%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU430+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:52 AM UTC 2026
% Result : Theorem 143.44s 46.46s
% Output : Refutation 150.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1867
% Syntax : Number of formulae : 4627 ( 967 unt; 0 typ; 84 def)
% Number of atoms : 20627 (4588 equ; 0 cnn)
% Maximal formula atoms : 58 ( 4 avg)
% Number of connectives : 70299 (3741 ~;1361 |;6805 &;51338 @)
% ( 324 <=>;6730 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 446 ( 443 usr; 156 con; 0-9 aty)
% Number of variables : 12696 ( 18 ^;11915 !; 679 ?;12696 :)
% ( 0 !>; 0 ?*; 0 @-; 84 @+)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(m2_finseq_1_decl,type,
m2_finseq_1: $i > $i > $o ).
thf(m2_pua2mss1_decl,type,
m2_pua2mss1: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k3_funct_5_decl,type,
k3_funct_5: $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_decl,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k13_finseq_1_decl,type,
k13_finseq_1: $i > $i ).
thf(k4_relset_1_decl,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k4_relat_1_decl,type,
k4_relat_1: $i > $i ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k5_funcop_1_decl,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(v1_finseq_1_decl,type,
v1_finseq_1: $i > $o ).
thf(k3_finseq_1_decl,type,
k3_finseq_1: $i > $i ).
thf(k3_funcop_1_decl,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k10_relat_1_decl,type,
k10_relat_1: $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(v2_relat_1_decl,type,
v2_relat_1: $i > $o ).
thf(k1_sysrel_decl,type,
k1_sysrel: $i > $i ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k6_relset_2_decl,type,
k6_relset_2: $i > $i > $i > $i ).
thf(k5_relset_2_decl,type,
k5_relset_2: $i > $i > $i ).
thf(k6_finseq_1_decl,type,
k6_finseq_1: $i > $i ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(k8_relat_1_decl,type,
k8_relat_1: $i > $i > $i ).
thf(k5_funct_5_decl,type,
k5_funct_5: $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k2_funct_4_decl,type,
k2_funct_4: $i > $i ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k4_card_3_decl,type,
k4_card_3: $i > $i ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(k6_funcop_1_decl,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k3_pua2mss1_decl,type,
k3_pua2mss1: $i > $i ).
thf(k4_funcop_1_decl,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(k7_relset_1_decl,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(k8_pboole_decl,type,
k8_pboole: $i > $i > $i > $i > $i ).
thf(a_2_1_pua2mss1_decl,type,
a_2_1_pua2mss1: $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_card_1_decl,type,
k1_card_1: $i > $i ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k9_relset_1_decl,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(r1_setfam_1_decl,type,
r1_setfam_1: $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(v3_ordinal1_decl,type,
v3_ordinal1: $i > $o ).
thf(r1_ordinal1_decl,type,
r1_ordinal1: $i > $i > $o ).
thf(v1_realset1_decl,type,
v1_realset1: $i > $o ).
thf(m4_realset1_decl,type,
m4_realset1: $i > $i > $o ).
thf(k3_pboole_decl,type,
k3_pboole: $i > $i > $i > $i ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(r2_pboole_decl,type,
r2_pboole: $i > $i > $i > $o ).
thf(k5_relset_1_decl,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(r2_wellord2_decl,type,
r2_wellord2: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k3_setfam_1_decl,type,
k3_setfam_1: $i > $i > $i ).
thf(k5_xboole_0_decl,type,
k5_xboole_0: $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(r5_pboole_decl,type,
r5_pboole: $i > $i > $i > $o ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(k5_mcart_1_decl,type,
k5_mcart_1: $i > $i > $i > $i > $i ).
thf(k6_mcart_1_decl,type,
k6_mcart_1: $i > $i > $i > $i > $i ).
thf(k7_mcart_1_decl,type,
k7_mcart_1: $i > $i > $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(k4_realset1_decl,type,
k4_realset1: $i > $i > $i > $i ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(k4_zfmisc_1_decl,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k8_mcart_1_decl,type,
k8_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k9_mcart_1_decl,type,
k9_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k10_mcart_1_decl,type,
k10_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k11_mcart_1_decl,type,
k11_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k5_pboole_decl,type,
k5_pboole: $i > $i > $i > $i ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(v3_relat_1_decl,type,
v3_relat_1: $i > $o ).
thf(k10_relset_1_decl,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k11_relset_1_decl,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k1_pboole_decl,type,
k1_pboole: $i > $i ).
thf(v1_card_1_decl,type,
v1_card_1: $i > $o ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
thf(k10_pboole_decl,type,
k10_pboole: $i > $i > $i ).
thf(r4_pboole_decl,type,
r4_pboole: $i > $i > $i > $o ).
thf(k11_pboole_decl,type,
k11_pboole: $i > $i > $i > $i ).
thf(k3_mcart_1_decl,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(k4_mcart_1_decl,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(r2_setfam_1_decl,type,
r2_setfam_1: $i > $i > $o ).
thf(m2_subset_1_decl,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(m3_pboole_decl,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(a_2_0_domain_1_decl,type,
a_2_0_domain_1: $i > $i > $i ).
thf(r7_relat_2_decl,type,
r7_relat_2: $i > $i > $o ).
thf(m2_pboole_decl,type,
m2_pboole: $i > $i > $i > $o ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k2_realset1_decl,type,
k2_realset1: $i > $i > $i > $i ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k7_pboole_decl,type,
k7_pboole: $i > $i > $i > $i > $i ).
thf(a_1_0_pua2mss1_decl,type,
a_1_0_pua2mss1: $i > $i ).
thf(a_4_0_domain_1_decl,type,
a_4_0_domain_1: $i > $i > $i > $i > $i ).
thf(k9_funcop_1_decl,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(k1_setfam_1_decl,type,
k1_setfam_1: $i > $i ).
thf(k10_funcop_1_decl,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(a_3_0_domain_1_decl,type,
a_3_0_domain_1: $i > $i > $i > $i ).
thf(m1_ordinal1_decl,type,
m1_ordinal1: $i > $i > $o ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $i > $o ).
thf(a_4_0_relset_2_decl,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k2_card_1_decl,type,
k2_card_1: $i > $i ).
thf(r5_relat_2_decl,type,
r5_relat_2: $i > $i > $o ).
thf(g1_group_1_decl,type,
g1_group_1: $i > $i > $i ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(g2_vectsp_1_decl,type,
g2_vectsp_1: $i > $i > $i > $i > $i ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_decl,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_3_domain_1_decl,type,
a_2_3_domain_1: $i > $i > $i ).
thf(k6_enumset1_decl,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k1_orders_1_decl,type,
k1_orders_1: $i > $i ).
thf(k3_relset_2_decl,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k4_domain_1_decl,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_subset_1_decl,type,
k7_subset_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(k3_realset1_decl,type,
k3_realset1: $i > $i > $i > $i ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(k5_domain_1_decl,type,
k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k7_setfam_1_decl,type,
k7_setfam_1: $i > $i > $i ).
thf(k3_enumset1_decl,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(r2_relat_2_decl,type,
r2_relat_2: $i > $i > $o ).
thf(k4_relset_2_decl,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k8_relset_2_decl,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k2_enumset1_decl,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(a_3_1_pua2mss1_decl,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(p1_s6_domain_1_decl,type,
p1_s6_domain_1: $i > $o ).
thf(p2_s6_domain_1_decl,type,
p2_s6_domain_1: $i > $o ).
thf(a_1_5_domain_1_decl,type,
a_1_5_domain_1: $i > $i ).
thf(a_1_6_domain_1_decl,type,
a_1_6_domain_1: $i > $i ).
thf(k2_domain_1_decl,type,
k2_domain_1: $i > $i > $i > $i ).
thf(k16_domain_1_decl,type,
k16_domain_1: $i > $i > $i > $i > $i ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(f1_s8_funct_2_decl,type,
f1_s8_funct_2: $i ).
thf(f2_s8_funct_2_decl,type,
f2_s8_funct_2: $i ).
thf(f3_s8_funct_2_decl,type,
f3_s8_funct_2: $i ).
thf(f4_s8_funct_2_decl,type,
f4_s8_funct_2: $i > $i > $i ).
thf(a_0_3_domain_1_decl,type,
a_0_3_domain_1: $i ).
thf(a_0_4_domain_1_decl,type,
a_0_4_domain_1: $i ).
thf(a_0_5_domain_1_decl,type,
a_0_5_domain_1: $i ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(k9_funct_2_decl,type,
k9_funct_2: $i > $i > $i > $i ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(v2_card_1_decl,type,
v2_card_1: $i > $o ).
thf(r2_realset1_decl,type,
r2_realset1: $i > $i > $i > $o ).
thf(k4_numbers_decl,type,
k4_numbers: $i ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(f1_s5_funct_2_decl,type,
f1_s5_funct_2: $i ).
thf(f2_s5_funct_2_decl,type,
f2_s5_funct_2: $i ).
thf(f3_s5_funct_2_decl,type,
f3_s5_funct_2: $i ).
thf(p1_s5_funct_2_decl,type,
p1_s5_funct_2: $i > $i > $i > $o ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k13_domain_1_decl,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(g1_vectsp_1_decl,type,
g1_vectsp_1: $i > $i > $i > $i ).
thf(k2_relset_2_decl,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k1_enumset1_decl,type,
k1_enumset1: $i > $i > $i > $i ).
thf(g1_rlvect_1_decl,type,
g1_rlvect_1: $i > $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k15_domain_1_decl,type,
k15_domain_1: $i > $i > $i > $i > $i ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(g3_vectsp_1_decl,type,
g3_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_decl,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k14_domain_1_decl,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(k3_domain_1_decl,type,
k3_domain_1: $i > $i > $i > $i ).
thf(k12_mcart_1_decl,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k7_relset_2_decl,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(k1_relset_2_decl,type,
k1_relset_2: $i > $i > $i > $i ).
thf(f1_s7_funct_2_decl,type,
f1_s7_funct_2: $i ).
thf(f2_s7_funct_2_decl,type,
f2_s7_funct_2: $i ).
thf(f3_s7_funct_2_decl,type,
f3_s7_funct_2: $i ).
thf(p1_s7_funct_2_decl,type,
p1_s7_funct_2: $i > $i > $i > $o ).
thf(f1_s14_funct_2_decl,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_decl,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_decl,type,
p1_s14_funct_2: $i > $i > $o ).
thf(a_1_1_domain_1_decl,type,
a_1_1_domain_1: $i > $i ).
thf(k17_domain_1_decl,type,
k17_domain_1: $i > $i > $i > $i > $i ).
thf(p1_s1_funct_1_decl,type,
p1_s1_funct_1: $i > $i > $o ).
thf(f1_s1_funct_1_decl,type,
f1_s1_funct_1: $i ).
thf(f1_s12_funct_2_decl,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_decl,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_decl,type,
f2_s12_funct_2: $i ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s13_funct_2_decl,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_decl,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_decl,type,
f2_s13_funct_2: $i ).
thf(a_3_8_domain_1_decl,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(f1_s2_funct_2_decl,type,
f1_s2_funct_2: $i ).
thf(f3_s2_funct_2_decl,type,
f3_s2_funct_2: $i > $i ).
