plain,
! [A: $i] : ( v1_relat_1 @ ( sk40 @ A ) ),
inference(pattern_uni,[status(thm)],[38285:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk40 @ D ))]]) ).
thf(38297,plain,
! [A: $i] : ( v1_relat_1 @ ( sk40 @ A ) ),
inference(simp,[status(thm)],[38286]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(3806,plain,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_relset_2 @ A @ B @ C @ D )
= ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_2) ).
thf(6504,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_relset_2 @ A @ B @ C @ D )
= ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1775,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
| ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ),
inference(cnf,[status(esa)],[1774]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_funct_1) ).
thf(4304,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_5) ).
thf(2207,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1087,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
& ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_sysrel) ).
thf(6785,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
& ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(9013,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,6907]) ).
thf(9018,plain,
sk465 != sk424,
inference(simp,[status(thm)],[9013]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_mcart_1 @ A @ B @ C )
= ( k3_mcart_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_mcart_1) ).
thf(3480,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_mcart_1 @ A @ B @ C )
= ( k3_mcart_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(3539,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(15484,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk465 ) ),
inference(paramod_ordered,[status(thm)],[4373,6907]) ).
thf(15496,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk465 ),
inference(simp,[status(thm)],[15484]) ).
thf(64269,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk534 ) ),
inference(paramod_ordered,[status(thm)],[64101,7843]) ).
thf(64290,plain,
( ( k4_relat_1 @ sk432 )
!= sk534 ),
inference(simp,[status(thm)],[64269]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(6255,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(5340,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(26927,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,8791]) ).
thf(26928,plain,
( ( v1_xboole_0 @ sk1 )
| ( v1_xboole_0 @ sk4 )
| ( m2_finseq_1 @ ( sk8 @ sk4 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[26927:[bind(A,$thf( sk4 )),bind(B,$thf( sk8 @ sk4 ))]]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k2_tarski @ C @ D ) ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( ( ( k2_mcart_1 @ A )
= C )
| ( ( k2_mcart_1 @ A )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_mcart_1) ).
thf(7603,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k2_tarski @ C @ D ) ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( ( ( k2_mcart_1 @ A )
= C )
| ( ( k2_mcart_1 @ A )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2365,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(741,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(5254,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(5775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(7030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(13959,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk453 ) ),
inference(paramod_ordered,[status(thm)],[8233,6733]) ).
thf(13963,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk453 ),
inference(simp,[status(thm)],[13959]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
= ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_mcart_1) ).
thf(2725,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
= ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1692,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= A )
| ( r2_hidden @ ( sk9 @ B @ A ) @ A )
| ( B
= ( k6_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1689]) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= A )
| ( B
= ( k6_relat_1 @ A ) )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk9 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[1692]) ).
thf(1699,plain,
! [A: $i] :
( ( ( k6_relat_1 @ ( k1_relat_1 @ A ) )
= A )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( r2_hidden @ ( sk9 @ A @ ( k1_relat_1 @ A ) ) @ ( k1_relat_1 @ A ) ) ),
inference(simp,[status(thm)],[1698]) ).
thf(169,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k4_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(2212,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k4_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k4_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(42036,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,6993]) ).
thf(42047,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[42036]) ).
thf(3748,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk184 @ B @ A ) ) ),
inference(cnf,[status(esa)],[3741]) ).
thf(3758,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk184 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[3748]) ).
thf(3759,plain,
! [A: $i] : ( v1_relat_1 @ ( sk184 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[3758]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_relat_1) ).
thf(3838,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(318,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
= ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funcop_1) ).
thf(2835,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
= ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(2765,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(3423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(50655,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk404 ) ),
inference(paramod_ordered,[status(thm)],[3513,8735]) ).
thf(50656,plain,
v1_funct_1 @ ( sk161 @ sk404 ),
inference(pattern_uni,[status(thm)],[50655:[bind(A,$thf( sk404 ))]]) ).
thf(9440,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[7899,6285]) ).
thf(9450,plain,
sk536 != sk420,
inference(simp,[status(thm)],[9440]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1113,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_domain_1) ).
thf(6930,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1428,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_2) ).
thf(8308,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(6738,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1362,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_2) ).
thf(8084,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(502,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(3953,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1390,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(8175,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3310,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1225,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(7434,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(7200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_2) ).
thf(5725,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( m2_pua2mss1 @ B @ A )
| ( v2_funct_1 @ B ) ),
inference(cnf,[status(esa)],[1725]) ).
thf(1211,axiom,
! [A: $i,B: $i] :
( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
= ( k4_zfmisc_1 @ B @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_mcart_1) ).
thf(7366,plain,
! [A: $i,B: $i] :
( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
= ( k4_zfmisc_1 @ B @ B @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(2967,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) ),
inference(cnf,[status(esa)],[2965]) ).
thf(64532,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk432 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6410,1795]) ).
thf(64533,plain,
v1_relat_1 @ ( k4_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[64532:[bind(A,$thf( sk432 ))]]) ).
thf(191,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(2303,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m2_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(7630,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m2_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) )
=> ( m2_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5403,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(617,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_finseq_2) ).
thf(4626,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(5693,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(5089,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1241,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(7506,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(7507,plain,
( ( m1_subset_1 @ sk514 @ f1_s13_funct_2 )
| sk513 ),
inference(cnf,[status(esa)],[7506]) ).
thf(17873,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk34 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2275,1654]) ).
thf(17874,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk34 ) ) @ ( k1_relat_1 @ sk34 ),
inference(pattern_uni,[status(thm)],[17873:[bind(A,$thf( sk34 ))]]) ).
thf(6730,plain,
v1_finset_1 @ sk453,
inference(cnf,[status(esa)],[6729]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(2867,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(2506,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1144,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(7049,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(422,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relset_1) ).
thf(3490,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(5619,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1301,axiom,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(7788,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(1036,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
<=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_relset_2) ).
thf(6540,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) )
& ( ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) )
=> ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1254,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(7578,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1520,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(8657,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(7122,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(8730,plain,
( ( v1_xboole_0 @ sk320 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,4841]) ).
thf(8731,plain,
sk320 != k1_xboole_0,
inference(simp,[status(thm)],[8730]) ).
thf(939,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(6083,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(8180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_partfun1) ).
thf(4331,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_finseq_2) ).
thf(4207,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_partfun1) ).
thf(1948,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(32785,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8233,32739]) ).
thf(32809,plain,
! [A: $i] :
( ( sk556 @ A )
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(simp,[status(thm)],[32785]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(5538,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ~ ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ~ ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(313,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(2816,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(15,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_1) ).
thf(1583,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
=> ( A
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_sysrel) ).
thf(1809,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
=> ( A
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(790,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_2) ).
thf(5424,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_realset1) ).
thf(4458,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1188,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(7296,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(24751,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,24716]) ).
thf(24767,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk432 ),
inference(simp,[status(thm)],[24751]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( k2_setfam_1 @ A @ B )
= ( k2_setfam_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_setfam_1) ).
thf(4868,plain,
! [A: $i,B: $i] :
( ( k2_setfam_1 @ A @ B )
= ( k2_setfam_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k1_funct_2 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(4886,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k1_funct_2 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1344,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(7975,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_mcart_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).
thf(3395,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_mcart_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(4456,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1189,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(7298,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(48417,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[3513,1544]) ).
thf(48418,plain,
( ( v1_funct_1 @ ( sk161 @ sk1 ) )
| ( m1_subset_1 @ sk3 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[48417:[bind(A,$thf( sk1 ))]]) ).
thf(1385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).
thf(8160,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1368,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m3_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).
thf(8099,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m3_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( m3_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(17896,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk536 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7900,1654]) ).
thf(17897,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk536 ) ) @ ( k1_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[17896:[bind(A,$thf( sk536 ))]]) ).
thf(99,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) ) ) )
& ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_sysrel) ).
thf(1905,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) ) ) )
& ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_relat_1) ).
thf(4529,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(26939,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk4 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,8938]) ).
thf(26940,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk5 ) @ sk1 )
| ( ( k2_zfmisc_1 @ sk1 @ sk2 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[26939:[bind(A,$thf( sk5 )),bind(B,$thf( sk8 @ sk5 ))]]) ).
thf(506,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(3981,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_relat_1) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1372,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(8116,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(5952,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( k10_pboole @ A @ B )
= ( k2_funcop_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_pboole) ).
thf(3048,plain,
! [A: $i,B: $i] :
( ( k10_pboole @ A @ B )
= ( k2_funcop_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(17267,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk13 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1808,1652]) ).
thf(17268,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk13 ) ) @ ( k1_relat_1 @ sk13 ),
inference(pattern_uni,[status(thm)],[17267:[bind(A,$thf( sk13 ))]]) ).
thf(12433,plain,
( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[12425,5002]) ).
thf(12434,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk332 ),
inference(simp,[status(thm)],[12433]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(6806,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(178,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2256,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(6843,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(569,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4355,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(8861,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ sk4 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ C @ sk1 )
| ( ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
!= ( m2_finseq_1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8794,8822]) ).
thf(8862,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ sk4 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8861:[bind(A,$thf( A )),bind(B,$thf( k2_zfmisc_1 @ sk1 @ sk2 )),bind(C,$thf( A ))]]) ).
thf(8885,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ~ ( m2_finseq_1 @ A @ sk5 )
| ( v1_xboole_0 @ sk4 )
| ~ ( m1_subset_1 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) @ ( k1_zfmisc_1 @ sk4 ) )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 ) ),
inference(simp,[status(thm)],[8862]) ).
thf(64120,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk42 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2425,1794]) ).
thf(64121,plain,
v1_xboole_0 @ ( k4_relat_1 @ sk42 ),
inference(pattern_uni,[status(thm)],[64120:[bind(A,$thf( sk42 ))]]) ).
thf(1351,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(8020,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(564,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_mcart_1) ).
thf(4336,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(17150,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,12488]) ).
thf(17151,plain,
v1_finset_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[17150:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
= ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_mcart_1) ).
thf(6132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
= ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2582,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(61545,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk421 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6306,1789]) ).
thf(61546,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk421 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk421 ) ),
inference(pattern_uni,[status(thm)],[61545:[bind(A,$thf( sk421 ))]]) ).
thf(6875,plain,
v1_funct_2 @ sk462 @ f1_s4_funct_2 @ f2_s4_funct_2,
inference(cnf,[status(esa)],[6872]) ).
thf(24759,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,24716]) ).
thf(24774,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk42 ),
inference(simp,[status(thm)],[24759]) ).
thf(11230,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_2_domain_1 )
| ( sk3 != f3_s9_domain_1 ) ),
inference(simp,[status(thm)],[10752]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(5822,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(4035,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(593,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(4490,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(1477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_domain_1) ).
thf(8466,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_partfun1) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1566,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
| ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ),
inference(cnf,[status(esa)],[1565]) ).
thf(17318,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk465 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6911,1652]) ).
thf(17319,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk465 ) ) @ ( k1_relat_1 @ sk465 ),
inference(pattern_uni,[status(thm)],[17318:[bind(A,$thf( sk465 ))]]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(4961,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( ( A != k1_xboole_0 )
=> ( ( B
= ( k1_setfam_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( B
= ( k1_setfam_1 @ A ) )
<=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(6367,plain,
! [A: $i,B: $i] :
( ( ( A != k1_xboole_0 )
=> ( ( ( B
= ( k1_setfam_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( B
= ( k1_setfam_1 @ A ) )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(6368,plain,
( ! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ! [B: $i] :
( ( B
= ( k1_setfam_1 @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( ! [B: $i] :
( ( B
= ( k1_setfam_1 @ A ) )
=> ( B = k1_xboole_0 ) )
& ! [B: $i] :
( ( B = k1_xboole_0 )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[6367]) ).
thf(6371,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( B
!= ( k1_setfam_1 @ A ) )
| ( B = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[6368]) ).
thf(6383,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( B
!= ( k1_setfam_1 @ A ) )
| ( B = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[6371]) ).
thf(6384,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[6383]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5446,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(4749,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(549,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(4255,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(9011,plain,
( ( v1_xboole_0 @ sk424 )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[6325,6046]) ).
thf(9022,plain,
sk424 != sk404,
inference(simp,[status(thm)],[9011]) ).
thf(26971,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk3 != f3_s9_domain_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_2_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11230]) ).
thf(26972,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_2_domain_1 ) @ sk1 )
| ( sk3 != f3_s9_domain_1 ) ),
inference(pattern_uni,[status(thm)],[26971:[bind(A,$thf( a_0_2_domain_1 )),bind(B,$thf( sk8 @ a_0_2_domain_1 ))]]) ).
thf(1541,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(8725,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(61557,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk283 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4511,1789]) ).
thf(61558,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk283 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk283 ) ),
inference(pattern_uni,[status(thm)],[61557:[bind(A,$thf( sk283 ))]]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6249,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(12486,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,3837]) ).
thf(12487,plain,
v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12486:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6238,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(3315,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(5514,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1440,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( C
!= ( k1_mcart_1 @ C ) )
& ( C
!= ( k2_mcart_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_mcart_1) ).
thf(8345,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( C
!= ( k1_mcart_1 @ C ) )
& ( C
!= ( k2_mcart_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(6399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(13958,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[8233,7808]) ).
thf(13967,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk533 ),
inference(simp,[status(thm)],[13958]) ).
thf(1172,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(7211,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(6051,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relset_2) ).
thf(8707,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(134,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_finseq_2) ).
thf(2060,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(4939,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A )
=> ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_tarski @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(5478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( ( k14_domain_1 @ A @ B @ C @ D )
= ( k17_mcart_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_domain_1) ).
thf(8598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( ( k14_domain_1 @ A @ B @ C @ D )
= ( k17_mcart_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(3260,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) )
& ( ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(33,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
=> ( v3_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_2) ).
thf(1646,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_2 @ A )
=> ( v3_relat_2 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1647,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v3_relat_2 @ A )
| ( v3_relat_2 @ ( k4_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1646]) ).
thf(1536,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(8701,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(64203,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk534 ) ),
inference(paramod_ordered,[status(thm)],[64099,7843]) ).
thf(64236,plain,
( ( k4_relat_1 @ sk536 )
!= sk534 ),
inference(simp,[status(thm)],[64203]) ).