thf(f2_s2_funct_2_decl,type,
f2_s2_funct_2: $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(f1_s6_funct_2_decl,type,
f1_s6_funct_2: $i ).
thf(f2_s6_funct_2_decl,type,
f2_s6_funct_2: $i ).
thf(f4_s6_funct_2_decl,type,
f4_s6_funct_2: $i > $i > $i ).
thf(f3_s6_funct_2_decl,type,
f3_s6_funct_2: $i ).
thf(f1_s1_funct_2_decl,type,
f1_s1_funct_2: $i ).
thf(f2_s1_funct_2_decl,type,
f2_s1_funct_2: $i ).
thf(p1_s1_funct_2_decl,type,
p1_s1_funct_2: $i > $i > $o ).
thf(a_2_0_relset_2_decl,type,
a_2_0_relset_2: $i > $i > $i ).
thf(p1_s5_domain_1_decl,type,
p1_s5_domain_1: $i > $o ).
thf(p2_s5_domain_1_decl,type,
p2_s5_domain_1: $i > $o ).
thf(a_1_3_domain_1_decl,type,
a_1_3_domain_1: $i > $i ).
thf(a_1_4_domain_1_decl,type,
a_1_4_domain_1: $i > $i ).
thf(a_4_2_domain_1_decl,type,
a_4_2_domain_1: $i > $i > $i > $i > $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k5_enumset1_decl,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(p1_s1_domain_1_decl,type,
p1_s1_domain_1: $i > $o ).
thf(a_3_0_relset_2_decl,type,
a_3_0_relset_2: $i > $i > $i > $i ).
thf(k13_mcart_1_decl,type,
k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_6_0_domain_1_decl,type,
a_6_0_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(p1_s2_domain_1_decl,type,
p1_s2_domain_1: $i > $i > $o ).
thf(f1_s2_orders_1_decl,type,
f1_s2_orders_1: $i ).
thf(p1_s2_orders_1_decl,type,
p1_s2_orders_1: $i > $i > $o ).
thf(a_0_2_domain_1_decl,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_decl,type,
f3_s9_domain_1: $i ).
thf(k14_mcart_1_decl,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_0_0_domain_1_decl,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_decl,type,
f1_s7_domain_1: $i ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $i > $i ).
thf(p1_s7_domain_1_decl,type,
p1_s7_domain_1: $i > $o ).
thf(f1_s3_subset_1_decl,type,
f1_s3_subset_1: $i ).
thf(p1_s3_subset_1_decl,type,
p1_s3_subset_1: $i > $o ).
thf(a_4_1_relset_2_decl,type,
a_4_1_relset_2: $i > $i > $i > $i > $i ).
thf(f1_s10_domain_1_decl,type,
f1_s10_domain_1: $i ).
thf(p1_s10_domain_1_decl,type,
p1_s10_domain_1: $i > $o ).
thf(p2_s10_domain_1_decl,type,
p2_s10_domain_1: $i > $o ).
thf(f1_s1_xboole_0_decl,type,
f1_s1_xboole_0: $i ).
thf(p1_s1_xboole_0_decl,type,
p1_s1_xboole_0: $i > $o ).
thf(k8_subset_1_decl,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_decl,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_decl,type,
f2_s8_domain_1: $i ).
thf(g2_struct_0_decl,type,
g2_struct_0: $i > $i > $i ).
thf(f1_s1_relset_1_decl,type,
f1_s1_relset_1: $i ).
thf(f2_s1_relset_1_decl,type,
f2_s1_relset_1: $i ).
thf(p1_s1_relset_1_decl,type,
p1_s1_relset_1: $i > $i > $o ).
thf(p1_s2_card_1_decl,type,
p1_s2_card_1: $i > $o ).
thf(f1_s2_xboole_0_decl,type,
f1_s2_xboole_0: $i ).
thf(p1_s2_xboole_0_decl,type,
p1_s2_xboole_0: $i > $o ).
thf(f2_s2_xboole_0_decl,type,
f2_s2_xboole_0: $i ).
thf(f1_s1_pboole_decl,type,
f1_s1_pboole: $i ).
thf(f2_s1_pboole_decl,type,
f2_s1_pboole: $i > $i ).
thf(a_8_0_domain_1_decl,type,
a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s8_domain_1_decl,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_decl,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_decl,type,
p1_s8_domain_1: $i > $o ).
thf(f1_s1_subset_1_decl,type,
f1_s1_subset_1: $i ).
thf(p1_s1_subset_1_decl,type,
p1_s1_subset_1: $i > $o ).
thf(p1_s2_ordinal1_decl,type,
p1_s2_ordinal1: $i > $o ).
thf(f1_s9_domain_1_decl,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_decl,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_decl,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_decl,type,
p1_s9_domain_1: $i > $i > $o ).
thf(a_4_1_domain_1_decl,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(f1_s2_pboole_decl,type,
f1_s2_pboole: $i ).
thf(f2_s2_pboole_decl,type,
f2_s2_pboole: $i ).
thf(p1_s2_pboole_decl,type,
p1_s2_pboole: $i > $i > $o ).
thf(p1_s1_card_1_decl,type,
p1_s1_card_1: $i > $o ).
thf(p1_s1_int_1_decl,type,
p1_s1_int_1: $i > $o ).
thf(p1_s4_domain_1_decl,type,
p1_s4_domain_1: $i > $i > $i > $i > $o ).
thf(f1_s2_subset_1_decl,type,
f1_s2_subset_1: $i ).
thf(p1_s2_subset_1_decl,type,
p1_s2_subset_1: $i > $o ).
thf(f1_s4_subset_1_decl,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_decl,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_decl,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_decl,type,
f3_s4_subset_1: $i ).
thf(f1_s2_relset_1_decl,type,
f1_s2_relset_1: $i ).
thf(f2_s2_relset_1_decl,type,
f2_s2_relset_1: $i ).
thf(p1_s2_relset_1_decl,type,
p1_s2_relset_1: $i > $i > $o ).
thf(p1_s1_tarski_decl,type,
p1_s1_tarski: $i > $i > $o ).
thf(f1_s1_tarski_decl,type,
f1_s1_tarski: $i ).
thf(p1_s3_domain_1_decl,type,
p1_s3_domain_1: $i > $i > $i > $o ).
thf(p1_s3_xboole_0_decl,type,
p1_s3_xboole_0: $i > $o ).
thf(f1_s1_orders_1_decl,type,
f1_s1_orders_1: $i ).
thf(p1_s1_orders_1_decl,type,
p1_s1_orders_1: $i > $i > $o ).
thf(f1_s1_relat_1_decl,type,
f1_s1_relat_1: $i ).
thf(f2_s1_relat_1_decl,type,
f2_s1_relat_1: $i ).
thf(p1_s1_relat_1_decl,type,
p1_s1_relat_1: $i > $i > $o ).
thf(f1_s2_pua2mss1_decl,type,
f1_s2_pua2mss1: $i ).
thf(f2_s2_pua2mss1_decl,type,
f2_s2_pua2mss1: $i ).
thf(p1_s2_pua2mss1_decl,type,
p1_s2_pua2mss1: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk27_decl,type,
sk27: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk70_decl,type,
sk70: $i ).
thf(sk81_decl,type,
sk81: $i ).
thf(sk82_decl,type,
sk82: $i > $i ).
thf(sk95_decl,type,
sk95: $i ).
thf(sk119_decl,type,
sk119: $i ).
thf(sk148_decl,type,
sk148: $i > $i ).
thf(sk149_decl,type,
sk149: $i ).
thf(sk153_decl,type,
sk153: $i ).
thf(sk180_decl,type,
sk180: $i ).
thf(sk181_decl,type,
sk181: $i > $i ).
thf(sk324_decl,type,
sk324: $i > $i ).
thf(sk328_decl,type,
sk328: $i ).
thf(sk364_decl,type,
sk364: $i > $i ).
thf(sk372_decl,type,
sk372: $o ).
thf(sk373_decl,type,
sk373: $i ).
thf(sk374_decl,type,
sk374: $i ).
thf(sk375_decl,type,
sk375: $i ).
thf(sk376_decl,type,
sk376: $i ).
thf(sk378_decl,type,
sk378: $i ).
thf(sk384_decl,type,
sk384: $i ).
thf(sk397_decl,type,
sk397: $i ).
thf(sk431_decl,type,
sk431: $i ).
thf(sk455_decl,type,
sk455: $i ).
thf(sk462_decl,type,
sk462: $i ).
thf(sk470_decl,type,
sk470: $i ).
thf(sk495_decl,type,
sk495: $o ).
thf(sk496_decl,type,
sk496: $i ).
thf(sk497_decl,type,
sk497: $i ).
thf(sk498_decl,type,
sk498: $i ).
thf(sk510_decl,type,
sk510: $o ).
thf(sk511_decl,type,
sk511: $i ).
thf(sk512_decl,type,
sk512: $i ).
thf(sk530_decl,type,
sk530: $o ).
thf(sk531_decl,type,
sk531: $i ).
thf(sk532_decl,type,
sk532: $i ).
thf(sk533_decl,type,
sk533: $i ).
thf(sk534_decl,type,
sk534: $i ).
thf(sk535_decl,type,
sk535: $o ).
thf(sk536_decl,type,
sk536: $i ).
thf(sk537_decl,type,
sk537: $i ).
thf(sk538_decl,type,
sk538: $o ).
thf(sk539_decl,type,
sk539: $i ).
thf(sk540_decl,type,
sk540: $i ).
thf(sk541_decl,type,
sk541: $i ).
thf(sk561_decl,type,
sk561: $i ).
thf(sk564_decl,type,
sk564: $o ).
thf(sk565_decl,type,
sk565: $i ).
thf(sk566_decl,type,
sk566: $i ).
thf(sk567_decl,type,
sk567: $i ).
thf(sk578_decl,type,
sk578: $i ).
thf(sk592_decl,type,
sk592: $i ).
thf(sk593_decl,type,
sk593: $i ).
thf(sk594_decl,type,
sk594: $i ).
thf(sk595_decl,type,
sk595: $i ).
thf(sk602_decl,type,
sk602: $o ).
thf(sk603_decl,type,
sk603: $i ).
thf(sk604_decl,type,
sk604: $i ).
thf(sk606_decl,type,
sk606: $o ).
thf(sk607_decl,type,
sk607: $i ).
thf(sk608_decl,type,
sk608: $i ).
thf(sk609_decl,type,
sk609: $i ).
thf(sk610_decl,type,
sk610: $o ).
thf(sk611_decl,type,
sk611: $i ).
thf(sk612_decl,type,
sk612: $i ).
thf(sk649_decl,type,
sk649: $i > $i ).
thf(sk650_decl,type,
sk650: $i ).
thf(sk654_decl,type,
sk654: $i ).
thf(sk679_decl,type,
sk679: $i ).
thf(sk689_decl,type,
sk689: $i ).
thf(sk690_decl,type,
sk690: $i ).
thf(sk702_decl,type,
sk702: $i ).
thf(sk708_decl,type,
sk708: $i ).
thf(sk715_decl,type,
sk715: $i ).
thf(sk721_decl,type,
sk721: $i > $i ).
thf(sk733_decl,type,
sk733: $o ).
thf(sk734_decl,type,
sk734: $i ).
thf(sk735_decl,type,
sk735: $i ).
thf(sk741_decl,type,
sk741: $i ).
thf(sk745_decl,type,
sk745: $o ).
thf(sk746_decl,type,
sk746: $i ).
thf(sk747_decl,type,
sk747: $i ).
thf(sk748_decl,type,
sk748: $i ).
thf(sk749_decl,type,
sk749: $i ).
thf(sk750_decl,type,
sk750: $i > $i ).
thf(sk777_decl,type,
sk777: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B = k1_xboole_0 ) )
=> ( ( A @ ( sk1 @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( sk1 @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B = k1_xboole_0 ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk2 @ ( A @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ m2_finseq_1 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ m2_finseq_1 ) )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( A @ k1_funct_1 ) )
= C )
=> ( ( C @ ( B @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( B @ k1_funct_1 ) )
= D )
=> ( ( D @ ( A @ k1_funct_1 ) )
= C ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ sk7 ) @ r2_hidden ) ) )
=> ( ( ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk7 ) ) )
=> ( ( B @ ( A @ sk7 ) @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( ( B @ ( A @ sk7 ) @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk7 ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m2_finseq_1 ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ~ ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ~ ( A @ ( B @ r2_hidden ) )
& ( B @ v3_ordinal1 ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk70_def,definition,
( sk70
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk82_def,definition,
( sk82
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v3_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ) ) ) ).
thf(sk95_def,definition,
( sk95
= ( @+[A: $i] :
( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk119_def,definition,
( sk119
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk148_def,definition,
( sk148
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
& ( B @ v3_ordinal1 ) ) ) ) ).
thf(sk149_def,definition,
( sk149
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk153_def,definition,
( sk153
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk180_def,definition,
( sk180
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk181_def,definition,
( sk181
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ) ) ) ).
thf(sk324_def,definition,
( sk324
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ).
thf(sk328_def,definition,
( sk328
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s8_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s8_funct_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s8_funct_2 ) ) ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk364_def,definition,
( sk364
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ k1_tarski ) ) ) ) ).
thf(sk373_def,definition,
( sk373
= ( @+[A: $i] :
( ? [B: $i] :
( ~ ? [C: $i] :
( ( C @ ( B @ ( A @ p1_s5_funct_2 ) ) )
& ( f3_s5_funct_2 @ ( C @ r2_hidden ) ) )
& ( f2_s5_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s5_funct_2 @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk374_def,definition,
( sk374
= ( @+[A: $i] :
( ~ ? [B: $i] :
( ( B @ ( A @ ( sk373 @ p1_s5_funct_2 ) ) )
& ( f3_s5_funct_2 @ ( B @ r2_hidden ) ) )
& ( f2_s5_funct_2 @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk375_def,definition,
( sk375
= ( @+[A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s5_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s5_funct_2 ) ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk376_def,definition,
( sk376
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk378_def,definition,
( sk378
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk384_def,definition,
( sk384
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk397_def,definition,
( sk397
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk431_def,definition,
( sk431
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk455_def,definition,
( sk455
= ( @+[A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk462_def,definition,
( sk462
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk470_def,definition,
( sk470
= ( @+[A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk496_def,definition,
( sk496
= ( @+[A: $i] :
~ ( ( f1_s7_funct_2 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ p1_s7_funct_2 ) ) )
& ( f3_s7_funct_2 @ ( C @ m1_subset_1 ) ) ) ) ) ) ) ).
thf(sk497_def,definition,
( sk497
= ( @+[A: $i] :
~ ( ( f2_s7_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ ( sk496 @ p1_s7_funct_2 ) ) )
& ( f3_s7_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk498_def,definition,
( sk498
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s7_funct_2 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s7_funct_2 ) ) ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk511_def,definition,
( sk511
= ( @+[A: $i] :
~ ( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk512_def,definition,
( sk512
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk531_def,definition,
( sk531
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) ) ) ) ).
thf(sk532_def,definition,
( sk532
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk531 @ p1_s1_funct_1 ) )
& ( A @ ( sk531 @ p1_s1_funct_1 ) ) )
=> ( A = B ) ) ) ) ).
thf(sk533_def,definition,
( sk533
= ( @+[A: $i] :
~ ( ( ( A @ ( sk531 @ p1_s1_funct_1 ) )
& ( sk532 @ ( sk531 @ p1_s1_funct_1 ) ) )
=> ( sk532 = A ) ) ) ) ).
thf(sk534_def,definition,
( sk534
= ( @+[A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk536_def,definition,
( sk536
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk537_def,definition,
( sk537
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk539_def,definition,
( sk539
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk540_def,definition,
( sk540
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk541_def,definition,
( sk541
= ( @+[A: $i] : ( A @ v1_card_1 ) ) ) ).
thf(sk561_def,definition,
( sk561
= ( @+[A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk565_def,definition,
( sk565
= ( @+[A: $i] :
~ ( ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
=> ( f2_s2_funct_2 @ ( A @ f3_s2_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk566_def,definition,
( sk566
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s2_funct_2 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s2_funct_2 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk567_def,definition,
( sk567
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk578_def,definition,
( sk578
= ( @+[A: $i] : ( A @ v1_int_1 ) ) ) ).
thf(sk592_def,definition,
( sk592
= ( @+[A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk593_def,definition,
( sk593
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk594_def,definition,
( sk594
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk595_def,definition,
( sk595
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk603_def,definition,
( sk603
= ( @+[A: $i] :
~ ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk604_def,definition,
( sk604
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk607_def,definition,
( sk607
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( f2_s6_funct_2 @ ( B @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( A @ r2_hidden ) ) )
=> ( f3_s6_funct_2 @ ( B @ ( A @ f4_s6_funct_2 ) @ r2_hidden ) ) ) ) ) ).
thf(sk608_def,definition,
( sk608
= ( @+[A: $i] :
~ ( ( ( f2_s6_funct_2 @ ( A @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( sk607 @ r2_hidden ) ) )
=> ( f3_s6_funct_2 @ ( A @ ( sk607 @ f4_s6_funct_2 ) @ r2_hidden ) ) ) ) ) ).
thf(sk609_def,definition,
( sk609
= ( @+[A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s6_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s6_funct_2 ) ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk611_def,definition,
( sk611
= ( @+[A: $i] :
( ~ ? [B: $i] :
( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk612_def,definition,
( sk612
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk649_def,definition,
( sk649
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk650_def,definition,
( sk650
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk654_def,definition,
( sk654
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s3_subset_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p1_s3_subset_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s3_subset_1 ) ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ) ) ) ).
thf(sk679_def,definition,
( sk679
= ( @+[A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ) ) ) ).
thf(sk689_def,definition,
( sk689
= ( @+[A: $i] :
( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk690_def,definition,
( sk690
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ) ) ).
thf(sk702_def,definition,
( sk702
= ( @+[A: $i] :
( ! [B: $i] :
( ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ) ) ) ).
thf(sk708_def,definition,
( sk708
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ( ! [C: $i] :
( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ) ) ) ).
thf(sk715_def,definition,
( sk715
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ p1_s1_int_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_int_1 ) ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ) ) ) ).
thf(sk721_def,definition,
( sk721
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk734_def,definition,
( sk734
= ( @+[A: $i] :
~ ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) ) ) ).
thf(sk735_def,definition,
( sk735
= ( @+[A: $i] :
~ ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) ) ) ).
thf(sk741_def,definition,
( sk741
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s2_relset_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_relset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s2_relset_1 ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( B @ p1_s2_relset_1 ) ) ) ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( A @ m2_relset_1 ) ) ) ) ) ) ).
thf(sk746_def,definition,
( sk746
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) ) ) ) ).
thf(sk747_def,definition,
( sk747
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk746 @ p1_s1_tarski ) )
& ( A @ ( sk746 @ p1_s1_tarski ) ) )
=> ( A = B ) ) ) ) ).
thf(sk748_def,definition,
( sk748
= ( @+[A: $i] :
~ ( ( ( A @ ( sk746 @ p1_s1_tarski ) )
& ( sk747 @ ( sk746 @ p1_s1_tarski ) ) )
=> ( sk747 = A ) ) ) ) ).
thf(sk749_def,definition,
( sk749
= ( @+[A: $i] :
( ! [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ) ) ) ).
thf(sk750_def,definition,
( sk750
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ ( B @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( B @ r2_hidden ) ) ) ) ) ).
thf(sk777_def,definition,
( sk777
= ( @+[A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(1372,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(8536,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(1698,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(10319,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(4682,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1769,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C @ p1_s3_xboole_0 ) )
& ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( C @ p1_s3_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_xboole_0) ).
thf(10790,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C @ p1_s3_xboole_0 )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C @ p1_s3_xboole_0 ) ) )
& ! [C: $i] :
( ( ( C @ p1_s3_xboole_0 )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( C @ p1_s3_xboole_0 ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(1310,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(8200,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1462,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(9032,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(251,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( C @ ( B @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funcop_1) ).
thf(2822,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( C @ ( B @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1480,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_ordinal1 ) )
=> ( B @ ( C @ m1_ordinal1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
thf(9131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_ordinal1 ) )
=> ( B @ ( C @ m1_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pua2mss1) ).
thf(6085,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(526,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(4188,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1282,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(7985,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(7986,plain,
( ( sk431 @ v1_finset_1 )
& ( sk431 @ v1_funct_1 )
& ( sk431 @ v1_relat_1 )
& ~ ( sk431 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7985]) ).
thf(7988,plain,
sk431 @ v1_relat_1,
inference(cnfConj,[status(thm)],[7986]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
& ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_sysrel) ).
thf(1897,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
& ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1898,plain,
! [A: $i] :
( ( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1897]) ).
thf(1900,plain,
! [A: $i] :
( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1898]) ).
thf(25678,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7988,1900]) ).
thf(25679,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25678]) ).
thf(25680,plain,
sk431 @ k2_relat_1 @ ( sk431 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25679:[bind(A,$thf( sk431 ))]]) ).
thf(1443,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(8930,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(1240,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(7766,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(534,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pboole) ).
thf(4216,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(4217,plain,
( ( sk119 @ v1_funct_1 )
& ( sk119 @ v3_relat_1 )
& ( sk119 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[4216]) ).
thf(4218,plain,
sk119 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4217]) ).
thf(1901,plain,
! [A: $i] :
( ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1898]) ).
thf(25983,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4218,1901]) ).
thf(25984,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25983]) ).
thf(25985,plain,
sk119 @ k1_relat_1 @ ( sk119 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25984:[bind(A,$thf( sk119 ))]]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(6836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1180,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relset_1) ).
thf(7427,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1194,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(7511,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(7512,plain,
( ( sk378 @ v1_finset_1 )
& ( sk378 @ v2_funct_1 )
& ( sk378 @ v1_funct_1 )
& ( sk378 @ v1_relat_1 )
& ( sk378 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7511]) ).
thf(7517,plain,
sk378 @ v1_relat_1,
inference(cnfConj,[status(thm)],[7512]) ).
thf(25926,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7517,1901]) ).
thf(25927,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25926]) ).
thf(25928,plain,
sk378 @ k1_relat_1 @ ( sk378 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25927:[bind(A,$thf( sk378 ))]]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_partfun1) ).
thf(5365,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1308,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(8186,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
<=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_2) ).