thf(534,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_realset1 @ A )
<=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_realset1) ).
thf(4200,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
=> ~ ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1386,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(8163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(5074,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_realset1 @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(5592,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_realset1 @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( r1_realset1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_eqrel_1) ).
thf(3949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v3_relat_2 @ D )
& ( v1_partfun1 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(917,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_realset1) ).
thf(5980,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2518,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(4517,plain,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(589,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(4469,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(63,axiom,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_relat_1) ).
thf(1780,plain,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1367,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(8096,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(2720,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(573,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_partfun1) ).
thf(4377,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(4630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1441,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(8350,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_domain_1) ).
thf(6481,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) )
=> ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1424,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(8295,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(1285,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(7724,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(8801,plain,
( ( v1_xboole_0 @ sk465 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,6907]) ).
thf(8813,plain,
sk465 != sk275,
inference(simp,[status(thm)],[8801]) ).
thf(155,axiom,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_relat_1) ).
thf(2160,plain,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2831,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1355,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(8039,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(560,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(4314,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(10497,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,5927]) ).
thf(10504,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk432 ),
inference(simp,[status(thm)],[10497]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(4145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1399,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( C
!= ( k1_mcart_1 @ C ) )
& ( C
!= ( k2_mcart_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_mcart_1) ).
thf(8206,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( C
!= ( k1_mcart_1 @ C ) )
& ( C
!= ( k2_mcart_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_5) ).
thf(3853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1275,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(7672,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(5955,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_relat_1) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1506,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(8612,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(18438,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk421 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6306,1655]) ).
thf(18439,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk421 ) ) @ ( k2_relat_1 @ sk421 ),
inference(pattern_uni,[status(thm)],[18438:[bind(A,$thf( sk421 ))]]) ).
thf(1790,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[1788]) ).
thf(117,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pua2mss1) ).
thf(1987,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ( D
!= ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
| ( r2_hidden @ ( k1_funct_1 @ D @ B ) @ ( k2_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(cnf,[status(esa)],[1707]) ).
thf(1715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( k1_funct_1 @ C @ A ) )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
| ( r2_hidden @ ( k1_funct_1 @ D @ B ) @ ( k2_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(lifteq,[status(thm)],[1710]) ).
thf(1716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_relat_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( v1_funct_1 @ ( k1_funct_1 @ C @ A ) )
| ~ ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
| ~ ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_funct_1 @ C @ A ) ) )
| ( r2_hidden @ ( k1_funct_1 @ ( k1_funct_1 @ C @ A ) @ B ) @ ( k2_relat_1 @ ( k4_funct_5 @ C ) ) ) ),
inference(simp,[status(thm)],[1715]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_mcart_1) ).
thf(6981,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) )
=> ( ( ( k1_mcart_1 @ A )
= B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(1270,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(7655,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(851,axiom,
! [A: $i] :
( ( k18_mcart_1 @ A )
= ( k2_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_mcart_1) ).
thf(5731,plain,
! [A: $i] :
( ( k18_mcart_1 @ A )
= ( k2_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(7429,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(456,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3691,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(2688,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(64215,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk533 ) ),
inference(paramod_ordered,[status(thm)],[64099,7808]) ).
thf(64223,plain,
( ( k4_relat_1 @ sk536 )
!= sk533 ),
inference(simp,[status(thm)],[64215]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_setfam_1) ).
thf(6912,plain,
! [A: $i,B: $i] :
( ( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) )
=> ( r1_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(5015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(3722,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(435,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(3554,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(5912,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(8625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(942,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(6093,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(8496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(7443,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(818,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_domain_1) ).
thf(5555,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) ) )
& ( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(8802,plain,
( ( v1_xboole_0 @ sk332 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,5003]) ).
thf(8808,plain,
sk332 != sk275,
inference(simp,[status(thm)],[8802]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_2) ).
thf(3202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_2) ).
thf(1869,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15548,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,15520]) ).
thf(15556,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk42 ),
inference(simp,[status(thm)],[15548]) ).
thf(26903,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f2_s8_domain_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_1_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11186]) ).
thf(26904,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_1_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_1_domain_1 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f2_s8_domain_1 ) ) ),
inference(pattern_uni,[status(thm)],[26903:[bind(A,$thf( a_0_1_domain_1 )),bind(B,$thf( sk8 @ a_0_1_domain_1 ))]]) ).
thf(1349,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(7988,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2429,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(3655,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1401,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(8216,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(5948,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(6513,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(184,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2276,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(8509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(726,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(5154,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(17271,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk421 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6306,1652]) ).
thf(17272,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk421 ) ) @ ( k1_relat_1 @ sk421 ),
inference(pattern_uni,[status(thm)],[17271:[bind(A,$thf( sk421 ))]]) ).
thf(432,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r1_tarski @ C @ D )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t188_relat_1) ).
thf(3544,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r1_tarski @ C @ D )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(3828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(7351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
& ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( r2_hidden @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_mcart_1) ).
thf(2486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
& ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( r2_hidden @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(40220,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,3314]) ).
thf(40239,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk275 ),
inference(simp,[status(thm)],[40220]) ).
thf(395,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(3329,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_partfun1) ).
thf(4737,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(7127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(17282,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk42 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2428,1652]) ).
thf(17283,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk42 ) ) @ ( k1_relat_1 @ sk42 ),
inference(pattern_uni,[status(thm)],[17282:[bind(A,$thf( sk42 ))]]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(6994,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(6330,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(10500,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,5927]) ).
thf(10509,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk42 ),
inference(simp,[status(thm)],[10500]) ).
thf(50005,plain,
! [B: $i,A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( sk522 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3513,42185]) ).
thf(50006,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( sk522 @ A ) ) ),
inference(pattern_uni,[status(thm)],[50005:[bind(A,$thf( sk522 @ C )),bind(B,$thf( C ))]]) ).
thf(52123,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( sk522 @ A ) ) ),
inference(simp,[status(thm)],[50006]) ).
thf(225,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2468,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( ( k1_relat_1 @ C )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pua2mss1) ).
thf(5277,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( ( k1_relat_1 @ C )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(18455,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk23 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1947,1655]) ).
thf(18456,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk23 ) ) @ ( k2_relat_1 @ sk23 ),
inference(pattern_uni,[status(thm)],[18455:[bind(A,$thf( sk23 ))]]) ).
thf(15544,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,15520]) ).
thf(15557,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk432 ),
inference(simp,[status(thm)],[15544]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(6633,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(40254,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,4671]) ).
thf(40264,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[40254]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(5633,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k5_relat_1 @ A @ B )
!= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( v2_funct_1 @ A ) ),
inference(cnf,[status(esa)],[1583]) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( ( k5_relat_1 @ A @ B )
!= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1584]) ).
thf(848,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_domain_1) ).
thf(5717,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(5472,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(4150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(8729,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(cnf,[status(esa)],[8728]) ).
thf(35766,plain,
( ( v1_realset1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ) )
!= ( v1_realset1 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[35098,5002]) ).
thf(35790,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= sk332 ),
inference(simp,[status(thm)],[35766]) ).
thf(1534,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(8696,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(7466,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
= ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).
thf(6337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
= ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
& ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
<=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).
thf(6825,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
& ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) ) )
& ( ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) )
=> ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1063,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_orders_1) ).
thf(6679,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(449,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3652,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(6874,plain,
m2_relset_1 @ sk462 @ f1_s4_funct_2 @ f2_s4_funct_2,
inference(cnf,[status(esa)],[6872]) ).
thf(10557,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C )
| ( ( m2_relset_1 @ sk462 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6874,1577]) ).
thf(10558,plain,
( ( k5_relat_1 @ sk462 @ ( k6_relat_1 @ f2_s4_funct_2 ) )
= sk462 ),
inference(pattern_uni,[status(thm)],[10557:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk462 ))]]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(2558,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(17307,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk275 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4437,1652]) ).
thf(17308,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk275 ) ) @ ( k1_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[17307:[bind(A,$thf( sk275 ))]]) ).
thf(2426,plain,
v2_funct_1 @ sk42,
inference(cnf,[status(esa)],[2424]) ).
thf(42042,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,6993]) ).
thf(42049,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk424 ),
inference(simp,[status(thm)],[42042]) ).
thf(9675,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk5 )
| ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( m2_finseq_1 @ A @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ~ ( m2_finseq_1 @ A @ sk4 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[9616]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(6601,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(7342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(994,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( ( k1_mcart_1 @ C )
= ( k1_mcart_1 @ D ) )
& ( ( k2_mcart_1 @ C )
= ( k2_mcart_1 @ D ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_domain_1) ).
thf(6318,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( ( k1_mcart_1 @ C )
= ( k1_mcart_1 @ D ) )
& ( ( k2_mcart_1 @ C )
= ( k2_mcart_1 @ D ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mssubfam) ).
thf(7461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(685,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(4976,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(4436,plain,
v1_finseq_1 @ sk275,
inference(cnf,[status(esa)],[4433]) ).
thf(1181,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(7251,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_relat_1) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(61531,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk453 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6732,1789]) ).
thf(61532,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk453 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk453 ) ),
inference(pattern_uni,[status(thm)],[61531:[bind(A,$thf( sk453 ))]]) ).
thf(11881,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk275 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10491]) ).
thf(11882,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk275 ),
inference(pattern_uni,[status(thm)],[11881:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1304,axiom,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_orders_1) ).
thf(7797,plain,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(4510,plain,
v1_funct_1 @ sk283,
inference(cnf,[status(esa)],[4508]) ).
thf(1260,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_domain_1) ).
thf(7621,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(5504,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(64246,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[64101,6046]) ).
thf(64288,plain,
( ( k4_relat_1 @ sk432 )
!= sk404 ),
inference(simp,[status(thm)],[64246]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(4991,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(6193,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1432,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_subset_1) ).
thf(8317,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(8602,plain,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8601]) ).
thf(1394,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).
thf(8185,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(581,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4431,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(5685,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(9016,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,7808]) ).
thf(9019,plain,
sk533 != sk424,
inference(simp,[status(thm)],[9016]) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ),
inference(cnf,[status(esa)],[1796]) ).
thf(28977,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,17155]) ).
thf(28978,plain,
v1_finset_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[28977:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(2949,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(64283,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk453 ) ),
inference(paramod_ordered,[status(thm)],[64101,6733]) ).
thf(64293,plain,
( ( k4_relat_1 @ sk432 )
!= sk453 ),
inference(simp,[status(thm)],[64283]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
= ( k7_relat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_relat_1) ).
thf(2728,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
= ( k7_relat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(26945,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_2_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10752]) ).
thf(26946,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_2_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_2_domain_1 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f3_s9_domain_1 ) ) ),
inference(pattern_uni,[status(thm)],[26945:[bind(A,$thf( a_0_2_domain_1 )),bind(B,$thf( sk8 @ a_0_2_domain_1 ))]]) ).
thf(1223,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(7426,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1363,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(8087,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(6358,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(92,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_relat_1) ).
thf(1881,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).
thf(6161,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(648,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(4795,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(3520,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(820,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( C
= ( k4_tarski @ ( k1_mcart_1 @ C ) @ ( k2_mcart_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_mcart_1) ).
thf(5596,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( C
= ( k4_tarski @ ( k1_mcart_1 @ C ) @ ( k2_mcart_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_relat_1) ).
thf(2584,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1380,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(8140,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(3398,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(9442,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk534 ) ),
inference(paramod_ordered,[status(thm)],[7899,7843]) ).
thf(9453,plain,
sk536 != sk534,
inference(simp,[status(thm)],[9442]) ).
thf(61579,plain,
! [A: $i] :
( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
| ( ( v1_relat_1 @ sk23 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1947,1789]) ).
thf(61580,plain,
r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ sk23 ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[61579:[bind(A,$thf( sk23 ))]]) ).
thf(1469,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_domain_1) ).
thf(8431,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(970,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(6220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( k2_relat_1 @ C )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_2) ).
thf(3288,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) )
& ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1616,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( ( k1_funcop_1 @ ( k1_funcop_1 @ A ) )
= A ) ),
inference(cnf,[status(esa)],[1615]) ).
thf(1617,plain,
! [A: $i] :
( ( ( k1_funcop_1 @ ( k1_funcop_1 @ A ) )
= A )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1616]) ).
thf(16406,plain,
! [A: $i] :
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
!= ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8650,1546]) ).
thf(16416,plain,
! [A: $i] :
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk1 )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16406]) ).
thf(16443,plain,
( ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( sk2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[16416]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( ( k2_mcart_1 @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_mcart_1) ).
thf(5917,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( ( k2_mcart_1 @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(5653,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(3874,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1251,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(7570,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_xboole_0 @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_setfam_1) ).
thf(4678,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(6711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(5771,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(6284,plain,
v1_finset_1 @ sk420,
inference(cnf,[status(esa)],[6283]) ).
thf(1529,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_subset_1) ).
thf(8681,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(8805,plain,
( ( v1_xboole_0 @ sk533 )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,7808]) ).
thf(8812,plain,
sk533 != sk275,
inference(simp,[status(thm)],[8805]) ).
thf(387,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_partfun1) ).
thf(3284,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1112,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(6928,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(2760,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_setfam_1 @ C @ ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ~ ( r1_tarski @ D @ A )
& ~ ( r1_tarski @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_setfam_1) ).
thf(7363,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_setfam_1 @ C @ ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ~ ( r1_tarski @ D @ A )
& ~ ( r1_tarski @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(6286,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(411,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(3400,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(3478,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_mcart_1) ).
thf(5939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(3946,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(371,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k4_funct_5 @ A ) )
<=> ( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
<=> ? [D: $i,E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ? [F: $i] :
( ( C
= ( k4_tarski @ D @ F ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( E
= ( k1_funct_1 @ A @ D ) )
& ( r2_hidden @ F @ ( k1_relat_1 @ E ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
& ( D
= ( k1_funct_1 @ A @ ( k1_mcart_1 @ C ) ) ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ D @ ( k2_mcart_1 @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_5) ).