thf(3883,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) )
& ( ( C @ ( B @ r1_partfun1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(726,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) @ k1_relat_1 )
= k1_xboole_0 )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(5116,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) @ k1_relat_1 )
= k1_xboole_0 )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(667,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(4835,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1520,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(9312,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(9313,plain,
( ( sk595 @ v1_funct_1 )
& ( sk595 @ v1_xboole_0 )
& ( sk595 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[9312]) ).
thf(9315,plain,
sk595 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[9313]) ).
thf(1313,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(8242,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(8243,plain,
( ( sk470 @ v1_setfam_1 )
& ~ ( sk470 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[8242]) ).
thf(8244,plain,
~ ( sk470 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[8243]) ).
thf(12594,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk470 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,8244]) ).
thf(12595,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk470 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12594]) ).
thf(12607,plain,
sk595 != sk470,
inference(simp,[status(thm)],[12595]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(6355,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(120,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2295,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(123,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2306,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(311,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A = B )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_card_1) ).
thf(3053,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) )
& ( ( A = B )
=> ( B @ ( A @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(7515,plain,
sk378 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[7512]) ).
thf(994,axiom,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_fraenkel )
& ~ ( A @ k13_finseq_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_finseq_1) ).
thf(6419,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_fraenkel )
& ~ ( A @ k13_finseq_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(6420,plain,
( ! [A: $i] : ( A @ k13_finseq_1 @ v1_fraenkel )
& ~ ? [A: $i] : ( A @ k13_finseq_1 @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[6419]) ).
thf(6421,plain,
! [B: $i,A: $i] :
( ( B @ k13_finseq_1 @ v1_fraenkel )
& ~ ( A @ k13_finseq_1 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6420]) ).
thf(6422,plain,
! [A: $i] :
~ ( A @ k13_finseq_1 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[6421]) ).
thf(15265,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,6422]) ).
thf(15266,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15265]) ).
thf(15278,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk378 ),
inference(simp,[status(thm)],[15266]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
thf(5593,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_setfam_1 ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_setfam_1) ).
thf(7854,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_setfam_1 ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_mcart_1) ).
thf(6231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = H ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1322,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(8288,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).
thf(7691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(74,axiom,
( ( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_5) ).
thf(2072,plain,
( ( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(7445,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(1389,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(8663,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(1297,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( B @ ( A @ ( C @ m2_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_pboole) ).
thf(8097,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_pboole ) ) ) )
& ( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4899,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(638,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(4705,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(4706,plain,
( ( sk149 @ v1_finseq_1 )
& ( sk149 @ v1_finset_1 )
& ( sk149 @ v2_funct_1 )
& ( sk149 @ v1_funct_1 )
& ( sk149 @ v1_relat_1 )
& ( sk149 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4705]) ).
thf(4710,plain,
sk149 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[4706]) ).
thf(1270,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_realset1) ).
thf(7930,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(7931,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_realset1 )
& ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[7930]) ).
thf(7932,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_tarski @ v1_realset1 )
& ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7931]) ).
thf(7933,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7932]) ).
thf(15586,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,7933]) ).
thf(15587,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15586]) ).
thf(15596,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk149 ),
inference(simp,[status(thm)],[15587]) ).
thf(1561,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s5_domain_1 )
=> ( B @ p2_s5_domain_1 ) ) )
=> ( A @ a_1_4_domain_1 @ ( A @ a_1_3_domain_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s5_domain_1) ).
thf(9516,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s5_domain_1 )
=> ( B @ p2_s5_domain_1 ) ) )
=> ( A @ a_1_4_domain_1 @ ( A @ a_1_3_domain_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(377,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(3405,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(3406,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk70 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk70 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk70 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3405]) ).
thf(3407,plain,
~ ( sk70 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3406]) ).
thf(11489,plain,
( ( ( sk378 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,3407]) ).
thf(11490,plain,
( ( sk378 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11489]) ).
thf(11504,plain,
sk378 != sk70,
inference(simp,[status(thm)],[11490]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pboole) ).
thf(5950,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1371,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_2) ).
thf(8514,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_mcart_1) ).
thf(2876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(7673,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(421,axiom,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_finset_1 )
& ( k1_xboole_0 @ v2_funct_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finseq_1) ).
thf(3609,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_finset_1 )
& ( k1_xboole_0 @ v2_funct_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(3610,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_finset_1 )
& ( k1_xboole_0 @ v2_funct_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3609]) ).
thf(3611,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3610]) ).
thf(1505,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(9268,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(9269,plain,
( ( sk594 @ v1_relat_1 )
& ~ ( sk594 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[9268]) ).
thf(9270,plain,
~ ( sk594 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[9269]) ).
thf(11227,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,9270]) ).
thf(11228,plain,
( ( sk594 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11227]) ).
thf(11235,plain,
sk594 != k1_xboole_0,
inference(simp,[status(thm)],[11228]) ).
thf(1623,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(9833,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(1320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(8283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(1246,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( C = k1_xboole_0 ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(7798,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( C = k1_xboole_0 )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( C = k1_xboole_0 ) ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1899,plain,
! [A: $i] :
( ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1898]) ).
thf(1605,axiom,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ~ ( C @ ( B @ p1_s2_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) ) ) )
& ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( B @ ( C @ p1_s2_orders_1 ) )
& ~ ( C @ ( B @ p1_s2_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s2_orders_1 @ ( A @ r1_tarski ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s2_orders_1 ) )
& ( B @ ( A @ p1_s2_orders_1 ) ) )
=> ( C @ ( A @ p1_s2_orders_1 ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ p1_s2_orders_1 ) )
& ( B @ ( A @ p1_s2_orders_1 ) ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s2_orders_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ p1_s2_orders_1 ) )
& ( A != B ) ) )
& ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_orders_1) ).
thf(9731,plain,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ~ ( C @ ( B @ p1_s2_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) ) ) )
& ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( B @ ( C @ p1_s2_orders_1 ) )
& ~ ( C @ ( B @ p1_s2_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s2_orders_1 @ ( A @ r1_tarski ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s2_orders_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s2_orders_1 ) )
& ( B @ ( A @ p1_s2_orders_1 ) ) )
=> ( C @ ( A @ p1_s2_orders_1 ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ p1_s2_orders_1 ) )
& ( B @ ( A @ p1_s2_orders_1 ) ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s2_orders_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_orders_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ ( B @ p1_s2_orders_1 ) )
& ( A != B ) ) )
& ( f1_s2_orders_1 @ ( A @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(3581,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(672,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(4848,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(4849,plain,
( ( sk153 @ v1_finseq_1 )
& ( sk153 @ v1_funct_1 )
& ( sk153 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[4848]) ).
thf(4852,plain,
sk153 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[4849]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(7143,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(3863,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1598,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).
thf(9685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(463,axiom,
? [A: $i] :
( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(3828,plain,
? [A: $i] :
( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(3829,plain,
( ( sk95 @ v3_relat_1 )
& ( sk95 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3828]) ).
thf(3830,plain,
sk95 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3829]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
thf(5676,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(981,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_domain_1) ).
thf(6317,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(7990,plain,
sk431 @ v1_finset_1,
inference(cnfConj,[status(thm)],[7986]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_funct_2) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1011,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(6512,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(151,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ~ ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ~ ( A @ ( B @ r2_hidden ) )
& ( B @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_ordinal1) ).
thf(2427,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ~ ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ~ ( A @ ( B @ r2_hidden ) )
& ( B @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1471,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(9076,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(1633,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_3_domain_1) ).
thf(9864,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_3_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_mcart_1) ).
thf(7072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_relat_1) ).
thf(5028,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relset_1) ).
thf(4728,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1091,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( F
= ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(6954,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( F
= ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1153,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( A @ v2_card_1 )
<=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( A
!= ( B @ k2_card_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_card_1) ).
thf(7285,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( A
!= ( B @ k2_card_1 ) ) )
=> ( A @ v2_card_1 ) )
& ( ( A @ v2_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( A
!= ( B @ k2_card_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1473,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(9091,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ r2_hidden ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
& ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_mcart_1) ).
thf(6057,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ r2_hidden ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
& ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_finseq_1) ).
thf(1926,plain,
! [A: $i] :
( ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1927,plain,
( ! [A: $i] : ( A @ ( A @ k6_finseq_1 @ m2_finseq_1 ) )
& ! [A: $i] : ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[1926]) ).
thf(1928,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ k6_finseq_1 @ m2_finseq_1 ) )
& ( A @ k6_finseq_1 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1927]) ).
thf(1929,plain,
! [A: $i] : ( A @ k6_finseq_1 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1928]) ).
thf(18170,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k13_finseq_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1929,6422]) ).
thf(18171,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k13_finseq_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[18170]) ).
thf(18194,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 )
!= ( B @ k13_finseq_1 ) ),
inference(simp,[status(thm)],[18171]) ).
thf(1739,axiom,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(10642,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(10643,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[10642]) ).
thf(10644,plain,
! [A: $i] :
( ( A @ k6_finseq_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[10643]) ).
thf(28977,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[18194,10644]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
<=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1873,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1874,plain,
! [B: $i,A: $i] :
( ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk7 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk7 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk7 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk7 ) ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( B @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( A @ k1_relat_1 @ ( A @ ( B @ sk7 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1873]) ).
thf(1875,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk7 ) ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1874]) ).
thf(1882,plain,
! [B: $i,A: $i] :
( ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk7 ) ) )
| ( ( A @ ( B @ sk8 ) )
= ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1875]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(6798,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1148,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(7253,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k5_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1468,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(9059,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(3680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(2073,plain,
( ( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2072]) ).
thf(2075,plain,
( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2073]) ).
thf(2077,plain,
( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2075]) ).
thf(1587,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(9621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(506,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( A
= ( C @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( ( ( A @ k2_relat_1 )
= C )
& ( ( A @ k1_relat_1 )
= B ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(4037,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( A
= ( C @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( ( ( A @ k2_relat_1 )
= C )
& ( ( A @ k1_relat_1 )
= B ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1496,axiom,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset1) ).
thf(9224,plain,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(9225,plain,
( ~ ( sk592 @ v1_realset1 )
& ~ ( sk592 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[9224]) ).
thf(9226,plain,
~ ( sk592 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[9225]) ).
thf(12588,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk592 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,9226]) ).
thf(12589,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk592 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12588]) ).
thf(12602,plain,
sk595 != sk592,
inference(simp,[status(thm)],[12589]) ).
thf(1681,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(10198,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1206,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(7570,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(7571,plain,
sk384 @ v1_xboole_0,
inference(cnf,[status(esa)],[7570]) ).
thf(1454,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_realset1) ).
thf(8983,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(8984,plain,
( ( sk561 @ v1_realset1 )
& ~ ( sk561 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[8983]) ).
thf(8985,plain,
~ ( sk561 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[8984]) ).
thf(11618,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,8985]) ).
thf(11619,plain,
( ( sk561 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11618]) ).
thf(11635,plain,
sk561 != sk384,
inference(simp,[status(thm)],[11619]) ).
thf(1293,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_domain_1) ).
thf(8044,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_partfun1) ).
thf(5168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1355,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
<=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_pboole) ).
thf(8434,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ v2_relat_1 ) )
& ( ( B @ v2_relat_1 )
=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(1711,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(10431,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(1172,axiom,
! [A: $i] :
( ( A @ v1_realset1 )
<=> ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_realset1) ).
thf(7382,plain,
! [A: $i] :
( ( ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ v1_realset1 ) )
& ( ( A @ v1_realset1 )
=> ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(7383,plain,
( ! [A: $i] :
( ~ ( ~ ? [B: $i] :
( A
= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ v1_realset1 ) )
& ! [A: $i] :
( ( A @ v1_realset1 )
=> ~ ( ~ ? [B: $i] :
( A
= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[7382]) ).
thf(7384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ v1_realset1 )
| ( B
!= ( C @ k1_tarski ) ) )
& ( ( B @ v1_realset1 )
| ~ ( B @ v1_xboole_0 ) )
& ( ( A
= ( A @ sk364 @ k1_tarski ) )
| ( A @ v1_xboole_0 )
| ~ ( A @ v1_realset1 ) ) ),
inference(cnf,[status(esa)],[7383]) ).
thf(7387,plain,
! [B: $i,A: $i] :
( ( A @ v1_realset1 )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[7384]) ).
thf(7390,plain,
! [B: $i,A: $i] :
( ( A @ v1_realset1 )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[7387]) ).
thf(7391,plain,
! [A: $i] : ( A @ k1_tarski @ v1_realset1 ),
inference(simp,[status(thm)],[7390]) ).
thf(9227,plain,
~ ( sk592 @ v1_realset1 ),
inference(cnfConj,[status(thm)],[9225]) ).
thf(23087,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_realset1 )
!= ( sk592 @ v1_realset1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7391,9227]) ).
thf(23088,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
!= ( sk592 @ v1_realset1 ) ),
inference(simp,[status(thm)],[23087]) ).
thf(23095,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk592 ),
inference(simp,[status(thm)],[23088]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_relat_1) ).
thf(5718,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(104,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(2230,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(2231,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(cnf,[status(esa)],[2230]) ).
thf(947,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_orders_1) ).
thf(6162,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1525,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(9351,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(6495,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3858,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(9251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(6106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1576,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(9590,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_sysrel @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A = B )
& ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_sysrel) ).
thf(2381,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_sysrel @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A = B )
& ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(718,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( ( ( B @ k6_finseq_1 @ ( E @ ( D @ k3_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) )
& ( ( F @ ( A @ k6_finseq_1 @ ( D @ k3_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_finseq_2) ).
thf(5069,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( ( ( B @ k6_finseq_1 @ ( E @ ( D @ k3_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) )
& ( ( F @ ( A @ k6_finseq_1 @ ( D @ k3_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_mcart_1) ).
thf(7958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = I ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(273,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2908,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_relat_1) ).
thf(5842,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1745,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski) ).
thf(10671,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(10672,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_tarski ) )
& ( B @ ( A @ p1_s1_tarski ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ p1_s1_tarski ) )
& ( f1_s1_tarski @ ( C @ r2_hidden ) ) ) ) ) ),
inference(miniscope,[status(thm)],[10671]) ).
thf(10673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk749 @ ( B @ r2_hidden ) )
| ~ ( B @ ( C @ p1_s1_tarski ) )
| ~ ( f1_s1_tarski @ ( C @ r2_hidden ) )
| ~ sk745 )
& ( ( A @ ( A @ sk750 @ p1_s1_tarski ) )
| ~ ( sk749 @ ( A @ r2_hidden ) )
| ~ sk745 )
& ( ( f1_s1_tarski @ ( A @ sk750 @ r2_hidden ) )
| ~ ( sk749 @ ( A @ r2_hidden ) )
| ~ sk745 )
& ( sk745
| ( sk747 != sk748 ) )
& ( sk745
| ( sk748 @ ( sk746 @ p1_s1_tarski ) ) )
& ( sk745
| ( sk747 @ ( sk746 @ p1_s1_tarski ) ) ) ),
inference(cnf,[status(esa)],[10672]) ).
thf(10679,plain,
( sk745
| ( sk748 @ ( sk746 @ p1_s1_tarski ) ) ),
inference(cnfConj,[status(thm)],[10673]) ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_5 @ v1_funct_1 )
& ( A @ k3_funct_5 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_5) ).
thf(1806,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_5 @ v1_funct_1 )
& ( A @ k3_funct_5 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1807,plain,
! [A: $i] :
( ( ( A @ k3_funct_5 @ v1_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ k3_funct_5 @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1806]) ).
thf(1808,plain,
! [A: $i] :
( ( A @ k3_funct_5 @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1807]) ).
thf(1534,axiom,
! [A: $i] : ( A @ ( A @ k3_pua2mss1 @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(9383,plain,
! [A: $i] : ( A @ ( A @ k3_pua2mss1 @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(1549,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(9456,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1607,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(9761,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(9762,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk649 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[9761]) ).
thf(9764,plain,
! [A: $i] : ( A @ sk649 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[9762]) ).
thf(24012,plain,
! [B: $i,A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k13_finseq_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,6422]) ).
thf(24013,plain,
! [B: $i,A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k13_finseq_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24012]) ).
thf(24037,plain,
! [B: $i,A: $i] :
( ( A @ sk649 )
!= ( B @ k13_finseq_1 ) ),
inference(simp,[status(thm)],[24013]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_domain_1) ).
thf(6813,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k10_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = I ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_sysrel) ).
thf(4391,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(2953,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(2590,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(6458,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_domain_1) ).
thf(6441,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k11_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = J ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(5173,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1588,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(9624,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(9625,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[9624]) ).
thf(7934,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[7932]) ).
thf(7936,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(simp,[status(thm)],[7934]) ).
thf(23454,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( k1_xboole_0 @ k1_zfmisc_1 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[9625,7936]) ).
thf(23455,plain,
k1_xboole_0 @ k1_zfmisc_1 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[23454:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
thf(2671,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(7198,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(4711,plain,
sk149 @ v2_funct_1,
inference(cnfConj,[status(thm)],[4706]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(6830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k4_relat_1 @ v1_relat_1 )
& ( A @ k4_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(1971,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k4_relat_1 @ v1_relat_1 )
& ( A @ k4_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1572,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(9572,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(7516,plain,
sk378 @ v2_funct_1,
inference(cnfConj,[status(thm)],[7512]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1785,plain,
~ ! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1786,plain,
! [A: $i] :
( ( ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
!= k1_xboole_0 )
| sk3 )
& ( ( A = k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 )
& ( ~ sk3
| ( sk4 != k1_xboole_0 ) )
& ( ~ sk3
| ( sk2 @ ( sk4 @ r2_hidden ) ) )
& ( ~ sk3
| ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( sk1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( sk2 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(1792,plain,
( ~ sk3
| ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
= k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(1793,plain,
( ~ sk3
| ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1792]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_partfun1) ).
thf(4614,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1442,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
thf(8928,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_funct_1) ).
thf(4973,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(5348,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(5383,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1716,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(10463,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(1751,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(10694,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( A @ ( B @ k7_relat_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_relat_1) ).
thf(5614,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( A @ ( B @ k7_relat_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1620,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(9818,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1791,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(1795,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1791]) ).
thf(11052,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,8244]) ).
thf(11053,plain,
( ( sk470 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11052]) ).
thf(11058,plain,
sk470 != k1_xboole_0,
inference(simp,[status(thm)],[11053]) ).
thf(11879,plain,
! [A: $i] :
( ( A != sk470 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11058]) ).
thf(11880,plain,
! [A: $i] :
( ( A != sk470 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11879]) ).
thf(11881,plain,
( ~ ( sk2 @ ( sk470 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[11880:[bind(A,$thf( sk470 ))]]) ).
thf(1344,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(8366,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(1482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(9135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1003,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(6480,plain,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(6295,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1247,axiom,
~ ( k4_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_numbers) ).
thf(7813,plain,
~ ( k4_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(572,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(4403,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = F ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_mcart_1) ).
thf(6939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = F ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( A @ ( A @ r1_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(4011,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( A @ ( A @ r1_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1776,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(10881,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = H ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_mcart_1) ).
thf(6634,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = H ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1774,axiom,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1) ).
thf(10846,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) ) )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(10847,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relat_1 ) )
& ( f2_s1_relat_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_relat_1 ) ),
inference(miniscope,[status(thm)],[10846]) ).
thf(10848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk777 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
| ~ ( D @ ( C @ p1_s1_relat_1 ) )
| ~ ( f2_s1_relat_1 @ ( D @ r2_hidden ) )
| ~ ( f1_s1_relat_1 @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ p1_s1_relat_1 ) )
| ~ ( sk777 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f2_s1_relat_1 @ ( B @ r2_hidden ) )
| ~ ( sk777 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f1_s1_relat_1 @ ( A @ r2_hidden ) )
| ~ ( sk777 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( sk777 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[10847]) ).
thf(10850,plain,
sk777 @ v1_relat_1,
inference(cnfConj,[status(thm)],[10848]) ).
thf(25277,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10850,1899]) ).
thf(25278,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25277]) ).
thf(25279,plain,
sk777 @ k1_relat_1 @ ( sk777 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25278:[bind(A,$thf( sk777 ))]]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_msualg_1) ).
thf(3895,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1410,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_realset1) ).
thf(8752,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(301,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(3017,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_partfun1) ).
thf(4543,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1788,plain,
( ~ sk3
| ( sk2 @ ( sk4 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(727,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_funcop_1 ) ) @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ ( D @ k5_relat_1 ) @ k3_funcop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(5120,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_funcop_1 ) ) @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ ( D @ k5_relat_1 ) @ k3_funcop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1217,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(7646,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(7647,plain,
( ( sk397 @ v1_relat_1 )
& ( sk397 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7646]) ).
thf(7648,plain,
sk397 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[7647]) ).
thf(15592,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,7933]) ).
thf(15593,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15592]) ).
thf(15598,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk397 ),
inference(simp,[status(thm)],[15593]) ).
thf(24884,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk397 ) ),
inference(paramod_ordered,[status(thm)],[9625,15598]) ).
thf(24885,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk397 ),
inference(pattern_uni,[status(thm)],[24884:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(971,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(6277,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(6278,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[6277]) ).
thf(1767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).
thf(10775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(1718,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(10484,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(1413,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(8765,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(517,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) )
& ( ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_sysrel) ).
thf(4090,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) )
& ( ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1563,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_2_domain_1 ) ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_domain_1) ).
thf(9526,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_2_domain_1 ) ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(6505,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(382,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(3429,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(5565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(989,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(6401,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1712,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B @ v1_realset1 )
& ? [C: $i] :
( ? [D: $i] :
( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) )
& ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
& ~ ( B @ v1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_realset1) ).
thf(10433,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B @ v1_realset1 )
& ? [C: $i] :
( ? [D: $i] :
( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) )
& ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
& ~ ( B @ v1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(800,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(5473,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(5474,plain,
( ( sk180 @ v1_funct_1 )
& ( sk180 @ v3_relat_1 )
& ( sk180 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[5473]) ).
thf(5475,plain,
sk180 @ v1_relat_1,
inference(cnfConj,[status(thm)],[5474]) ).
thf(25309,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5475,1899]) ).
thf(25310,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25309]) ).
thf(25311,plain,
sk180 @ k1_relat_1 @ ( sk180 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25310:[bind(A,$thf( sk180 ))]]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k7_relat_1 ) )
= ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_relat_1) ).