thf(3139,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k4_funct_5 @ A ) )
=> ( ! [C: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
=> ? [D: $i,E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ? [F: $i] :
( ( C
= ( k4_tarski @ D @ F ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( E
= ( k1_funct_1 @ A @ D ) )
& ( r2_hidden @ F @ ( k1_relat_1 @ E ) ) ) ) )
& ( ? [D: $i,E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ? [F: $i] :
( ( C
= ( k4_tarski @ D @ F ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( E
= ( k1_funct_1 @ A @ D ) )
& ( r2_hidden @ F @ ( k1_relat_1 @ E ) ) ) )
=> ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) )
& ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
& ( D
= ( k1_funct_1 @ A @ ( k1_mcart_1 @ C ) ) ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ D @ ( k2_mcart_1 @ C ) ) ) ) ) ) )
& ( ( ! [C: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
=> ? [D: $i,E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ? [F: $i] :
( ( C
= ( k4_tarski @ D @ F ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( E
= ( k1_funct_1 @ A @ D ) )
& ( r2_hidden @ F @ ( k1_relat_1 @ E ) ) ) ) )
& ( ? [D: $i,E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ? [F: $i] :
( ( C
= ( k4_tarski @ D @ F ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( E
= ( k1_funct_1 @ A @ D ) )
& ( r2_hidden @ F @ ( k1_relat_1 @ E ) ) ) )
=> ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) )
& ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
& ( D
= ( k1_funct_1 @ A @ ( k1_mcart_1 @ C ) ) ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ D @ ( k2_mcart_1 @ C ) ) ) ) ) )
=> ( B
= ( k4_funct_5 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
<=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1649,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_relat_1 @ ( k4_funct_5 @ A ) ) ),
inference(cnf,[status(esa)],[1648]) ).
thf(1316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F )
& ( r1_tarski @ G @ H ) )
=> ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_mcart_1) ).
thf(7844,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F )
& ( r1_tarski @ G @ H ) )
=> ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(1148,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( A
= ( k3_zfmisc_1 @ B @ C @ D ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_domain_1) ).
thf(7061,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( ( A
= ( k3_zfmisc_1 @ B @ C @ D ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) ) )
& ( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(4424,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_relat_1) ).
thf(4138,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(1099,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(6846,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1535,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(8698,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(228,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(2479,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_funct_1) ).
thf(6985,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
thf(2045,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_2) ).
thf(8028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(4587,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(641,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(4770,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1295,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(7764,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(17616,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk432 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6409,1653]) ).
thf(17617,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk432 ) ) @ ( k2_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[17616:[bind(A,$thf( sk432 ))]]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(7627,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1683]) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1684]) ).
thf(285,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(2696,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_2) ).
thf(2870,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_zfmisc_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(4165,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(2828,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(10496,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,5927]) ).
thf(10508,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk536 ),
inference(simp,[status(thm)],[10496]) ).
thf(43112,plain,
! [A: $i] :
( ( m1_eqrel_1 @ k1_xboole_0 @ A )
| ( ( k3_pua2mss1 @ k1_xboole_0 )
!= ( k3_pua2mss1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8506,8729]) ).
thf(43113,plain,
m1_eqrel_1 @ k1_xboole_0 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[43112:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) )
<=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_mcart_1) ).
thf(5777,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) )
=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 ) )
& ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1192,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k5_funcop_1 @ E @ D @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_finseq_2) ).
thf(7306,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k5_funcop_1 @ E @ D @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_partfun1) ).
thf(4873,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).
thf(5386,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_relat_1) ).
thf(4944,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(140,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_finseq_2) ).
thf(2078,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(578,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funcop_1) ).
thf(4419,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(3548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(17639,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk465 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6911,1653]) ).
thf(17640,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk465 ) ) @ ( k2_relat_1 @ sk465 ),
inference(pattern_uni,[status(thm)],[17639:[bind(A,$thf( sk465 ))]]) ).
thf(644,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(4780,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(263,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(2611,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(3928,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1116,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(6938,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1781,plain,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1780]) ).
thf(1456,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(8392,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(5907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( B
= ( k8_relat_1 @ A @ C ) )
<=> ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( B
= ( k8_relat_1 @ A @ C ) )
=> ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
=> ( B
= ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(32784,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,32739]) ).
thf(32818,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk432 ),
inference(simp,[status(thm)],[32784]) ).
thf(1406,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(8228,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(18459,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk432 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6409,1655]) ).
thf(18460,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk432 ) ) @ ( k2_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[18459:[bind(A,$thf( sk432 ))]]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_finseq_2) ).
thf(3346,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(3320,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1382,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(8153,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(1229,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(7446,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1807,plain,
v3_relat_1 @ sk13,
inference(cnf,[status(esa)],[1806]) ).
thf(729,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
= ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funcop_1) ).
thf(5184,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
= ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(4121,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(2273,plain,
v1_funct_1 @ sk34,
inference(cnf,[status(esa)],[2272]) ).
thf(26907,plain,
! [B: $i,A: $i] :
( sk500
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s12_funct_2 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk501 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10772]) ).
thf(26908,plain,
( sk500
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk501 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk501 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s12_funct_2 ) ),
inference(pattern_uni,[status(thm)],[26907:[bind(A,$thf( sk501 )),bind(B,$thf( sk8 @ sk501 ))]]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_relat_1) ).
thf(5191,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_sysrel) ).
thf(4250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(64544,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk275 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4434,1795]) ).
thf(64545,plain,
v1_relat_1 @ ( k4_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[64544:[bind(A,$thf( sk275 ))]]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(5899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1437,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(8336,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(64244,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk432 ) )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[64101,6285]) ).
thf(64297,plain,
( ( k4_relat_1 @ sk432 )
!= sk420 ),
inference(simp,[status(thm)],[64244]) ).
thf(6910,plain,
v1_funct_1 @ sk465,
inference(cnf,[status(esa)],[6906]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_setfam_1 @ A @ B )
& ( r1_setfam_1 @ B @ C ) )
=> ( r1_setfam_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_setfam_1) ).
thf(5394,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_setfam_1 @ A @ B )
& ( r1_setfam_1 @ B @ C ) )
=> ( r1_setfam_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(7120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(64529,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
| ( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7899,1795]) ).
thf(64530,plain,
v1_relat_1 @ ( k4_relat_1 @ sk536 ),
inference(pattern_uni,[status(thm)],[64529:[bind(A,$thf( sk536 ))]]) ).
thf(702,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
=> ( ( k7_relat_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t187_relat_1) ).
thf(5055,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
=> ( ( k7_relat_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F ) )
=> ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_mcart_1) ).
thf(7034,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F ) )
=> ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1443,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(8356,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(1403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).
thf(8221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(625,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( ( ( k3_funcop_1 @ D @ ( k6_finseq_1 @ A ) @ F )
= ( k6_finseq_1 @ C ) )
& ( ( k3_funcop_1 @ D @ E @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_finseq_2) ).
thf(4710,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( ( ( k3_funcop_1 @ D @ ( k6_finseq_1 @ A ) @ F )
= ( k6_finseq_1 @ C ) )
& ( ( k3_funcop_1 @ D @ E @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(17315,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk164 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3533,1652]) ).
thf(17316,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk164 ) ) @ ( k1_relat_1 @ sk164 ),
inference(pattern_uni,[status(thm)],[17315:[bind(A,$thf( sk164 ))]]) ).
thf(346,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_partfun1) ).
thf(2988,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_relat_1) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(2174,plain,
v3_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2173]) ).
thf(1094,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(6818,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1269,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_2) ).
thf(7653,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(44722,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C )
| ( ( m2_relset_1 @ sk462 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6874,1764]) ).
thf(44723,plain,
( ( k5_relat_1 @ ( k6_relat_1 @ f1_s4_funct_2 ) @ sk462 )
= sk462 ),
inference(pattern_uni,[status(thm)],[44722:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk462 ))]]) ).
thf(1672,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v2_funct_1 @ A )
| ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[1671]) ).
thf(1674,plain,
! [A: $i] :
( ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1672]) ).
thf(472,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(3789,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1639,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v1_funct_1 @ ( k1_funcop_1 @ A ) ) ),
inference(cnf,[status(esa)],[1637]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(5272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_setfam_1) ).
thf(4615,plain,
! [A: $i,B: $i] :
( ( ( r2_setfam_1 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) )
=> ( r2_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(40223,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2176,3314]) ).
thf(40236,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[40223]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(2406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1203,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(7344,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(24752,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8233,24716]) ).
thf(24769,plain,
! [A: $i] :
( ( sk556 @ A )
!= ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(simp,[status(thm)],[24752]) ).
thf(1088,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(6790,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(1748,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( ( k2_relat_1 @ A )
!= ( k1_tarski @ k1_xboole_0 ) )
| ( v3_relat_1 @ A ) ),
inference(cnf,[status(esa)],[1746]) ).
thf(1751,plain,
! [A: $i] :
( ( ( k2_relat_1 @ A )
!= ( k1_tarski @ k1_xboole_0 ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v3_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[1748]) ).
thf(43561,plain,
! [A: $i] :
( ( ( k2_relat_1 @ A )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( v3_relat_1 @ A ) ),
inference(rewrite,[status(thm)],[1751,8184]) ).
thf(626,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(4715,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(6023,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk403 @ B @ A ) ),
inference(cnf,[status(esa)],[6020]) ).
thf(49979,plain,
! [B: $i,A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3513,43501]) ).
thf(49980,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[49979:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(52116,plain,
! [A: $i] : ( v1_funct_1 @ ( sk161 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[49980]) ).
thf(1504,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_subset_1) ).
thf(8606,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(2608,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(35029,plain,
! [B: $i,A: $i] :
( ( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
!= sk424 )
| ( ( k1_tarski @ ( k4_tarski @ A @ A ) )
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1553,28949]) ).
thf(35030,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
!= sk424 ),
inference(pattern_uni,[status(thm)],[35029:[bind(A,$thf( D )),bind(B,$thf( k4_tarski @ D @ D ))]]) ).
thf(35049,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_tarski @ A ) ) ) ) )
!= sk424 ),
inference(simp,[status(thm)],[35030]) ).
thf(396,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= A )
& ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_sysrel) ).
thf(3331,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= A )
& ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(9447,plain,
( ( v1_xboole_0 @ sk536 )
!= ( v1_xboole_0 @ sk453 ) ),
inference(paramod_ordered,[status(thm)],[7899,6733]) ).
thf(9449,plain,
sk536 != sk453,
inference(simp,[status(thm)],[9447]) ).
thf(15549,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4373,15520]) ).
thf(15561,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(simp,[status(thm)],[15549]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(7125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3368,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(13948,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk420 ) ),
inference(paramod_ordered,[status(thm)],[8233,6285]) ).
thf(13969,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk420 ),
inference(simp,[status(thm)],[13948]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(4969,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(17592,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk453 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6732,1653]) ).
thf(17593,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk453 ) ) @ ( k2_relat_1 @ sk453 ),
inference(pattern_uni,[status(thm)],[17592:[bind(A,$thf( sk453 ))]]) ).
thf(1508,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(8617,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_funct_1) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(6799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(26977,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_0_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11150]) ).
thf(26978,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_0_domain_1 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(pattern_uni,[status(thm)],[26977:[bind(A,$thf( a_0_0_domain_1 )),bind(B,$thf( sk8 @ a_0_0_domain_1 ))]]) ).
thf(1412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k16_domain_1 @ A @ B @ C @ D )
= ( k19_mcart_1 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k16_domain_1) ).
thf(8240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k16_domain_1 @ A @ B @ C @ D )
= ( k19_mcart_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(821,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(5600,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_partfun1 @ A @ B @ C @ D )
= ( k7_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_partfun1 @ A @ B @ C @ D )
= ( k7_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(8119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_sysrel @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_sysrel) ).
thf(2394,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_sysrel @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) )
& ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(5828,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(3497,plain,
v1_finseq_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3495]) ).
thf(136,axiom,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_1) ).
thf(2066,plain,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(40249,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,4671]) ).
thf(40268,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk275 ),
inference(simp,[status(thm)],[40249]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(5128,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(888,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(5864,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2421,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(2447,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1389,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(8172,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(40260,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk424 ) ),
inference(paramod_ordered,[status(thm)],[6325,4671]) ).
thf(40271,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk424 ),
inference(simp,[status(thm)],[40260]) ).
thf(11209,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk432 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10490]) ).
thf(11210,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk432 ),
inference(pattern_uni,[status(thm)],[11209:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(457,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(3694,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(611,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4602,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(533,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(4197,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(8369,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(307,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(2796,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(8272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(6430,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1101,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_2) ).
thf(6854,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(18446,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk283 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4511,1655]) ).
thf(18447,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk283 ) ) @ ( k2_relat_1 @ sk283 ),
inference(pattern_uni,[status(thm)],[18446:[bind(A,$thf( sk283 ))]]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(5532,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(6181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
thf(3585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(6554,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(8638,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(4299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(7312,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
= ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).
thf(5409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
= ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(164,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_sysrel @ A ) @ A )
& ( r1_tarski @ ( k1_sysrel @ A ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_sysrel) ).
thf(2198,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_sysrel @ A ) @ A )
& ( r1_tarski @ ( k1_sysrel @ A ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v2_funct_1 @ C )
| ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ),
inference(cnf,[status(esa)],[1705]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(5699,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1161,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_2) ).
thf(7157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(202,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(2362,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(2161,plain,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[2160]) ).
thf(2162,plain,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[2161]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(5549,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1034,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(6536,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(980,axiom,
! [A: $i] :
( ( k20_mcart_1 @ A )
= ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_mcart_1) ).
thf(6252,plain,
! [A: $i] :
( ( k20_mcart_1 @ A )
= ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(51212,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[3513,16443]) ).
thf(51213,plain,
( ( v1_funct_1 @ ( sk161 @ sk2 ) )
| ( m1_subset_1 @ sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[51212:[bind(A,$thf( sk2 ))]]) ).
thf(959,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(6166,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(26911,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_0_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11151]) ).
thf(26912,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_0_domain_1 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk4 )
!= ( k1_zfmisc_1 @ f1_s7_domain_1 ) ) ),
inference(pattern_uni,[status(thm)],[26911:[bind(A,$thf( a_0_0_domain_1 )),bind(B,$thf( sk8 @ a_0_0_domain_1 ))]]) ).