thf(4739,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k7_relat_1 ) )
= ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1301,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(8145,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(8146,plain,
( ( sk455 @ v1_finseq_1 )
& ( sk455 @ v1_finset_1 )
& ( sk455 @ v1_funct_1 )
& ( sk455 @ v1_relat_1 )
& ~ ( sk455 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[8145]) ).
thf(8150,plain,
sk455 @ v1_relat_1,
inference(cnfConj,[status(thm)],[8146]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(7697,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1191,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(7495,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(7496,plain,
( ( sk376 @ v1_finset_1 )
& ~ ( sk376 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7495]) ).
thf(7497,plain,
~ ( sk376 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7496]) ).
thf(11022,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,7497]) ).
thf(11023,plain,
( ( sk376 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11022]) ).
thf(11029,plain,
sk376 != k1_xboole_0,
inference(simp,[status(thm)],[11023]) ).
thf(891,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( C @ k4_card_3 @ ( B @ r2_hidden ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) )
& ( A @ k3_tarski @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pua2mss1) ).
thf(5906,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( C @ k4_card_3 @ ( B @ r2_hidden ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) )
& ( A @ k3_tarski @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(299,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(3000,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(3001,plain,
( ( sk44 @ v1_funct_1 )
& ( sk44 @ v2_relat_1 )
& ( sk44 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3000]) ).
thf(3004,plain,
sk44 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3001]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(6675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1766,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_setfam_1 ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_setfam_1) ).
thf(10772,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_setfam_1 ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_1) ).
thf(3648,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1453,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(8981,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(6127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(15582,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,7933]) ).
thf(15583,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15582]) ).
thf(15600,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk384 ),
inference(simp,[status(thm)],[15583]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_partfun1) ).
thf(1867,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4220,plain,
sk119 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4217]) ).
thf(1503,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_card_1) ).
thf(9261,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(153,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2435,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(2436,plain,
( ( sk27 @ v1_xboole_0 )
& ( sk27 @ v2_funct_1 )
& ( sk27 @ v1_funct_1 )
& ( sk27 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2435]) ).
thf(2440,plain,
sk27 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2436]) ).
thf(15259,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,6422]) ).
thf(15260,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15259]) ).
thf(15282,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk27 ),
inference(simp,[status(thm)],[15260]) ).
thf(386,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3446,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(54,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(1999,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1121,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(7096,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1391,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(8667,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(1365,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(8490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(1571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(9565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(1756,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(10715,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(1190,axiom,
( ! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ ( A @ p1_s5_funct_2 ) ) )
& ( f3_s5_funct_2 @ ( C @ r2_hidden ) ) )
& ( f2_s5_funct_2 @ ( B @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s5_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s5_funct_2 ) ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s5_funct_2) ).
thf(7484,plain,
( ! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ ( A @ p1_s5_funct_2 ) ) )
& ( f3_s5_funct_2 @ ( C @ r2_hidden ) ) )
& ( f2_s5_funct_2 @ ( B @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s5_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s5_funct_2 ) ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k1_setfam_1 )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_setfam_1) ).
thf(6416,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k1_setfam_1 )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
thf(1870,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) )
| ~ ( B @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1870]) ).
thf(1872,plain,
! [B: $i,A: $i] :
( ~ ( B @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ),
inference(lifteq,[status(thm)],[1871]) ).
thf(3616,plain,
k1_xboole_0 @ v1_finset_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(6515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(4279,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1631,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_subset_1) ).
thf(9855,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(10938,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,7497]) ).
thf(10939,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10938]) ).
thf(10940,plain,
sk376 != sk27,
inference(simp,[status(thm)],[10939]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
<=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_2) ).
thf(2476,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) )
& ( ( D @ ( C @ r1_partfun1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(7147,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k5_funct_5 @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_5) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k5_funct_5 @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(3826,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(6241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k2_relat_1 )
= ( A @ k6_relat_1 @ k2_relat_1 @ ( B @ k2_relat_1 @ k4_xboole_0 ) ) ) )
& ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k1_relat_1 )
= ( A @ k6_relat_1 @ k1_relat_1 @ ( B @ k1_relat_1 @ k4_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_sysrel) ).
thf(3414,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k2_relat_1 )
= ( A @ k6_relat_1 @ k2_relat_1 @ ( B @ k2_relat_1 @ k4_xboole_0 ) ) ) )
& ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k1_relat_1 )
= ( A @ k6_relat_1 @ k1_relat_1 @ ( B @ k1_relat_1 @ k4_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(4294,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_mcart_1) ).
thf(10726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pboole) ).
thf(6117,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ r2_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1386,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_subset_1 )
= ( A @ a_1_1_domain_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_domain_1) ).
thf(8650,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_subset_1 )
= ( A @ a_1_1_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(4435,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(8201,plain,
! [A: $i] :
( ( ( ( A @ ( sk462 @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s4_funct_2 ) )
| ~ ( f1_s4_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk462 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk462 @ v1_funct_2 ) ) )
& ( sk462 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[8200]) ).
thf(8204,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk462 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[8201]) ).
thf(1508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_domain_1) ).
thf(9278,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_partfun1) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1833]) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1834]) ).
thf(133,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 )
= ( A @ k4_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(2348,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 )
= ( A @ k4_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1379,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_finseq_1 @ ( D @ ( E @ k5_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_finseq_2) ).
thf(8578,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_finseq_1 @ ( D @ ( E @ k5_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(8671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(4198,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(9396,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_sysrel) ).
thf(2516,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(249,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2814,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(2815,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2814]) ).
thf(2817,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2815]) ).
thf(2819,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2817]) ).
thf(1701,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ( ( A @ k3_pua2mss1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_relset_2) ).
thf(10336,plain,
! [A: $i] :
( ( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k3_pua2mss1 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(6570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_1) ).
thf(2972,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(3634,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(6251,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2432,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
thf(3994,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_partfun1) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(165,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ ( B @ k4_funcop_1 ) ) )
= ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( A @ ( B @ k3_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(2491,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ ( B @ k4_funcop_1 ) ) )
= ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( A @ ( B @ k3_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1513,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(9292,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(1295,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(8086,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(24006,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk561 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,8985]) ).
thf(24007,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk561 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24006]) ).
thf(24047,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk561 ),
inference(simp,[status(thm)],[24007]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(2763,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(7814,plain,
~ ( k4_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[7813]) ).
thf(24002,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,7814]) ).
thf(24003,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24002]) ).
thf(24041,plain,
! [A: $i] :
( ( A @ sk649 )
!= k4_numbers ),
inference(simp,[status(thm)],[24003]) ).
thf(1334,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(8325,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(1781,axiom,
! [A: $i] :
( ( a_0_5_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_5_domain_1) ).
thf(10908,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_5_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_5_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_relat_1) ).
thf(5123,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(561,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k3_pua2mss1 )
= ( A @ a_1_0_pua2mss1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pua2mss1) ).
thf(4371,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k3_pua2mss1 )
= ( A @ a_1_0_pua2mss1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_relat_1) ).
thf(4079,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(23075,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( k1_xboole_0 @ k1_zfmisc_1 @ v1_realset1 ) ),
inference(paramod_ordered,[status(thm)],[9625,7391]) ).
thf(23076,plain,
k1_xboole_0 @ k1_zfmisc_1 @ v1_realset1,
inference(pattern_uni,[status(thm)],[23075:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(23118,plain,
( ( ( k1_xboole_0 @ k1_zfmisc_1 @ v1_realset1 )
!= ( sk592 @ v1_realset1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23076,9227]) ).
thf(23119,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ v1_realset1 )
!= ( sk592 @ v1_realset1 ) ),
inference(simp,[status(thm)],[23118]) ).
thf(23130,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk592 ),
inference(simp,[status(thm)],[23119]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(4266,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1192,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
<=> ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_realset1) ).
thf(7499,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ m4_realset1 ) ) )
& ( ( A @ ( B @ m4_realset1 ) )
=> ? [C: $i] :
( ( B
= ( C @ k1_tarski ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k4_relat_1 )
= ( A @ k4_relat_1 @ ( B @ k4_relat_1 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_relat_1) ).
thf(2020,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k4_relat_1 )
= ( A @ k4_relat_1 @ ( B @ k4_relat_1 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(7136,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(4679,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1090,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(6951,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(6952,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[6951]) ).
thf(6953,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[6952]) ).
thf(15290,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,6953]) ).
thf(15291,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15290]) ).
thf(15318,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk595 ),
inference(simp,[status(thm)],[15291]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B
= ( C @ ( A @ k8_relat_1 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
thf(3088,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( B
= ( C @ ( A @ k8_relat_1 ) ) ) )
& ( ( B
= ( C @ ( A @ k8_relat_1 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(455,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k1_card_1 @ r1_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_card_1) ).
thf(3777,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k1_card_1 @ r1_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(5476,plain,
sk180 @ v3_relat_1,
inference(cnfConj,[status(thm)],[5474]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_2) ).
thf(6583,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_1) ).
thf(3308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_partfun1 ) ) )
= ( B @ ( A @ ( C @ k8_relat_1 ) @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_partfun1) ).
thf(1935,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_partfun1 ) ) )
= ( B @ ( A @ ( C @ k8_relat_1 ) @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(858,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(5723,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1433,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finset_1) ).
thf(8866,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(3809,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(2173,plain,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(8025,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = G ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_mcart_1) ).
thf(9148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = G ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(4963,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k7_relat_1 ) @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_relat_1) ).
thf(2825,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k7_relat_1 ) @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1461,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_orders_1) ).
thf(9013,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(6291,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_pboole) ).
thf(7918,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(615,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B
= ( A @ k1_pboole ) )
& ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_pboole) ).
thf(4610,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B
= ( A @ k1_pboole ) )
& ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(2531,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_mcart_1) ).
thf(6182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(416,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v3_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pboole) ).
thf(3592,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v3_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(3593,plain,
! [A: $i] :
( ( A @ sk82 @ v1_funct_1 )
& ( A @ sk82 @ v3_relat_1 )
& ( A @ sk82 @ v1_relat_1 )
& ( A @ ( A @ sk82 @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[3592]) ).
thf(3597,plain,
! [A: $i] : ( A @ sk82 @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[3593]) ).
thf(7987,plain,
~ ( sk431 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7986]) ).
thf(10980,plain,
! [A: $i] :
( ( A != sk431 )
| ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,7987]) ).
thf(10981,plain,
( ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( sk431 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[10980:[bind(A,$thf( sk431 ))]]) ).
thf(11249,plain,
( ~ $true
| ~ ( sk2 @ ( sk431 @ r2_hidden ) )
| sk3 ),
inference(rewrite,[status(thm)],[10981,3611]) ).
thf(11250,plain,
( ~ ( sk2 @ ( sk431 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11249]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(7311,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1736,axiom,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_5) ).
thf(10633,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(1731,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(10584,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(1460,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(9009,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(9010,plain,
( ( sk567 @ v1_funct_1 )
& ( sk567 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[9009]) ).
thf(9011,plain,
sk567 @ v1_relat_1,
inference(cnfConj,[status(thm)],[9010]) ).
thf(25330,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9011,1899]) ).
thf(25331,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25330]) ).