thf(17871,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk432 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6409,1654]) ).
thf(17872,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk432 ) ) @ ( k1_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[17871:[bind(A,$thf( sk432 ))]]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_mcart_1) ).
thf(5119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ A )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_finseq_2) ).
thf(1893,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ A )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(2032,plain,
! [A: $i] : ( v8_relat_2 @ ( k1_eqrel_1 @ A ) ),
inference(cnf,[status(esa)],[2029]) ).
thf(2036,plain,
! [A: $i] : ( v8_relat_2 @ ( k1_eqrel_1 @ A ) ),
inference(simp,[status(thm)],[2032]) ).
thf(1252,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
thf(7574,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(2494,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(12490,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C )
| ( ( m2_relset_1 @ sk557 @ f1_s11_funct_2 @ f2_s11_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8253,1577]) ).
thf(12491,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k5_relat_1 @ sk557 @ ( k6_relat_1 @ f2_s11_funct_2 ) )
= sk557 ) ),
inference(pattern_uni,[status(thm)],[12490:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk557 ))]]) ).
thf(40637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D )
= D )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ D @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5851,1600]) ).
thf(40638,plain,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40637:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( k1_xboole_0 ))]]) ).
thf(40670,plain,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[40638]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(6462,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(434,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3552,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(6499,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(2779,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(5852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(17296,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk432 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6409,1652]) ).
thf(17297,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk432 ) ) @ ( k1_relat_1 @ sk432 ),
inference(pattern_uni,[status(thm)],[17296:[bind(A,$thf( sk432 ))]]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(5430,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3337,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(6580,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(179,axiom,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_sysrel) ).
thf(2258,plain,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1439,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k1_tarski @ A ) )
=> ( ( k7_setfam_1 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(8341,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k1_tarski @ A ) )
=> ( ( k7_setfam_1 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1641,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[1640]) ).
thf(1642,plain,
! [A: $i] :
( ( ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
= A )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1641]) ).
thf(17845,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk453 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6732,1654]) ).
thf(17846,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk453 ) ) @ ( k1_relat_1 @ sk453 ),
inference(pattern_uni,[status(thm)],[17845:[bind(A,$thf( sk453 ))]]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(5009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(6326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1221,axiom,
! [A: $i] :
( ( k17_mcart_1 @ A )
= ( k1_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_mcart_1) ).
thf(7419,plain,
! [A: $i] :
( ( k17_mcart_1 @ A )
= ( k1_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(8070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
=> ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(3705,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(109,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funcop_1) ).
thf(1957,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).
thf(4472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) ) )
& ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) )
=> ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(1133,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(7016,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1207,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(7355,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(207,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 )
=> ( ( ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k7_relat_1 @ A @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 )
=> ( ( ( k8_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k8_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_sysrel) ).
thf(2385,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 )
=> ( ( ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k7_relat_1 @ A @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 )
=> ( ( ( k8_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k8_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(5606,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_mcart_1) ).
thf(7634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_2) ).
thf(3232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(6007,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1480,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k3_domain_1 @ A @ B @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_domain_1) ).
thf(8478,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k3_domain_1 @ A @ B @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(6822,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(1397,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(8193,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_partfun1) ).
thf(5004,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(653,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(4811,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(7231,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1291,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(7744,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(24750,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk536 ) ),
inference(paramod_ordered,[status(thm)],[7899,24716]) ).
thf(24773,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk536 ),
inference(simp,[status(thm)],[24750]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(6563,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funct_2) ).
thf(2233,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1273,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(7666,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(20580,plain,
! [A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ a_0_0_domain_1 )
| ( sk4 != f1_s7_domain_1 ) ),
inference(simp,[status(thm)],[11151]) ).
thf(1313,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(7836,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( v3_relat_1 @ ( k7_relat_1 @ B @ A ) )
| ~ ( v3_relat_1 @ B ) ),
inference(cnf,[status(esa)],[1624]) ).
thf(508,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_mcart_1) ).
thf(3987,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(7712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_funct_1) ).
thf(2951,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(710,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(5078,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(42033,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,6993]) ).
thf(42048,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk275 ),
inference(simp,[status(thm)],[42033]) ).
thf(18449,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk42 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2428,1655]) ).
thf(18450,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk42 ) ) @ ( k2_relat_1 @ sk42 ),
inference(pattern_uni,[status(thm)],[18449:[bind(A,$thf( sk42 ))]]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_partfun1) ).
thf(4523,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(24753,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,24716]) ).
thf(24768,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= sk275 ),
inference(simp,[status(thm)],[24753]) ).
thf(40218,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,3314]) ).
thf(40235,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk432 ),
inference(simp,[status(thm)],[40218]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(5527,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(7248,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(4357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(7209,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[7208]) ).
thf(7210,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[7209]) ).
thf(303,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2768,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(6226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(5760,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(8922,plain,
( ( v1_xboole_0 @ sk421 )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[6305,6046]) ).
thf(8933,plain,
sk421 != sk404,
inference(simp,[status(thm)],[8922]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(6782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(18434,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk453 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6732,1655]) ).
thf(18435,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ sk453 ) ) @ ( k2_relat_1 @ sk453 ),
inference(pattern_uni,[status(thm)],[18434:[bind(A,$thf( sk453 ))]]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_1) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1458,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(8400,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
thf(5990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(17305,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ k1_xboole_0 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2175,1652]) ).
thf(17306,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ k1_xboole_0 ) ) @ ( k1_relat_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[17305:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(17810,plain,
r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ k1_xboole_0 ) ) @ k1_xboole_0,
inference(rewrite,[status(thm)],[17306,2741]) ).
thf(10573,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ~ ( m2_finseq_1 @ B @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( m1_subset_1 @ sk498 @ f1_s14_funct_2 )
!= ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7382,8825]) ).
thf(10582,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ~ ( m2_finseq_1 @ B @ A )
| ( sk498 != A )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s14_funct_2 ) ),
inference(simp,[status(thm)],[10573]) ).
thf(10586,plain,
! [A: $i] :
( sk497
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ A @ sk1 )
| ~ ( m2_finseq_1 @ A @ sk498 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s14_funct_2 ) ),
inference(simp,[status(thm)],[10582]) ).
thf(26991,plain,
! [B: $i,A: $i] :
( sk497
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s14_funct_2 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk498 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,10586]) ).
thf(26992,plain,
( sk497
| ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk498 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk498 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= f1_s14_funct_2 ) ),
inference(pattern_uni,[status(thm)],[26991:[bind(A,$thf( sk498 )),bind(B,$thf( sk8 @ sk498 ))]]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(7278,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1244,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(7525,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_vectsp_1 @ A @ B @ C )
= ( g1_vectsp_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_vectsp_1) ).
thf(6411,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_vectsp_1 @ A @ B @ C )
= ( g1_vectsp_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1198,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).
thf(7323,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) )
=> ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1493,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(8542,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(1319,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(7851,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(1054,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(6627,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(165,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
thf(2201,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_5) ).
thf(1989,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_5) ).
thf(4350,plain,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1492,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ A )
<=> ( p1_s2_subset_1 @ C ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ B )
<=> ( p1_s2_subset_1 @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_subset_1) ).
thf(8521,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ A )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ A ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ B )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ B ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(26959,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ B @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,8794]) ).
thf(26960,plain,
( ( v1_xboole_0 @ ( k2_zfmisc_1 @ sk1 @ sk2 ) )
| ( v1_xboole_0 @ sk5 )
| ( m2_finseq_1 @ ( sk8 @ sk5 ) @ ( k2_zfmisc_1 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26959:[bind(A,$thf( sk5 )),bind(B,$thf( sk8 @ sk5 ))]]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(7184,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(4157,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_relat_1) ).
thf(5019,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1466,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(8424,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_relat_1) ).
thf(2572,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1039,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(6558,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(8515,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[8514]) ).
thf(8516,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8515]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(7474,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(15485,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[4373,5003]) ).
thf(15493,plain,
! [A: $i] :
( ( k2_funcop_1 @ k1_xboole_0 @ A )
!= sk332 ),
inference(simp,[status(thm)],[15485]) ).
thf(1420,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(8277,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(740,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_relat_1) ).
thf(5251,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(17867,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk23 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1947,1654]) ).
thf(17868,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk23 ) ) @ ( k1_relat_1 @ sk23 ),
inference(pattern_uni,[status(thm)],[17867:[bind(A,$thf( sk23 ))]]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_relat_1) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(469,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3765,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(8268,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(12430,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= k1_xboole_0 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8184,10494]) ).
thf(12431,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12430:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(13953,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk534 ) ),
inference(paramod_ordered,[status(thm)],[8233,7843]) ).
thf(13966,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk534 ),
inference(simp,[status(thm)],[13953]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(6040,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(6929,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[6928]) ).
thf(452,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(3673,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(6272,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(cnf,[status(esa)],[6271]) ).
thf(6273,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(lifteq,[status(thm)],[6272]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relset_1) ).
thf(2063,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1610,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v8_relat_2 @ E )
| ~ ( v1_partfun1 @ E @ A @ A )
| ~ ( m2_relset_1 @ E @ A @ A )
| ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ E )
| ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
| ( r2_hidden @ ( k4_tarski @ B @ D ) @ E ) ),
inference(cnf,[status(esa)],[1609]) ).
thf(794,axiom,
! [A: $i] :
( ( k19_mcart_1 @ A )
= ( k1_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_mcart_1) ).
thf(5440,plain,
! [A: $i] :
( ( k19_mcart_1 @ A )
= ( k1_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2651,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_2) ).
thf(4318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(8236,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[8235]) ).
thf(15546,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
!= ( v1_xboole_0 @ sk275 ) ),
inference(paramod_ordered,[status(thm)],[4434,15520]) ).
thf(15553,plain,
( ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= sk275 ),
inference(simp,[status(thm)],[15546]) ).
thf(349,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(3025,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(9032,plain,
( ( v1_xboole_0 @ sk534 )
!= ( v1_xboole_0 @ sk432 ) ),
inference(paramod_ordered,[status(thm)],[6410,7843]) ).
thf(9038,plain,
sk534 != sk432,
inference(simp,[status(thm)],[9032]) ).
thf(354,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(3057,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1064,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(6697,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(4506,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(4484,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(5060,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(7755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(1527,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(8675,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( ( k1_mcart_1 @ ( k4_tarski @ A @ B ) )
= A )
& ( ( k2_mcart_1 @ ( k4_tarski @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(3244,plain,
! [A: $i,B: $i] :
( ( ( k1_mcart_1 @ ( k4_tarski @ A @ B ) )
= A )
& ( ( k2_mcart_1 @ ( k4_tarski @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
= ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
=> ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_vectsp_1) ).
thf(6771,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
= ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
=> ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_mcart_1) ).
thf(7214,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
=> ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
& ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(6190,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(2810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(293,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(2731,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_partfun1) ).
thf(5204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_5) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(42043,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk421 ) ),
inference(paramod_ordered,[status(thm)],[6305,6993]) ).
thf(42053,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk421 ),
inference(simp,[status(thm)],[42043]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(8444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_mcart_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_mcart_1) ).
thf(4382,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_mcart_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(721,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_relat_1) ).
thf(5140,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(9014,plain,
( ( v1_xboole_0 @ sk424 )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[6325,5003]) ).
thf(9023,plain,
sk424 != sk332,
inference(simp,[status(thm)],[9014]) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
| ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ),
inference(cnf,[status(esa)],[1581]) ).
thf(671,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(4876,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) )
& ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(545,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_partfun1) ).
thf(4239,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(7387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(4831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1212,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(7370,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(910,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(5958,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1471,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(8437,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(32793,plain,
( ( v1_xboole_0 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) ) )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,32739]) ).
thf(32812,plain,
( ( k6_relat_1 @ ( k6_relat_1 @ ( k6_relat_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ) )
!= sk42 ),
inference(simp,[status(thm)],[32793]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ~ ( r1_xboole_0 @ A @ D )
& ~ ( r1_xboole_0 @ B @ E )
& ~ ( r1_xboole_0 @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_mcart_1) ).
thf(5236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ~ ( r1_xboole_0 @ A @ D )
& ~ ( r1_xboole_0 @ B @ E )
& ~ ( r1_xboole_0 @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(4936,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4395,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m2_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(5468,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m2_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(242,axiom,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_realset1) ).
thf(2539,plain,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( ( k2_mcart_1 @ A )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_mcart_1) ).
thf(5354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( ( ( k1_mcart_1 @ A )
= B )
| ( ( k1_mcart_1 @ A )
= C ) )
& ( ( k2_mcart_1 @ A )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(324,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
= ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_relat_1) ).
thf(2864,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
= ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_relat_1) ).
thf(3113,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(1902,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pua2mss1) ).
thf(5376,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1037,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(6548,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1427,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(8305,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(17848,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk421 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6306,1654]) ).
thf(17849,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk421 ) ) @ ( k1_relat_1 @ sk421 ),
inference(pattern_uni,[status(thm)],[17848:[bind(A,$thf( sk421 ))]]) ).
thf(768,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(5344,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1483,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_domain_1) ).
thf(8493,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
thf(2138,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(2879,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(64207,plain,
( ( v1_xboole_0 @ ( k4_relat_1 @ sk536 ) )
!= ( v1_xboole_0 @ sk332 ) ),
inference(paramod_ordered,[status(thm)],[64099,5003]) ).
thf(64225,plain,
( ( k4_relat_1 @ sk536 )
!= sk332 ),
inference(simp,[status(thm)],[64207]) ).
thf(845,axiom,
( ( ( v1_finset_1 @ f1_s2_finset_1 )
& ( p1_s2_finset_1 @ k1_xboole_0 )
& ! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ f1_s2_finset_1 )
& ( r1_tarski @ B @ f1_s2_finset_1 )
& ( p1_s2_finset_1 @ B ) )
=> ( p1_s2_finset_1 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) ) ) )
=> ( p1_s2_finset_1 @ f1_s2_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_finset_1) ).