thf(25332,plain,
sk567 @ k1_relat_1 @ ( sk567 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25331:[bind(A,$thf( sk567 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
<=> ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_partfun1) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( A
= ( D @ ( C @ k2_xboole_0 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ r1_tarski ) ) )
=> ( E
= ( D @ ( E @ k7_relat_1 ) @ ( C @ ( E @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_sysrel) ).
thf(5533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( A
= ( D @ ( C @ k2_xboole_0 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ r1_tarski ) ) )
=> ( E
= ( D @ ( E @ k7_relat_1 ) @ ( C @ ( E @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(4386,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(6892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(6538,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(3689,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(3612,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_finseq_1) ).
thf(1812,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ m2_finseq_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) )
=> ( B
= ( A @ k13_finseq_1 ) ) )
& ( ( B
= ( A @ k13_finseq_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m2_finseq_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1813,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) )
=> ( B
= ( A @ k13_finseq_1 ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1812]) ).
thf(1814,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k13_finseq_1 ) )
| ~ ( F @ ( E @ ( F @ sk6 ) @ r2_hidden ) )
| ~ ( E @ ( E @ ( F @ sk5 ) @ m2_finseq_1 ) ) )
& ( ( F
= ( E @ k13_finseq_1 ) )
| ( E @ ( E @ ( F @ sk6 ) @ m2_finseq_1 ) )
| ~ ( E @ ( E @ ( F @ sk5 ) @ m2_finseq_1 ) ) )
& ( ( F
= ( E @ k13_finseq_1 ) )
| ~ ( F @ ( E @ ( F @ sk6 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk5 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k13_finseq_1 ) )
| ( E @ ( E @ ( F @ sk6 ) @ m2_finseq_1 ) )
| ( F @ ( E @ ( F @ sk5 ) @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
| ~ ( A @ ( D @ m2_finseq_1 ) )
| ( B
!= ( A @ k13_finseq_1 ) ) )
& ( ( A @ ( C @ m2_finseq_1 ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k13_finseq_1 ) ) ) ),
inference(cnf,[status(esa)],[1813]) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ~ ( A @ ( C @ m2_finseq_1 ) )
| ( B
!= ( A @ k13_finseq_1 ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ~ ( A @ ( C @ m2_finseq_1 ) )
| ( B
!= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1819]) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( A @ k13_finseq_1 @ ( B @ r2_hidden ) )
| ~ ( A @ ( B @ m2_finseq_1 ) ) ),
inference(simp,[status(thm)],[1825]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) )
= ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_pboole) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pboole ) ) )
= ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_mcart_1) ).
thf(5279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( E
!= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1306,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_2) ).
thf(8178,plain,
! [A: $i,B: $i] :
( ( ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_sysrel) ).
thf(5553,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_relat_1) ).
thf(3204,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(5953,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1779,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(10903,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(9271,plain,
sk594 @ v1_relat_1,
inference(cnfConj,[status(thm)],[9269]) ).
thf(25365,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9271,1899]) ).
thf(25366,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25365]) ).
thf(25367,plain,
sk594 @ k1_relat_1 @ ( sk594 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25366:[bind(A,$thf( sk594 ))]]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( B @ k7_relat_1 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funct_1) ).
thf(3221,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( B @ k7_relat_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1488,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_mcart_1) ).
thf(9172,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1368,axiom,
( ! [A: $i] :
( ( f1_s7_funct_2 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ p1_s7_funct_2 ) ) )
& ( f3_s7_funct_2 @ ( C @ m1_subset_1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s7_funct_2 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s7_funct_2 ) ) ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_funct_2) ).
thf(8498,plain,
( ! [A: $i] :
( ( f1_s7_funct_2 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ p1_s7_funct_2 ) ) )
& ( f3_s7_funct_2 @ ( C @ m1_subset_1 ) ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s7_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s7_funct_2 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s7_funct_2 ) ) ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(8499,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ k4_tarski ) @ ( sk498 @ k1_funct_1 ) @ ( C @ ( B @ p1_s7_funct_2 ) ) )
| ~ ( f2_s7_funct_2 @ ( C @ m1_subset_1 ) )
| ~ ( f1_s7_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk495 )
& ( ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( sk498 @ m2_relset_1 ) ) )
| ~ sk495 )
& ( ( f3_s7_funct_2 @ ( f2_s7_funct_2 @ ( f1_s7_funct_2 @ k2_zfmisc_1 ) @ ( sk498 @ v1_funct_2 ) ) )
| ~ sk495 )
& ( ( sk498 @ v1_funct_1 )
| ~ sk495 )
& ( sk495
| ~ ( A @ ( sk497 @ ( sk496 @ p1_s7_funct_2 ) ) )
| ~ ( f3_s7_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk495
| ( f2_s7_funct_2 @ ( sk497 @ m1_subset_1 ) ) )
& ( sk495
| ( f1_s7_funct_2 @ ( sk496 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[8498]) ).
thf(8500,plain,
( sk495
| ( f2_s7_funct_2 @ ( sk497 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[8499]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(7914,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1696,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_card_1) ).
thf(10305,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(11650,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,8985]) ).
thf(11651,plain,
( ( sk561 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11650]) ).
thf(11667,plain,
sk561 != sk397,
inference(simp,[status(thm)],[11651]) ).
thf(1475,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(9099,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(2735,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k4_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_sysrel) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k4_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(4422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1732,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(10587,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(7825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1790,plain,
( ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
!= k1_xboole_0 )
| sk3 ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(1796,plain,
( sk3
| ( ( sk2 @ ( sk1 @ k5_setfam_1 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1790]) ).
thf(10995,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ k5_setfam_1 ) ) )
| sk3
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,1796]) ).
thf(10996,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ k5_setfam_1 ) ) )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[10995]) ).
thf(10997,plain,
( ~ ( sk2 @ ( sk2 @ ( sk1 @ k5_setfam_1 ) @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[10996:[bind(A,$thf( sk2 @ ( sk1 @ k5_setfam_1 ) ))]]) ).
thf(1296,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(8089,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1021,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(6547,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1569,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k1_card_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_card_1) ).
thf(9561,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k1_card_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_partfun1) ).
thf(3342,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(6095,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1657,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( B @ ( C @ ( A @ k1_relset_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).
thf(10053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( B @ ( C @ ( A @ k1_relset_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(1342,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(8357,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(397,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ v2_funct_1 )
& ( D @ k2_relat_1 @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ m2_pua2mss1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pua2mss1) ).
thf(3495,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ v2_funct_1 )
& ( D @ k2_relat_1 @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ m2_pua2mss1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(650,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( D @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(4761,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( D @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
thf(7528,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1165,axiom,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_int_1) ).
thf(7349,plain,
! [A: $i] :
( ( k4_numbers @ ( A @ m1_subset_1 ) )
=> ( A @ v1_int_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(745,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(5188,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(460,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3821,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(25,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(1906,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1907,plain,
! [A: $i] : ( A @ ( A @ sk9 @ m2_finseq_1 ) ),
inference(cnf,[status(esa)],[1906]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
<=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(6066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(10382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(3617,plain,
k1_xboole_0 @ v3_relat_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(1685,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(10221,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(2437,plain,
sk27 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2436]) ).
thf(25628,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2437,1900]) ).
thf(25629,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25628]) ).
thf(25630,plain,
sk27 @ k2_relat_1 @ ( sk27 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25629:[bind(A,$thf( sk27 ))]]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(7541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3485,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pboole) ).
thf(4778,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_mcart_1) ).
thf(9360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(4275,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(4349,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(2185,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_domain_1) ).
thf(6713,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k8_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1651,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(10010,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(5130,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(936,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(6113,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ ( C @ k1_relat_1 @ k6_relat_1 @ ( C @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k2_relat_1 @ k4_xboole_0 ) @ ( B @ r2_hidden ) ) )
| ( A = B ) ) )
& ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ k1_relat_1 @ k6_relat_1 @ ( C @ k4_xboole_0 ) @ ( C @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_sysrel) ).
thf(3845,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ ( C @ k1_relat_1 @ k6_relat_1 @ ( C @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k2_relat_1 @ k4_xboole_0 ) @ ( B @ r2_hidden ) ) )
| ( A = B ) ) )
& ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ k1_relat_1 @ k6_relat_1 @ ( C @ k4_xboole_0 ) @ ( C @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2488,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1816,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
| ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1831,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1816]) ).
thf(1832,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(simp,[status(thm)],[1831]) ).
thf(12586,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,3407]) ).
thf(12587,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12586]) ).
thf(12606,plain,
sk595 != sk70,
inference(simp,[status(thm)],[12587]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(5712,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1013,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(6519,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1497,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(9228,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(9229,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[9228]) ).
thf(9230,plain,
~ ( sk593 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[9229]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(7000,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
= ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(8147,plain,
~ ( sk455 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[8146]) ).
thf(11046,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,8147]) ).
thf(11047,plain,
( ( sk455 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11046]) ).
thf(11051,plain,
sk455 != sk27,
inference(simp,[status(thm)],[11047]) ).
thf(852,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( C @ ( B @ ( A @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(5706,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( C @ ( B @ ( A @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(700,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(4984,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(469,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(3855,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(24020,plain,
! [B: $i,A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,7933]) ).
thf(24021,plain,
! [B: $i,A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24020]) ).
thf(24045,plain,
! [B: $i,A: $i] :
( ( A @ sk649 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[24021]) ).
thf(30909,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( B @ k1_tarski ) )
| ( ( A @ sk649 )
!= ( k1_xboole_0 @ k1_zfmisc_1 ) ) ),
inference(paramod_ordered,[status(thm)],[9625,24045]) ).
thf(30910,plain,
! [A: $i] :
( ( A @ sk649 )
!= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(pattern_uni,[status(thm)],[30909:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(10464,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[10463]) ).
thf(10465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk721 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[10464]) ).
thf(10466,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[10465]) ).
thf(10468,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[10466]) ).
thf(10469,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[10468]) ).
thf(1436,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) )
=> ( B
= ( A @ k1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pboole) ).
thf(8880,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) )
=> ( B
= ( A @ k1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2713,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1583,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(9612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(1626,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(9843,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1682,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(10206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(1300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_mcart_1) ).
thf(8126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(3866,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_1) ).
thf(4008,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1609,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(9768,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(1415,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_domain_1) ).
thf(8770,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(7835,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(5744,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ m2_pua2mss1 ) )
<=> ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pua2mss1) ).
thf(1918,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) )
=> ( A @ ( B @ m2_pua2mss1 ) ) )
& ( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1919,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ m2_pua2mss1 ) )
| ~ ( B @ v2_funct_1 )
| ~ ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) )
& ( ( B @ v2_funct_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) )
& ( ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) )
| ~ ( A @ ( B @ m2_pua2mss1 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1918]) ).
thf(1922,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
| ~ ( B @ v2_funct_1 )
| ~ ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1919]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(6010,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(11630,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,7987]) ).
thf(11631,plain,
( ( sk431 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11630]) ).
thf(11641,plain,
sk431 != sk384,
inference(simp,[status(thm)],[11631]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finseq_2) ).
thf(1800,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_partfun1) ).
thf(8278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(1888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ~ ( D @ k1_relat_1 @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) )
& ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) )
& ( ( B @ ( A @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) )
& ( ( D @ k1_relat_1 @ ( A @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1887]) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ~ ( D @ k1_relat_1 @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1888]) ).