thf(5707,plain,
( ( ( v1_finset_1 @ f1_s2_finset_1 )
& ( p1_s2_finset_1 @ k1_xboole_0 )
& ! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ f1_s2_finset_1 )
& ( r1_tarski @ B @ f1_s2_finset_1 )
& ( p1_s2_finset_1 @ B ) )
=> ( p1_s2_finset_1 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) ) ) )
=> ( p1_s2_finset_1 @ f1_s2_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(6810,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(2453,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(5293,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(50763,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( A != sk320 ) ),
inference(paramod_ordered,[status(thm)],[3513,8731]) ).
thf(50764,plain,
v1_funct_1 @ ( sk161 @ sk320 ),
inference(pattern_uni,[status(thm)],[50763:[bind(A,$thf( sk320 ))]]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k8_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(3960,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k8_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k8_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(7195,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1605,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[1604]) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
| ~ ( v1_relat_1 @ B ) ),
inference(lifteq,[status(thm)],[1605]) ).
thf(17628,plain,
! [A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk275 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4437,1653]) ).
thf(17629,plain,
r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ sk275 ) ) @ ( k2_relat_1 @ sk275 ),
inference(pattern_uni,[status(thm)],[17628:[bind(A,$thf( sk275 ))]]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( r2_hidden @ D @ A )
<=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(6961,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ~ ( r2_hidden @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
& ( ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) )
=> ~ ( r2_hidden @ D @ A ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(3921,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3919]) ).
thf(3924,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3921]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(5986,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1945,plain,
v1_funct_1 @ sk23,
inference(cnf,[status(esa)],[1944]) ).
thf(1445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k9_relset_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(8363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k9_relset_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1318,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(7848,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(5458,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(358,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3096,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(329,axiom,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(2887,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(4767,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1146,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(7056,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1197,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(7320,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(8738,plain,
( ( v1_xboole_0 @ sk404 )
!= ( v1_xboole_0 @ sk42 ) ),
inference(paramod_ordered,[status(thm)],[2425,6046]) ).
thf(8741,plain,
sk404 != sk42,
inference(simp,[status(thm)],[8738]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(6718,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(40649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) )
= D )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ D @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5851,1599]) ).
thf(40650,plain,
! [A: $i] :
( ( k5_relat_1 @ k1_xboole_0 @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40649:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( k1_xboole_0 ))]]) ).
thf(40663,plain,
! [A: $i] :
( ( k5_relat_1 @ k1_xboole_0 @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[40650]) ).
thf(26955,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ sk560 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,11169]) ).
thf(26956,plain,
( ( v1_xboole_0 @ sk3 )
| ( v1_xboole_0 @ sk560 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ sk560 ) @ sk1 )
| ( ( k1_zfmisc_1 @ sk3 )
!= ( k1_zfmisc_1 @ f1_s3_subset_1 ) ) ),
inference(pattern_uni,[status(thm)],[26955:[bind(A,$thf( sk560 )),bind(B,$thf( sk8 @ sk560 ))]]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_sysrel) ).
thf(2018,plain,
! [A: $i,B: $i] :
( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(27553,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ k1_xboole_0 )
= k1_xboole_0 )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2072,1685]) ).
thf(27554,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ k1_xboole_0 @ A ) ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[27553:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(27587,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ k1_xboole_0 @ A ) ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[27554]) ).
thf(33992,plain,
( ( k4_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[27587,7962]) ).
thf(34022,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) @ k1_xboole_0 )
!= ( k4_xboole_0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33992,1685]) ).
thf(34023,plain,
( ( k4_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) @ ( k6_relat_1 @ ( k6_relat_1 @ k1_xboole_0 ) ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[34022:[bind(A,$thf( k6_relat_1 @ k1_xboole_0 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(34947,plain,
( ( k4_xboole_0 @ k1_xboole_0 @ ( k6_relat_1 @ k1_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[34023,2072]) ).
thf(8179,plain,
! [A: $i] : ( m1_subset_1 @ ( sk553 @ A ) @ A ),
inference(cnf,[status(esa)],[8178]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( B
= ( k7_relat_1 @ C @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
thf(2436,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( B
= ( k7_relat_1 @ C @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
=> ( B
= ( k7_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(83,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_relat_1) ).
thf(1848,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1102,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(6857,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(6761,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3432,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(13949,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk556 @ A ) )
!= ( v1_xboole_0 @ sk404 ) ),
inference(paramod_ordered,[status(thm)],[8233,6046]) ).
thf(13962,plain,
! [A: $i] :
( ( sk556 @ A )
!= sk404 ),
inference(simp,[status(thm)],[13949]) ).
thf(1500,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(8596,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(7267,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(26987,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ B @ sk1 )
| ( sk4 != f1_s7_domain_1 )
| ( ( m2_finseq_1 @ ( sk8 @ A ) @ A )
!= ( m2_finseq_1 @ B @ a_0_0_domain_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1682,20580]) ).
thf(26988,plain,
( ( v1_xboole_0 @ sk4 )
| ( v1_xboole_0 @ a_0_0_domain_1 )
| ( v1_xboole_0 @ sk1 )
| ( m2_finseq_1 @ ( sk8 @ a_0_0_domain_1 ) @ sk1 )
| ( sk4 != f1_s7_domain_1 ) ),
inference(pattern_uni,[status(thm)],[26987:[bind(A,$thf( a_0_0_domain_1 )),bind(B,$thf( sk8 @ a_0_0_domain_1 ))]]) ).
thf(162,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_sysrel) ).
thf(2191,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(75,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1812,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
<=> ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_mcart_1) ).
thf(4858,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) ) )
& ( ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) )
=> ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_relat_1) ).
thf(2470,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(51650,plain,
! [A: $i] :
( ( v1_funct_1 @ ( sk161 @ A ) )
| ( ( k4_subset_1 @ sk1 @ sk3 @ k1_xboole_0 )
!= sk4 )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[3513,8737]) ).
thf(51651,plain,
( ( v1_funct_1 @ ( sk161 @ sk4 ) )
| ( ( k4_subset_1 @ sk1 @ sk3 @ k1_xboole_0 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[51650:[bind(A,$thf( sk4 ))]]) ).
thf(1460,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(8405,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1525,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relset_2) ).
thf(8670,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1108,axiom,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).
thf(6896,plain,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(6933,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(2655,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_mcart_1) ).
thf(4734,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1384,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(8157,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(95329,plain,
$false,
inference(e,[status(thm)],[2163,6979,6172,8475,5385,5437,1665,6085,2822,7304,1586,7373,8930,26920,5422,1718,3944,5365,2744,6355,2131,7854,11211,1633,46998,11186,1767,2072,5260,1559,52049,42095,4729,26942,1729,5950,6651,3434,8514,5320,6283,15558,48864,8507,1899,6285,10495,41974,1840,20544,4852,2427,1982,7396,6014,1950,5131,1549,47344,1554,1686,6808,10507,2250,8434,2622,5069,2527,1591,2114,8366,30018,4532,16898,3534,7601,6057,15490,8855,6022,6587,7040,9020,7888,4037,24772,7886,28949,7477,12426,2210,7940,1596,7083,6944,3317,8044,2808,6106,3762,2381,6744,8709,2776,1808,2659,5242,8402,1618,8811,9045,3460,1569,1939,2671,1544,3910,5793,8315,1728,3108,8271,29537,3498,4215,1971,1793,8928,4623,6031,4973,7341,5348,6017,7208,6732,4487,12013,4739,4279,4440,1640,4435,7980,6640,7793,8320,1705,6522,1788,3530,64355,5814,10775,4234,1671,8733,3794,1608,4633,6764,1655,64302,3429,7203,8551,18482,7697,7695,7405,4839,5755,10772,3135,3942,3365,2740,8747,8353,8490,8519,6089,2933,7669,6727,2141,5257,8298,5146,7949,1872,4058,17609,3826,7422,1761,13960,3121,7188,2901,61568,6117,8650,1954,7748,17285,5412,6046,2575,3370,7018,3350,8578,5921,8256,2082,1724,1623,7028,6138,1746,3103,6236,4792,16868,2972,5977,6909,49168,1914,13965,7637,6268,2548,1782,40238,3502,5935,42809,5518,6872,3513,6623,7734,7235,7729,2010,1935,42667,4803,4124,1650,5723,1645,17843,1601,5301,3809,2173,8678,6306,4607,8025,4760,4963,7761,2819,5269,6608,11151,4610,7043,7178,8224,4467,4511,10584,5352,5797,8603,7390,2957,8178,1792,4422,5188,2274,43544,8374,7743,5765,4439,7241,4546,7790,3221,49574,32811,7277,4743,2039,3275,6034,8426,5883,6538,4956,3116,7401,6274,5284,3689,17857,3342,2755,3495,4224,6878,6723,12046,17598,7528,6423,6749,26934,5274,40266,4654,6350,7771,3125,1826,17613,2682,17270,1577,6713,5640,46908,5712,6519,1992,7000,3353,2126,3803,2466,5836,8880,2356,5461,7011,13961,6502,4368,1815,17884,8257,5744,1545,2691,7862,6010,8121,6240,3099,1800,5338,8054,4353,5866,8389,2403,5521,40234,36002,1704,44486,7803,8819,5193,8571,8468,1609,5622,5323,1572,16452,8235,5925,1741,6936,52292,7857,5052,4675,17588,42385,7436,3312,5851,3657,29943,8615,3951,17181,64295,3835,3708,29362,4265,1773,9039,5076,8126,1963,3557,8037,44627,6025,6734,3231,4302,3866,5617,7112,7500,7309,28591,4669,1847,18479,8293,5974,1946,8190,6840,7894,5084,5861,5856,8659,2456,2007,5682,8109,2237,4988,5264,10729,7107,7144,1714,8416,3724,17635,30962,4600,7969,26916,1632,8627,26938,8934,7104,2451,6410,8791,6135,8929,1682,7537,4147,3525,10757,35098,4724,10491,7677,5032,7532,15554,6054,2291,4134,7739,25584,8642,1677,5805,4871,2555,8246,8511,4798,3923,1960,1581,17862,7139,49338,4783,2073,8664,4162,7899,5834,11168,4842,2190,4307,4825,64101,24776,8050,2964,1843,6591,4751,26974,8274,15494,2367,7036,6648,5773,3068,4230,9616,4033,7613,5401,2281,6110,5384,2483,11876,8817,9452,6947,18097,1796,26926,1622,2424,6347,4996,5296,4040,2002,3756,3955,42052,32806,2799,2286,7830,6156,1600,5137,3588,4379,51989,3559,5819,8094,2154,5824,6103,3906,5328,4211,12306,9024,2586,2982,4065,5695,1564,8742,2762,8421,5298,1604,3229,3503,7859,5968,3679,8751,2954,1651,10494,7674,5174,5961,7254,8170,64227,5406,3591,7782,2204,7471,61573,4589,8640,6020,2473,8046,3567,7022,8302,6015,7393,8233,3720,6731,29499,8243,3984,3265,6047,10506,7814,3531,8382,5443,32739,7217,24716,61292,12425,7937,8397,5291,3995,7357,12068,2737,6307,2296,3054,2641,5519,31051,6741,2496,4312,1768,9041,8668,9043,2773,17642,1636,5122,8712,7439,1723,5734,6605,4434,24731,2606,42631,2015,2264,42051,6122,2428,5630,2805,38295,40262,8091,2596,8329,4397,5002,7827,7353,1580,6264,51591,5512,1570,1676,18471,5455,24775,6565,2969,4344,30054,3752,8334,4204,64230,17193,7640,4493,1824,3816,7984,6496,5396,6178,3286,5843,7301,7957,8746,1560,8623,9455,59326,5021,2179,4746,6096,1656,7767,5769,3271,3958,7237,6303,8810,7977,2758,8255,5879,10756,5983,4140,4849,32807,8371,7842,5465,7576,10490,4585,8270,2433,1968,2565,51929,8386,6427,2663,35118,7449,3314,4994,4947,47002,5690,17606,1888,4553,7503,6708,4776,1687,2068,23568,1624,7934,8847,29981,5858,7891,8226,2741,8031,8287,64350,1634,4732,5936,2228,3931,3033,1573,3799,5066,8155,4063,2653,1804,2709,3060,16893,46992,15559,8238,7540,4808,5313,6795,2245,1592,3467,5626,7281,5904,8446,6324,6677,3831,16910,5609,17314,42045,2157,1762,2515,3254,6101,1851,1772,2946,2990,44721,6940,1794,7962,6153,4512,2685,5006,8562,4248,5615,6195,8282,2359,8339,6603,60521,5635,6459,4789,1856,24771,15065,7838,8931,8041,8619,2509,8014,3518,50740,1878,2631,4930,1719,4227,8187,39244,8636,5811,6360,4840,6958,8429,30096,5081,8572,64108,8662,16620,5233,7809,5687,8138,5475,40237,7898,2323,6304,15495,9085,2978,3573,12045,6299,1567,8792,1683,7101,4333,6862,64235,8704,64139,8631,17890,6175,1964,1942,5915,3846,8938,5181,17619,7717,2561,6720,29372,7846,7981,16348,3094,17895,5992,10528,3714,6363,7318,8743,8687,2312,10776,2196,2240,7841,13964,8132,8499,6630,1937,1791,7930,3194,7480,2551,7059,7806,3643,6946,64220,2666,6625,10752,51649,4814,6271,7523,2317,2968,7340,46988,2536,5134,8690,4934,5058,32810,4347,1759,5317,1776,4846,5850,8458,8673,8219,40265,5374,5149,8326,6033,7463,4508,7014,2845,3354,4068,6999,7966,3770,8410,1668,1974,6433,6475,2355,6876,9448,15560,61530,1947,43486,3628,6005,5305,6908,8455,6465,8775,2862,31044,1599,6418,8090,5801,1720,5603,18452,1979,8142,40233,2272,7624,7333,6224,6988,43501,5245,2370,8935,29461,4535,5310,17293,2702,26958,16644,5964,2963,15520,1732,7646,7661,3476,8846,2634,6409,1779,7052,48568,7721,26932,15499,2043,49856,4966,42185,6859,9044,1563,6716,2057,1712,7414,26986,43136,10503,5419,15552,4448,6756,1663,8609,6610,8378,2645,2189,6038,13968,3841,7972,6869,5840,18462,1648,6637,1754,1680,5359,4438,8728,8771,5928,4453,6598,8807,2121,2144,1727,6314,9040,1764,2413,51647,7046,4131,5524,6507,2176,5808,26910,3358,2275,2033,2149,5762,2253,3871,4594,7459,8195,3257,2717,6699,10030,17299,17321,5230,42097,5048,8480,9021,46997,6243,8591,6001,3738,2028,3375,1595,2734,7382,6228,3111,7785,7118,3686,8311,9451,3696,6492,5715,5758,4365,1833,1884,5923,3272,5612,8167,1965,64130,3536,6140,9617,7709,3372,6234,7833,4998,7714,4268,5933,6493,8259,2048,3925,2859,1615,1784,6510,6108,6949,6312,7736,7233,17280,2657,4159,8580,4309,9025,1652,5627,8809,2674,8124,8684,5831,4605,5876,1795,1701,2398,8092,5350,7180,7963,3404,3868,5752,40263,5799,18477,2134,7038,2959,5535,3796,48530,7534,6334,8387,8301,8381,8601,5427,1669,3773,50894,8107,64304,3118,1707,8549,3051,7270,2308,4837,3646,4112,18484,5331,4236,1865,1635,4672,6991,4822,8359,8624,6302,3594,1997,4764,3123,7924,10493,7800,2055,7347,3700,4060,2166,1765,8212,1897,6123,17611,7658,2425,7843,1638,7315,4245,10505,18431,4433,1675,26984,16632,3532,17860,11169,6478,15492,6920,3270,2284,6340,2839,2945,5381,8419,2346,2521,25661,5071,3352,17892,16883,5143,7594,7514,6308,3251,2151,7643,9454,5325,8135,1574,1806,4828,28877,11878,8237,7379,6197,7607,8693,1603,6321,2299,8461,3106,8254,1722,7330,4805,8313,2669,4213,7360,7206,3197,47003,1801,5093,6289,2802,3500,6184,4374,5972,8794,11883,7502,4773,26994,4509,7731,5267,6216,12015,1667,5552,32813,15497,2267,4985,7186,2553,2974,8932,9042,8735,5816,17637,8605,4541,64300,2742,8633,7699,50053,1557,64221,8156,2625,7292,2111,8103,6849,1630,7566,8517,4818,2261,1731,6725,8750,50952,1862,6645,6747,2410,7778,2593,5656,2874,7869,10489,7675,8473,6044,4726,2252,8652,6568,61594,2842,5838,8413,7901,1688,38297,3806,7960,6504,1775,4304,2207,6785,9018,3480,3539,15496,64290,6255,28989,5340,26928,7603,2365,5254,5775,7030,13963,2725,1699,2212,12432,42047,3759,3838,2835,8776,6907,2765,3423,50656,9450,2481,6930,8308,6738,8084,4373,1643,3953,8175,3310,7434,7200,5725,1726,7366,2967,64533,6325,2303,7630,5403,4626,5693,5089,7507,17874,6730,2867,2506,1562,7049,3490,5619,7788,6540,7578,7897,8657,7122,8731,6083,1626,8180,4331,9097,4207,1948,32809,5538,2816,1583,1809,5424,4458,7296,24767,4868,4886,43837,7975,3395,4456,10488,7298,48418,8160,8099,17897,1905,4529,2037,26940,3981,2503,8116,5952,3048,17268,12434,6806,2256,6843,4355,8885,64121,8020,4336,1551,5003,17151,6132,2582,61546,6875,24774,11230,5822,4035,4490,8466,1566,17319,4961,6384,5446,4749,4255,1798,9022,26972,5624,8725,61558,6249,12487,6120,6238,8772,3315,5927,5514,28584,8345,6399,13967,7211,6051,1611,8707,2060,4939,5478,5399,8598,3260,2588,6367,64099,1647,8701,64236,4200,8163,5074,5592,3949,5980,2518,4517,2175,4469,1780,8096,2720,4377,7618,4630,8350,6481,8295,7724,8813,2160,2831,8039,4314,47000,10504,24828,4145,8206,3853,2354,7672,5955,2569,8612,4437,18439,1790,1987,1716,6981,7655,5731,7429,3691,1637,2688,64223,6912,5015,3722,3554,5912,8625,6093,8231,8496,7443,5555,8808,3202,1869,15556,26904,1785,7988,2429,3655,8216,5948,6513,2276,8509,5154,17272,3544,3828,7351,2322,5001,2486,40239,3329,4737,7127,17283,6994,6330,10509,52123,2468,5277,18456,15557,6633,40264,5633,1585,5717,5472,4150,8729,35790,8696,7466,1543,6337,6825,6679,3652,10558,2558,17308,2426,42049,9675,1702,6601,7342,6318,7461,4976,4436,7251,5240,61532,11882,7797,4510,7621,5504,2320,64288,4991,6193,8317,8602,8185,4431,10568,1670,5685,9019,1797,28978,2949,64293,2728,26946,7426,1717,8087,32765,6358,1881,6161,4795,3520,5596,2584,4671,8140,3398,9453,61580,8431,36025,6220,3288,1617,16443,5917,5653,3533,3874,7570,4678,6711,5771,6284,8681,8812,3284,6928,2760,7363,6286,3400,3478,5939,3946,3139,3620,1649,7844,7061,2352,4424,4138,6846,8698,7676,2479,11150,6985,2045,8028,4587,4770,7764,6408,17617,7627,1685,2696,1553,2870,4165,2828,10508,7904,43113,6013,5777,7306,4873,5386,4944,2078,4419,8183,3548,17640,1654,8825,4780,2611,3928,6938,17155,1781,8392,5907,2997,32818,8228,18460,3346,3320,8153,1575,2071,7446,1807,5184,4121,2273,26908,5191,4250,64545,5899,8336,64297,6910,5394,7120,64530,2591,5055,1646,7034,8356,2707,8221,4710,17316,2988,2594,1721,2174,6818,7653,44723,1674,3789,1639,5272,4615,40236,2406,7344,24769,6790,43561,4715,6023,52116,8606,2608,35049,3331,9449,15561,7125,3368,13969,4969,17593,8617,2416,6799,26978,1558,8240,5600,4261,8119,2394,5828,3497,2066,40268,5128,5864,2421,2447,2944,8172,8506,40271,1689,8253,11210,3694,4602,6305,4197,8369,2796,8272,6430,6854,18447,5532,6181,2648,3585,1777,6554,8638,4299,7312,5409,2198,1706,5699,7157,2362,2162,5549,1607,6536,6252,51213,6166,12427,26912,17872,5119,5517,2230,1893,2036,7574,2494,12491,40670,6462,3552,6499,5336,2779,51645,5852,1774,17297,5430,4841,3337,6580,2258,8341,1642,17846,5009,6326,7419,8070,3705,1725,1578,1957,4472,7016,7355,2385,1678,5606,7634,6997,3232,6007,8478,6822,8193,5004,17140,4811,7231,7744,24773,6563,2233,7666,9318,20580,1546,7836,1625,3987,1593,3837,7712,2951,5078,42048,18450,4523,24768,40235,5527,6490,6906,7248,4357,7210,2768,6226,16341,5760,8933,6782,18435,1859,8400,8737,5990,12307,15533,17810,1561,26992,7278,8822,7525,6411,7323,8542,7851,6627,2201,1989,4350,8521,26960,7184,4157,5019,8424,2572,6558,8516,7474,1789,6729,2961,15493,8277,5251,17868,4865,3765,8268,12431,7808,8648,13966,6040,6929,3673,6273,2063,1610,5440,2651,4318,8236,15553,3025,9038,3057,6697,4506,4484,5060,7755,8675,6874,3244,6771,7214,6190,2810,2731,5204,1829,42053,8444,5151,2600,4382,3570,7506,5140,7915,9023,1582,6993,4876,1550,4239,7387,4831,7370,5958,8437,32812,5236,4936,4395,5468,2539,5354,2864,3740,3113,6911,1902,5376,2699,6548,8305,10586,17849,3918,5344,8493,2138,2879,64225,5707,12488,6810,2453,5293,8232,50764,3960,7195,7900,1606,3474,17629,8184,10492,6961,1653,1944,3924,5986,1945,8363,7848,5458,3096,6733,1681,2887,4767,7056,7320,1565,8741,6718,40663,26956,2018,34947,8179,2436,1848,6857,16659,6761,3432,13962,8596,7267,30088,26988,8380,2191,1812,8818,10750,4858,2470,51651,8405,8670,6896,2177,6933,2655,4734,8157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU427+2 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 13:44:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.48/1.30 % [INFO] Parsing done (430ms).
% 2.48/1.31 % [INFO] Running in sequential loop mode.
% 3.19/1.51 % [INFO] eprover registered as external prover.
% 3.19/1.51 % [INFO] cvc4 registered as external prover.
% 3.19/1.51 % [INFO] Scanning for conjecture ...
% 3.93/1.75 % [INFO] Found a conjecture and 4497 axioms. Running axiom selection ...
% 6.11/2.34 % [INFO] Axiom selection finished. Selected 1540 axioms (removed 2957 axioms).
% 7.84/2.91 % [INFO] Problem is first-order (TPTP FOF).
% 8.06/2.95 % [INFO] Type checking passed.
% 8.06/2.96 % [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 ...
% 256.14/53.85 % External prover 'e' found a proof!
% 256.14/53.85 % [INFO] Killing All external provers ...
% 256.14/53.86 % Time passed: 53323ms (effective reasoning time: 52544ms)
% 256.14/53.86 % 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)>
% 256.17/53.88 % Axioms used in derivation (1540): t119_funct_2, t106_xboole_1, t15_finset_1, t158_relat_1, t39_funct_5, t63_mcart_1, t44_xboole_1, t72_xboole_1, t189_relat_1, t86_partfun1, dt_m2_pua2mss1, t42_xboole_1, dt_k15_domain_1, t34_subset_1, t34_sysrel, t14_realset1, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t87_funct_1, t32_funcop_1, t21_zfmisc_1, t5_boole, t84_finseq_2, t13_zfmisc_1, t30_funct_2, t55_funcop_1, t13_relset_1, t181_relat_1, t131_partfun1, t38_funcop_1, t175_relat_1, fc4_finset_1, fraenkel_a_4_2_domain_1, t48_funcop_1, fraenkel_a_4_0_pua2mss1, t36_funcop_1, t177_relat_1, free_g1_group_1, t25_mcart_1, t177_orders_1, d6_finseq_1, t42_relat_2, fc1_zfmisc_1, d1_tarski, t147_funct_1, d4_funct_1, t19_mcart_1, fraenkel_a_3_2_domain_1, d1_sysrel, t19_xboole_1, t99_relat_1, t17_xboole_1, t23_setfam_1, t90_relat_1, t112_xboole_1, t130_partfun1, t42_subset_1, t41_setfam_1, t55_mcart_1, t43_subset_1, t86_funct_1, t7_funcop_1, cc2_finset_1, t20_zfmisc_1, t54_relat_1, t35_subset_1, t101_relat_1, t135_zfmisc_1, t17_zfmisc_1, fc11_finseq_1, fc3_finset_1, t25_relset_1, d3_mcart_1, t148_funct_1, t66_funct_2, t143_funct_1, t19_eqrel_1, t67_relat_1, t66_partfun1, t5_relset_2, t154_relat_1, t60_funcop_1, t49_setfam_1, t70_funct_2, t6_setfam_1, t35_funct_2, t14_finset_1, t20_mcart_1, t53_subset_1, dt_k9_domain_1, d5_relat_1, t105_zfmisc_1, t140_zfmisc_1, redefinition_k12_mcart_1, t63_funcop_1, t38_mcart_1, t20_funct_2, dt_k8_funcop_1, redefinition_k8_relset_2, t73_xboole_1, t109_xboole_1, t66_mcart_1, idempotence_k3_xboole_0, t67_funcop_1, rc4_finset_1, redefinition_k9_domain_1, t110_xboole_1, t57_funcop_1, t13_sysrel, t161_funct_2, t1_boole, t62_relat_1, t7_subset_1, t92_xboole_1, t84_mcart_1, t2_realset1, t32_funct_2, t66_xboole_1, t23_xboole_1, t95_partfun1, commutativity_k1_relset_2, t75_relat_1, t27_funct_2, t50_relat_1, t85_mcart_1, t195_orders_1, t29_mcart_1, redefinition_k5_subset_1, t9_setfam_1, t3_xboole_1, t97_xboole_1, t24_mcart_1, t3_realset1, t137_funct_1, d3_subset_1, t40_funct_5, t12_pua2mss1, t183_relat_1, t98_relat_1, t25_funct_1, t7_mcart_1, t18_funcop_1, dt_k7_domain_1, t113_xboole_1, t42_sysrel, t8_subset_1, d12_relat_1, s3_funct_2, redefinition_k7_funct_2, t45_funcop_1, t20_setfam_1, fc1_xboole_0, t16_funct_2, t113_zfmisc_1, t140_partfun1, t116_partfun1, t48_domain_1, t34_xboole_1, dt_k7_subset_1, rc7_finseq_1, t91_relat_1, t88_mcart_1, t111_zfmisc_1, dt_k2_subset_1, t64_funct_5, t25_setfam_1, t81_partfun1, t56_partfun1, t38_funct_1, t3_relset_2, t53_funct_2, d5_tarski, t83_mcart_1, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t156_funct_1, t101_xboole_1, t52_sysrel, t4_ordinal1, t139_funct_1, t59_partfun1, s12_funct_2, t53_funcop_1, t158_funct_1, t44_relat_1, fc4_funct_1, t1_subset, t147_relat_1, t10_partfun1, t158_partfun1, d5_xboole_0, t10_mssubfam, t81_zfmisc_1, t7_funct_2, t18_xboole_1, t36_sysrel, dt_k1_subset_1, t6_xboole_1, t33_mcart_1, t25_sysrel, t32_mcart_1, t29_subset_1, t24_setfam_1, t151_funct_1, t52_zfmisc_1, t144_relat_1, commutativity_k2_setfam_1, t57_domain_1, t18_setfam_1, fc4_subset_1, t71_funct_1, t22_funct_1, fc3_realset1, free_g3_vectsp_1, t34_relat_2, t79_funcop_1, dt_k3_funct_2, t168_funct_2, t43_xboole_1, fraenkel_a_8_0_domain_1, t10_relset_1, t43_relat_2, t135_partfun1, t55_domain_1, t4_funcop_1, d17_mcart_1, t3_mcart_1, t155_funct_1, fc3_relat_1, t96_zfmisc_1, t42_zfmisc_1, t23_relat_2, t85_funct_1, t117_partfun1, t13_funcop_1, t19_zfmisc_1, d8_funct_1, idempotence_k1_relset_2, t19_relat_1, t70_xboole_1, d4_zfmisc_1, dt_k13_domain_1, t117_relat_1, t19_finset_1, t25_xboole_1, t2_boole, d5_setfam_1, fc2_finseq_1, t14_sysrel, t11_realset1, t73_funcop_1, t24_relset_2, t47_relat_1, fc9_relat_1, t148_partfun1, t36_partfun1, fc5_finset_1, t68_xboole_1, t41_mcart_1, t35_zfmisc_1, t12_relset_2, t1_funcop_1, t11_pua2mss1, t82_relat_1, t117_zfmisc_1, t65_partfun1, t186_partfun1, t44_funct_2, t117_funct_1, dt_k4_realset1, t26_funct_5, t17_setfam_1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, t122_zfmisc_1, t4_mcart_1, t139_relat_1, fc6_funcop_1, dt_m1_realset1, t110_zfmisc_1, t64_domain_1, t43_zfmisc_1, t103_zfmisc_1, fraenkel_a_1_2_domain_1, rc2_partfun1, t61_subset_1, t18_relat_1, t27_finseq_2, t171_relat_1, t6_mssubfam, t162_partfun1, t64_funcop_1, t30_relat_2, dt_k6_partfun1, t63_domain_1, t70_zfmisc_1, t63_partfun1, t91_finseq_2, t153_funct_1, t95_zfmisc_1, t96_partfun1, t78_funcop_1, t15_relset_1, t45_ordinal1, t99_zfmisc_1, t44_mcart_1, d14_funct_1, d9_funct_1, free_g1_vectsp_1, rc3_funct_1, t81_xboole_1, t47_setfam_1, t49_funct_2, dt_k17_domain_1, dt_k5_domain_1, fc1_funct_1, rc3_finseq_1, t7_orders_1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, rc1_finseq_1, t123_relat_1, t50_funct_2, t39_relat_1, t69_zfmisc_1, t56_relat_1, t84_funct_1, cc1_relat_1, dt_k5_funct_5, t95_xboole_1, d7_partfun1, fc8_finset_1, t102_relat_1, t29_partfun1, dt_k14_domain_1, t3_setfam_1, t41_relat_1, t27_zfmisc_1, t23_mcart_1, t37_xboole_1, t26_funct_2, t17_funct_1, t9_xboole_1, t82_funct_1, t59_subset_1, t41_zfmisc_1, dt_m2_relset_1, t9_mssubfam, t18_finset_1, dt_k7_funct_2, t6_eqrel_1, t131_zfmisc_1, redefinition_k2_funct_2, idempotence_k5_subset_1, t50_zfmisc_1, t2_funct_1, t36_subset_1, redefinition_k6_setfam_1, t49_zfmisc_1, commutativity_k3_xboole_0, t154_funct_1, t176_partfun1, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t6_relset_2, t70_partfun1, t3_funcop_1, t138_funct_1, t152_funct_2, t80_funcop_1, t25_relset_2, s13_funct_2, dt_k8_relset_2, d2_tarski, rc1_funct_1, d1_relset_2, d4_setfam_1, t97_finseq_2, t7_eqrel_1, t64_funct_2, t115_zfmisc_1, t52_funcop_1, t62_funct_1, t76_funct_2, t65_funct_2, t19_funct_1, fc11_finset_1, dt_k14_mcart_1, t24_funct_2, t29_finset_1, t42_funct_5, t127_relat_1, t137_zfmisc_1, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_partfun1, t30_funcop_1, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t99_funct_1, t89_xboole_1, redefinition_k14_domain_1, t83_funcop_1, t25_funct_2, fc2_xboole_0, t87_partfun1, dt_m2_realset1, t32_subset_1, t168_relat_1, t22_funcop_1, t46_sysrel, t29_funct_5, t76_partfun1, t15_mcart_1, d1_xboole_0, t108_xboole_1, dt_k9_funct_2, t2_mssubfam, t3_mssubfam, t64_relat_1, t133_relat_1, d2_funcop_1, t16_pua2mss1, t30_finset_1, t112_relat_1, t46_funct_2, t75_funct_2, t31_finset_1, t175_partfun1, t15_relat_1, t19_relset_2, t154_funct_2, t48_funct_2, fraenkel_a_3_7_domain_1, t173_relat_1, t49_mcart_1, t172_relat_1, t27_relat_1, t58_mcart_1, t156_funct_2, t47_ordinal1, t89_mcart_1, t5_mssubfam, dt_m1_eqrel_1, t49_funct_1, t40_funct_1, redefinition_k8_funcop_1, t138_zfmisc_1, t59_funct_5, rc6_finseq_1, t25_subset_1, t23_funct_1, t130_zfmisc_1, t51_xboole_1, dt_k10_funcop_1, t36_mcart_1, t48_sysrel, t108_zfmisc_1, t96_relat_1, t165_funct_2, t15_funcop_1, t29_funct_2, t60_partfun1, t118_funct_2, t14_relset_1, t16_relset_1, rc3_relat_1, t56_zfmisc_1, t47_funct_2, existence_m2_pua2mss1, t27_relset_1, t12_mcart_1, t52_domain_1, t52_relset_1, t34_funct_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, s4_subset_1, t8_funct_2, dt_k6_finseq_1, fc10_finset_1, existence_m1_realset1, t26_finset_1, t92_finseq_2, t53_relset_1, t30_sysrel, t6_mcart_1, t56_domain_1, d13_relat_1, t46_zfmisc_1, t31_partfun1, t37_partfun1, dt_k2_relset_2, t171_partfun1, t164_funct_2, fc2_funct_2, t6_boole, t12_funct_1, t4_orders_1, t3_funct_2, t18_subset_1, rc2_subset_1, fc9_finset_1, t46_mcart_1, t63_funct_1, t38_sysrel, t50_xboole_1, dt_k6_subset_1, t10_relat_1, t59_setfam_1, d1_relat_1, dt_k3_relset_2, t185_partfun1, t104_relat_1, t39_funcop_1, t55_relat_1, t3_partfun1, t75_xboole_1, fc17_finset_1, redefinition_k13_mcart_1, t131_relat_1, commutativity_k2_xboole_0, t5_subset, d9_realset1, t57_mcart_1, t1_xboole_1, redefinition_k4_relset_2, t26_relset_1, t72_relat_1, t66_funct_5, t122_relat_1, d3_realset1, t64_partfun1, t52_relat_1, t136_relat_1, t77_funct_2, t59_domain_1, s2_finset_1, t20_funct_1, t82_finseq_2, t12_sysrel, t68_partfun1, t17_domain_1, t7_setfam_1, t4_setfam_1, t32_partfun1, t73_relat_1, t83_partfun1, redefinition_k4_funct_2, d6_tarski, t4_relat_1, t38_setfam_1, fc5_funcop_1, t28_subset_1, t52_xboole_1, t185_relat_1, t2_pboole, t116_relat_1, t21_finset_1, t160_funct_1, t13_eqrel_1, t15_domain_1, t79_partfun1, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t149_funct_1, t75_zfmisc_1, t48_zfmisc_1, t7_mssubfam, t65_xboole_1, t20_finseq_1, s8_domain_1, t163_relat_1, t45_funct_2, t79_zfmisc_1, t25_zfmisc_1, d4_relat_1, t94_zfmisc_1, t11_mcart_1, t8_mcart_1, t4_xboole_0, t41_funcop_1, t65_finseq_1, d2_realset1, t32_sysrel, fc6_finset_1, t63_funct_5, fc17_finseq_1, d6_partfun1, t150_relat_1, existence_m1_relset_1, commutativity_k5_subset_1, t55_setfam_1, dt_k2_domain_1, t1_zfmisc_1, t77_mcart_1, t12_setfam_1, t5_setfam_1, t52_funct_1, t28_mcart_1, dt_k1_sysrel, t123_zfmisc_1, fc2_subset_1, t5_funct_2, t176_relat_1, dt_k8_funct_2, t128_relat_1, t35_setfam_1, d4_relset_2, t58_sysrel, redefinition_k10_pboole, t167_funct_2, t60_zfmisc_1, fc1_orders_1, t11_funct_2, d3_zfmisc_1, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t72_mcart_1, t9_relat_1, t33_xboole_1, s9_domain_1, t2_zfmisc_1, cc1_finseq_1, rc4_funct_1, t24_finset_1, t97_zfmisc_1, redefinition_k7_domain_1, fc2_funct_1, t73_funct_1, dt_k3_realset1, t40_funct_2, t102_xboole_1, t49_sysrel, t28_relset_1, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, t2_tarski, t56_mcart_1, t18_relset_2, t16_funct_1, t79_relat_1, t14_relat_1, t72_zfmisc_1, t142_funct_2, t82_funct_2, fc6_subset_1, t28_zfmisc_1, t62_subset_1, t122_funct_1, t53_sysrel, t52_setfam_1, t166_relat_1, t22_sysrel, t61_funcop_1, t114_xboole_1, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t74_funcop_1, dt_k1_partfun1, t84_xboole_1, t57_zfmisc_1, t4_subset, t30_xboole_1, dt_k2_funct_1, t74_zfmisc_1, cc1_funct_2, t39_subset_1, t14_funct_1, t43_funct_1, t71_funcop_1, fc13_relat_1, t52_subset_1, t5_ordinal1, t4_boole, t36_funct_2, t53_xboole_1, t146_funct_1, d2_funct_2, t23_zfmisc_1, d13_funct_1, t109_relat_1, t133_funct_2, t125_funct_1, t46_funcop_1, d5_realset1, t21_xboole_1, t120_relat_1, t98_zfmisc_1, t114_partfun1, t58_subset_1, dt_k11_relset_1, dt_k4_relat_1, t162_funct_1, t32_domain_1, dt_k9_relset_2, t28_funct_5, t76_xboole_1, t25_funcop_1, fc3_xboole_0, t38_subset_1, t178_relat_1, t29_sysrel, t176_orders_1, t16_funcop_1, t169_funct_2, t33_sysrel, t29_funcop_1, d14_mcart_1, d2_xboole_0, dt_k8_domain_1, t15_realset1, t76_relat_1, t32_relat_2, t32_xboole_1, t52_funct_5, d4_tarski, t134_relat_1, t141_zfmisc_1, t12_zfmisc_1, t26_mcart_1, t174_relat_1, redefinition_k10_relset_1, t47_funcop_1, t93_partfun1, t129_relat_1, dt_k4_funct_5, t132_funct_2, s3_domain_1, t65_funcop_1, t61_partfun1, t93_finseq_2, rc2_realset1, t2_relset_2, t80_xboole_1, t147_partfun1, t58_funct_1, t25_finset_1, t9_zfmisc_1, t148_funct_2, t79_xboole_1, t106_relat_1, t51_funct_2, t67_xboole_1, t39_setfam_1, existence_m2_realset1, existence_m3_realset1, redefinition_k10_funcop_1, t10_mcart_1, t56_subset_1, redefinition_k14_mcart_1, redefinition_k5_setfam_1, dt_k1_domain_1, t58_zfmisc_1, t4_pua2mss1, t17_funct_2, t1_xboole_0, existence_m1_ordinal1, t35_relat_2, involutiveness_k4_relat_1, t35_sysrel, d6_setfam_1, t29_xboole_1, t5_orders_1, t179_relat_1, t96_xboole_1, t89_funct_1, fc1_realset1, t74_mcart_1, t7_realset1, dt_k6_relset_2, t22_relset_2, commutativity_k5_xboole_0, t59_funct_1, t139_zfmisc_1, t6_realset1, t7_boole, cc1_funct_1, t4_funct_2, t24_funcop_1, t36_setfam_1, s11_funct_2, t138_partfun1, s2_domain_1, d10_setfam_1, t143_relat_1, t13_finset_1, t105_relat_1, t120_funct_1, t37_sysrel, t160_funct_2, d3_relset_2, t136_partfun1, t138_relat_1, d3_partfun1, t104_zfmisc_1, t118_relat_1, t42_mcart_1, d10_relat_1, t55_zfmisc_1, d2_subset_1, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, fc5_funct_1, t29_finseq_1, t33_relat_2, t77_relat_1, t22_relat_1, redefinition_k6_partfun1, t48_xboole_1, dt_k3_pua2mss1, dt_k6_domain_1, t157_funct_1, t85_partfun1, t3_ordinal1, t9_domain_1, t45_relset_1, t16_mcart_1, dt_k16_domain_1, t8_pua2mss1, t66_funcop_1, t26_zfmisc_1, t158_funct_2, t48_funct_1, t152_funct_1, t85_xboole_1, redefinition_k1_domain_1, t21_funct_2, d2_setfam_1, t16_subset_1, dt_k2_partfun1, t20_eqrel_1, t69_partfun1, t7_ordinal1, t153_relat_1, rc2_funct_1, t34_funct_5, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, t64_funct_1, t149_funct_2, dt_k3_domain_1, t41_sysrel, t81_funcop_1, t187_relat_1, t7_relset_2, t54_setfam_1, t47_funct_1, d11_relat_1, t31_xboole_1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t88_xboole_1, involutiveness_k1_funcop_1, t19_funct_2, t51_funct_1, t130_relat_1, t22_finset_1, t67_funct_1, t74_relat_1, t162_funct_2, t14_zfmisc_1, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, d4_realset1, t76_funcop_1, t51_setfam_1, t45_relat_1, t17_relset_2, d1_eqrel_1, t56_funct_1, t78_finseq_2, t110_relat_1, t113_funct_2, t71_partfun1, t69_xboole_1, d5_funct_2, t27_sysrel, t4_realset1, t159_funct_2, t116_zfmisc_1, redefinition_k13_domain_1, t64_zfmisc_1, d7_xboole_0, redefinition_k6_relset_2, fc5_relat_1, t125_relat_1, t151_relat_1, t83_xboole_1, t14_funct_2, t155_funct_2, t137_relat_1, t20_xboole_1, t178_orders_1, s2_subset_1, commutativity_k3_setfam_1, t97_relat_1, t31_funct_5, t16_zfmisc_1, t101_zfmisc_1, redefinition_k8_domain_1, t65_funct_1, t140_relat_1, d14_relat_1, t37_setfam_1, t124_zfmisc_1, t188_relat_1, fraenkel_a_3_1_domain_1, t60_funct_2, d16_mcart_1, t82_xboole_1, dt_k1_eqrel_1, t107_relat_1, t32_zfmisc_1, t54_xboole_1, t186_relat_1, t55_xboole_1, s1_subset_1, d2_mcart_1, d7_relat_1, cc2_funct_1, t120_zfmisc_1, t89_relat_1, redefinition_k2_domain_1, t21_funcop_1, t46_setfam_1, t9_relset_2, t169_partfun1, t49_funct_5, t18_funct_1, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, dt_k4_funct_2, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, s1_domain_1, t31_sysrel, t78_relat_1, t8_mssubfam, t44_sysrel, s4_funct_2, t59_sysrel, t7_pua2mss1, t76_funct_1, t124_funct_1, fraenkel_a_3_1_pua2mss1, t55_subset_1, t79_funct_2, t46_funct_1, dt_k6_setfam_1, d15_mcart_1, dt_k1_funcop_1, t115_relat_1, t56_funcop_1, t29_setfam_1, fraenkel_a_2_1_domain_1, t14_relset_2, commutativity_k7_subset_1, d2_zfmisc_1, dt_k13_mcart_1, fc11_relat_1, t51_funct_5, fc5_subset_1, existence_m1_subset_1, commutativity_k2_tarski, t3_relat_1, t24_relat_1, t8_relset_1, t35_xboole_1, t106_zfmisc_1, d6_xboole_0, t84_funcop_1, t51_sysrel, redefinition_k5_domain_1, fraenkel_a_2_1_pua2mss1, t17_relset_1, dt_k3_funct_5, d5_subset_1, t29_zfmisc_1, fraenkel_a_6_0_domain_1, t16_relset_2, t125_zfmisc_1, t73_funct_2, t30_subset_1, t54_mcart_1, dt_k2_funct_2, dt_k7_relat_1, redefinition_k4_subset_1, t14_xboole_1, t44_setfam_1, t11_relset_1, t124_relat_1, t44_zfmisc_1, t83_finseq_2, t155_relat_1, d8_relat_1, t47_xboole_1, t134_funct_2, t145_funct_1, t61_funct_1, fc1_finset_1, t15_subset_1, t36_funct_5, t47_sysrel, free_g2_struct_0, t37_funct_2, t94_relat_1, t48_setfam_1, t86_finseq_2, t39_sysrel, t31_funcop_1, t118_funct_1, t132_zfmisc_1, t92_zfmisc_1, t146_relat_1, t99_partfun1, t107_zfmisc_1, t9_realset1, existence_m2_subset_1, t95_relat_1, t98_finseq_2, t142_partfun1, t121_funct_2, t70_funct_1, t58_partfun1, t100_zfmisc_1, t22_zfmisc_1, t15_xboole_1, redefinition_k1_relset_2, t60_funct_5, dt_k5_subset_1, dt_k9_funcop_1, rc1_pua2mss1, redefinition_k7_subset_1, t37_mcart_1, t116_funct_2, t114_zfmisc_1, t31_zfmisc_1, t19_funcop_1, d1_zfmisc_1, t16_xboole_1, free_g2_vectsp_1, dt_k8_relat_1, d8_setfam_1, t26_xboole_1, t63_xboole_1, redefinition_k7_funcop_1, t57_setfam_1, t43_funct_2, commutativity_k4_subset_1, t91_partfun1, t86_zfmisc_1, rc2_relat_1, existence_m2_relset_1, t98_xboole_1, t53_funct_5, t49_funcop_1, t54_domain_1, t38_zfmisc_1, t145_partfun1, t65_mcart_1, t34_funcop_1, t72_funct_1, t157_relat_1, t142_funct_1, t23_relset_2, t45_funct_5, t87_finseq_2, t61_domain_1, dt_k7_funcop_1, involutiveness_k10_funcop_1, t84_zfmisc_1, fc4_funcop_1, t6_funct_2, t40_sysrel, t69_funcop_1, fraenkel_a_1_0_pua2mss1, t41_subset_1, fraenkel_a_3_6_domain_1, t44_relat_2, s4_domain_1, t168_partfun1, s14_funct_2, redefinition_k4_domain_1, t92_partfun1, t26_subset_1, t82_partfun1, t51_subset_1, t97_funct_1, t21_subset_1, t111_xboole_1, involutiveness_k7_setfam_1, t22_xboole_1, t3_pua2mss1, t8_setfam_1, t36_zfmisc_1, redefinition_k6_funcop_1, t94_partfun1, dt_k12_mcart_1, redefinition_k17_domain_1, dt_k3_partfun1, t8_xboole_1, t37_relat_1, d3_tarski, t53_domain_1, t46_subset_1, t43_funcop_1, d8_realset1, t54_funct_1, t54_zfmisc_1, fraenkel_a_3_4_domain_1, t148_relat_1, t73_finseq_1, t100_xboole_1, t8_realset1, t103_xboole_1, t58_funcop_1, t6_relset_1, t78_xboole_1, t28_xboole_1, t56_sysrel, d1_relset_1, redefinition_k16_domain_1, cc6_funct_2, t33_domain_1, t60_subset_1, t39_zfmisc_1, d1_realset1, t5_xboole_0, t131_funct_2, t119_zfmisc_1, t121_relat_1, rc1_relat_1, t34_mcart_1, t13_xboole_1, t60_relat_1, t83_zfmisc_1, t170_relat_1, t80_finseq_2, t40_subset_1, dt_k5_relat_1, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, t6_orders_1, dt_k6_relat_1, t143_funct_2, redefinition_k1_partfun1, t20_finset_1, t1_realset1, t2_xboole_1, rc1_pboole, redefinition_k2_realset1, t34_funct_2, t6_zfmisc_1, t1_mssubfam, t48_relat_1, dt_k10_relset_1, t12_eqrel_1, d2_orders_1, s3_subset_1, t5_mcart_1, t93_relat_1, t18_funct_2, t144_funct_1, dt_k4_relset_2, t121_zfmisc_1, t10_subset_1, t161_relat_1, t56_setfam_1, t27_finset_1, reflexivity_r2_setfam_1, t4_relset_2, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_relset_1, t9_mcart_1, t7_msualg_1, t34_setfam_1, t37_funcop_1, t59_zfmisc_1, fc6_relat_1, dt_k4_domain_1, t32_funct_5, t1_partfun1, t41_xboole_1, t150_funct_1, t57_subset_1, t47_zfmisc_1, t84_partfun1, t2_setfam_1, t66_funct_1, d4_xboole_0, t18_zfmisc_1, t6_pua2mss1, t17_funcop_1, d6_eqrel_1, t144_partfun1, t20_relat_1, t94_xboole_1, t90_xboole_1, t8_relset_2, t51_relat_1, t31_domain_1, t113_partfun1, redefinition_k11_domain_1, t46_relat_1, fc1_setfam_1, t39_mcart_1, t14_pua2mss1, t35_funct_1, t29_relset_1, rc1_realset1, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, redefinition_k11_relset_1, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, dt_k8_subset_1, rc8_finseq_1, t73_zfmisc_1, t47_subset_1, t43_sysrel, t151_funct_2, dt_k12_domain_1, t46_relset_1, dt_m2_subset_1, t12_funct_2, t64_xboole_1, dt_k7_setfam_1, t21_setfam_1, t49_xboole_1, t136_zfmisc_1, t64_mcart_1, t16_sysrel, fc3_funct_1, reflexivity_r1_setfam_1, t68_zfmisc_1, t54_subset_1, t53_funct_1, t27_finseq_1, rc1_finset_1, t127_zfmisc_1, t123_funct_1, t70_funcop_1, t11_setfam_1, t44_subset_1, t87_relat_1, cc1_finset_1, t14_mcart_1, t93_xboole_1, t21_funct_1, t50_funct_1, fc12_finset_1, t50_sysrel, t42_funct_1, t126_relat_1, t73_mcart_1, fc1_relat_1, t4_mssubfam, t47_partfun1, t1_relset_2, t77_xboole_1, t10_setfam_1, t8_boole, t169_relat_1, rc1_xboole_0, t18_sysrel, t1_funct_5, t1_mcart_1, t11_xboole_1, t23_finset_1, t81_finseq_2, t24_partfun1, redefinition_k8_funct_2, t35_mcart_1, d1_orders_1, t80_zfmisc_1, t34_zfmisc_1, t28_relat_2, t5_relat_1, t24_zfmisc_1, t23_relat_1, t16_finset_1, t75_funcop_1, t149_finseq_2, t156_relat_1, t54_sysrel, t20_funcop_1, d4_mcart_1, fc8_relat_1, t24_sysrel, t40_relat_1, t45_sysrel, t31_setfam_1, dt_m1_orders_1, t182_relat_1, t54_funcop_1, t120_funct_2, t31_mcart_1, t67_mcart_1, redefinition_k3_funct_2, d4_funct_5, redefinition_k9_relset_2, t59_funct_2, t12_xboole_1, t10_zfmisc_1, t2_subset, t20_sysrel, reflexivity_r1_partfun1, t38_funct_2, t33_partfun1, d3_relat_1, t85_funct_2, fc7_relat_1, t14_funcop_1, t111_relat_1, t180_relat_1, t60_funct_1, fc2_relat_1, t14_finseq_1, t37_zfmisc_1, fc12_relat_1, t65_relat_1, t21_relat_1, t53_zfmisc_1, d5_funct_5, t135_relat_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, d1_setfam_1, t152_relat_1, symmetry_r1_xboole_0, t20_relset_2, t134_zfmisc_1, t86_relat_1, t28_finset_1, free_g1_rlvect_1, t100_relat_1, t25_partfun1, t49_relat_1, t126_zfmisc_1, t12_domain_1, t161_funct_1, t27_funct_1, t92_relat_1, t10_realset1, t82_funcop_1, d1_funcop_1, t55_sysrel, t175_orders_1, redefinition_k3_domain_1, t27_funct_5, t99_finseq_2, t13_mcart_1, t48_subset_1, t26_funcop_1, dt_k1_relset_2, dt_k5_relset_2, t145_relat_1, t40_setfam_1, t50_subset_1, d15_relat_1, d10_xboole_0, t149_relat_1, t10_relset_2, t58_domain_1, t115_funct_2, idempotence_k2_xboole_0, t28_relat_1, t17_mcart_1, d1_funct_1, t30_setfam_1, t115_partfun1, fc2_funcop_1, t9_tarski, t11_relset_2, t46_xboole_1, t107_xboole_1, d3_pua2mss1, fc2_realset1, t74_xboole_1, fc2_finset_1, redefinition_k10_domain_1, t7_xboole_1, t77_funcop_1, t37_funct_1, t108_relat_1, t33_funct_1, t159_funct_1, t57_funct_1, t3_xboole_0, symmetry_r1_partfun1, t3_boole, t146_partfun1, cc1_realset1, t58_setfam_1, t12_relset_1, fc3_funcop_1, t5_xboole_1, t49_subset_1, fc1_funcop_1, t44_funcop_1, t7_tarski, t43_mcart_1, rc1_partfun1, t126_funct_1, t91_xboole_1, t33_finseq_2, t67_partfun1, t132_relat_1, d5_funct_1, t6_ordinal1, t53_mcart_1, dt_k10_pboole, redefinition_k6_subset_1, t93_zfmisc_1, t21_relset_2, t44_funct_1, cc5_funct_2, t57_sysrel, redefinition_m2_subset_1, t59_funcop_1, t25_relat_1, t22_funct_2, t99_xboole_1, t16_domain_1, fc1_sysrel, fc16_finset_1, t19_setfam_1, t80_relat_1, t26_sysrel, t143_partfun1, t184_relat_1, t87_xboole_1, t81_relat_1, rc2_xboole_0, s7_domain_1, existence_m1_orders_1, t112_zfmisc_1, t40_xboole_1, redefinition_k2_partfun1, fc14_finset_1, t103_relat_1, t40_mcart_1, t30_zfmisc_1, dt_k10_domain_1, t15_sysrel, fraenkel_a_0_1_domain_1, fc13_finset_1, t45_mcart_1, t139_partfun1, fc7_finset_1, idempotence_k4_subset_1, t40_zfmisc_1, t72_funcop_1, t174_partfun1, t55_funct_2, fraenkel_a_3_5_domain_1, t45_xboole_1, t66_relat_1, dt_m3_realset1, t2_xboole_0, existence_m2_finseq_1, t37_funct_5, t6_relat_1, d3_setfam_1, redefinition_k9_funcop_1, d3_xboole_0, d2_relat_1, t39_xboole_1, t23_funcop_1, t15_relset_2, t26_relat_1, t167_relat_1, t61_funct_2, t52_mcart_1, t62_domain_1, t10_xboole_1, redefinition_k12_domain_1, t28_funct_2, dt_k3_subset_1, fraenkel_a_0_2_domain_1, d2_relset_2, fc1_funct_2, t172_partfun1, t33_subset_1, t159_relat_1, t13_relset_2, fraenkel_a_3_8_domain_1, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1, t38_xboole_1, fraenkel_a_4_1_domain_1, t13_pua2mss1, t190_relat_1, t71_relat_1, t119_relat_1, antisymmetry_r2_hidden, d1_mcart_1, t53_setfam_1, fc15_finset_1, t88_relat_1, redefinition_k15_domain_1, t18_mcart_1, t53_relat_1, t22_subset_1, redefinition_k6_domain_1
% 256.17/53.88 % No. of inferences in proof: 4441
% 256.17/53.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 53323 ms resp. 52544 ms w/o parsing
% 258.34/54.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 258.41/54.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------