thf(1381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( B @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_mcart_1) ).
thf(8590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( B @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ k7_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funcop_1) ).
thf(2403,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ k7_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1554,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
<=> ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_pboole) ).
thf(9480,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r4_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ! [D: $i] :
~ ( ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( A @ k1_funct_2 ) @ ( B @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( A @ k1_funct_2 ) @ ( B @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k1_funct_2 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_funct_5) ).
thf(5521,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( A @ k1_funct_2 ) @ ( B @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( A @ k1_funct_2 ) @ ( B @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k1_funct_2 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k1_sysrel @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_sysrel) ).
thf(2049,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k1_sysrel @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(11493,plain,
( ( ( sk378 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,7497]) ).
thf(11494,plain,
( ( sk378 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11493]) ).
thf(11512,plain,
sk378 != sk376,
inference(simp,[status(thm)],[11494]) ).
thf(11485,plain,
( ( ( sk378 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,7814]) ).
thf(11486,plain,
( ( sk378 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11485]) ).
thf(11510,plain,
sk378 != k4_numbers,
inference(simp,[status(thm)],[11486]) ).
thf(1890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1888]) ).
thf(747,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(5193,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( I @ r2_hidden ) )
=> ( ( H @ ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( G @ ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( F @ ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( E @ ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_mcart_1) ).
thf(5604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( I @ r2_hidden ) )
=> ( ( H @ ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( G @ ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( F @ ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ r2_hidden ) )
& ( E @ ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_relat_1) ).
thf(4492,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(619,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_relat_1) ).
thf(4622,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1383,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(8600,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(7857,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(2929,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(629,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_partfun1) ).
thf(4675,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(391,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(3470,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_pboole) ).
thf(3312,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(11126,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,9226]) ).
thf(11127,plain,
( ( sk592 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11126]) ).
thf(11132,plain,
sk592 != k1_xboole_0,
inference(simp,[status(thm)],[11127]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(5942,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(7649,plain,
sk397 @ v1_relat_1,
inference(cnfConj,[status(thm)],[7647]) ).
thf(26023,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7649,1901]) ).
thf(26024,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26023]) ).
thf(26025,plain,
sk397 @ k1_relat_1 @ ( sk397 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26024:[bind(A,$thf( sk397 ))]]) ).
thf(623,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4632,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(3835,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(9314,plain,
sk595 @ v1_relat_1,
inference(cnfConj,[status(thm)],[9313]) ).
thf(25368,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9314,1899]) ).
thf(25369,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25368]) ).
thf(25370,plain,
sk595 @ k1_relat_1 @ ( sk595 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25369:[bind(A,$thf( sk595 ))]]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k1_sysrel @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_sysrel) ).
thf(2301,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel @ k1_relat_1 )
= ( A @ k1_sysrel @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1752,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ a_2_0_relset_2 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
thf(10702,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ a_2_0_relset_2 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k2_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_2) ).
thf(4383,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k2_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(662,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4793,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1291,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_card_1) ).
thf(8037,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(1215,axiom,
! [A: $i] :
~ ( A @ k13_finseq_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finseq_1) ).
thf(7633,plain,
! [A: $i] :
~ ( A @ k13_finseq_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(654,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( B @ ( C @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ k4_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(4771,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( B @ ( C @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ k4_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1746,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(10682,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1303,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(8161,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(7112,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pboole) ).
thf(7733,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1144,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(7226,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1323,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(8291,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(8292,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[8291]) ).
thf(8293,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[8292]) ).
thf(24010,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk592 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,9226]) ).
thf(24011,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk592 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24010]) ).
thf(24040,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk592 ),
inference(simp,[status(thm)],[24011]) ).
thf(848,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(5682,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(383,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_relat_1 )
= B )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_relat_1 )
= A ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_sysrel) ).
thf(3431,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_relat_1 )
= B )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_relat_1 )
= A ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(7104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1157,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).
thf(7317,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_2) ).
thf(2777,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1522,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(9319,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(1023,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_card_1) ).
thf(6562,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( ( A != B )
& ( B @ ( A @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(966,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(6259,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) )
=> ( ( D @ ( C @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( D @ ( C @ k2_xboole_0 ) @ ( B @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t185_relat_1) ).
thf(2950,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) )
=> ( ( D @ ( C @ k2_xboole_0 ) @ ( A @ k7_relat_1 ) )
= ( D @ ( C @ k2_xboole_0 ) @ ( B @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_sysrel) ).
thf(4205,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1492,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(9204,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(1517,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(9304,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(1124,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(7107,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(3322,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1515,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(9298,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_relat_1) ).
thf(2616,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1577,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(9593,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(25651,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5475,1900]) ).
thf(25652,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25651]) ).
thf(25653,plain,
sk180 @ k2_relat_1 @ ( sk180 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25652:[bind(A,$thf( sk180 ))]]) ).
thf(1151,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(7273,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(887,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(5892,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1510,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(9283,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(4583,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1348,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(8379,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(4443,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_partfun1) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
| ~ ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1810]) ).
thf(78,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ m1_eqrel_1 ) )
=> ( A @ ( B @ ( A @ a_2_1_pua2mss1 ) @ m1_eqrel_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pua2mss1) ).
thf(2090,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ m1_eqrel_1 ) )
=> ( A @ ( B @ ( A @ a_2_1_pua2mss1 ) @ m1_eqrel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(5861,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(10623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(297,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_card_1) ).
thf(2994,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(2995,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(miniscope,[status(thm)],[2994]) ).
thf(2996,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(cnf,[status(esa)],[2995]) ).
thf(446,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_5) ).
thf(3724,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1908,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( C @ k2_funct_1 @ v1_funct_1 )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1908]) ).
thf(1911,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1909]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(709,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(5032,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(5033,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5032]) ).
thf(5034,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5033]) ).
thf(26880,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,5034]) ).
thf(26881,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26880]) ).
thf(26916,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk595 ),
inference(simp,[status(thm)],[26881]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= ( D @ ( C @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_1) ).
thf(4297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= ( D @ ( C @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_relat_1) ).
thf(2469,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(644,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(4733,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(329,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3163,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( A @ ( C @ k7_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_relat_1) ).
thf(5856,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( A @ ( C @ k7_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1782,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(10918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ r1_xboole_0 ) )
=> ( ~ ( H @ ( D @ r1_xboole_0 ) )
& ~ ( G @ ( C @ r1_xboole_0 ) )
& ~ ( F @ ( B @ r1_xboole_0 ) )
& ~ ( E @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_mcart_1) ).
thf(6410,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ r1_xboole_0 ) )
=> ( ~ ( H @ ( D @ r1_xboole_0 ) )
& ~ ( G @ ( C @ r1_xboole_0 ) )
& ~ ( F @ ( B @ r1_xboole_0 ) )
& ~ ( E @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1417,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1) ).
thf(8783,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(8784,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(miniscope,[status(thm)],[8783]) ).
thf(8785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk534 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
| ~ ( D @ ( C @ p1_s1_funct_1 ) )
| ~ ( f1_s1_funct_1 @ ( C @ r2_hidden ) )
| ~ sk530 )
& ( ( B @ ( A @ p1_s1_funct_1 ) )
| ~ ( sk534 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
| ~ sk530 )
& ( ( f1_s1_funct_1 @ ( A @ r2_hidden ) )
| ~ ( sk534 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
| ~ sk530 )
& ( ( sk534 @ v1_funct_1 )
| ~ sk530 )
& ( ( sk534 @ v1_relat_1 )
| ~ sk530 )
& ( sk530
| ( sk532 != sk533 ) )
& ( sk530
| ( sk533 @ ( sk531 @ p1_s1_funct_1 ) ) )
& ( sk530
| ( sk532 @ ( sk531 @ p1_s1_funct_1 ) ) ) ),
inference(cnf,[status(esa)],[8784]) ).
thf(8791,plain,
( sk530
| ( sk532 @ ( sk531 @ p1_s1_funct_1 ) ) ),
inference(cnfConj,[status(thm)],[8785]) ).
thf(12581,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,7814]) ).
thf(12582,plain,
( ( sk595 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12581]) ).
thf(12610,plain,
sk595 != k4_numbers,
inference(simp,[status(thm)],[12582]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(5680,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3438,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( D @ v1_finseq_1 )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( ( D
= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
& ( ( F @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) )
=> ( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
& ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_finseq_2) ).
thf(1857,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( D @ v1_finseq_1 )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( ( D
= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
& ( ( F @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) )
=> ( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
& ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1858,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) )
| ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) )
| ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1857]) ).
thf(1860,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) )
| ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1858]) ).
thf(1863,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1860]) ).
thf(1864,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ m2_finseq_1 ) )
| ~ ( A @ ( E @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_finseq_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_funct_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
| ( ( E @ k3_finseq_1 )
!= ( F @ k3_finseq_1 ) ) ),
inference(simp,[status(thm)],[1863]) ).
thf(26892,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,5034]) ).
thf(26893,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26892]) ).
thf(26919,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26893]) ).
thf(1333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_1) ).
thf(8321,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(11194,plain,
( ( ( sk149 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,7814]) ).
thf(11195,plain,
( ( sk149 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11194]) ).
thf(11215,plain,
sk149 != k4_numbers,
inference(simp,[status(thm)],[11195]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(6176,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(1662,axiom,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relset_1) ).
thf(10085,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(4724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1827,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1820]) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(simp,[status(thm)],[1827]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_partfun1) ).
thf(1978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_pboole) ).
thf(5914,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
& ( B @ v2_relat_1 ) )
=> ( C @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1542,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(9415,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_pboole) ).
thf(5311,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B )
& ( ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_funct_2) ).
thf(2034,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B )
& ( ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(6559,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_sysrel) ).
thf(1960,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1314,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(8246,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(1208,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_funct_2) ).
thf(7581,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2335,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1412,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(8759,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(6157,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(2017,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1519,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(9309,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_partfun1) ).
thf(2058,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(4718,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1585,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(9616,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_mcart_1) ).
thf(6755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ k2_tarski ) @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(6498,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_setfam_1 ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_setfam_1) ).
thf(4924,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r2_setfam_1 ) ) )
& ( ( B @ ( A @ r2_setfam_1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1665,axiom,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_card_1) ).
thf(10106,plain,
( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_card_1 ) ) )
=> ( A @ p1_s2_card_1 ) ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(1524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(9347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1233,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(7722,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1666,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_subset_1) ).
thf(10113,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_relat_1) ).
thf(5572,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pboole) ).
thf(2508,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1635,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(9875,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(290,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k8_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_relat_1) ).
thf(2964,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k8_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(11192,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,9230]) ).
thf(11193,plain,
( ( sk593 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11192]) ).
thf(11218,plain,
sk593 != sk149,
inference(simp,[status(thm)],[11193]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_2) ).
thf(7036,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1039,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_pboole) ).
thf(6648,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) )
=> ( B @ v3_relat_1 ) )
& ( ( B @ v3_relat_1 )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_1) ).
thf(4033,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(2833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relset_2) ).
thf(3189,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2281,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_pua2mss1) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ( ( B @ v2_funct_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) )
& ( ( B @ v2_relat_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ) ),
inference(cnf,[status(esa)],[1893]) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ( B @ v2_funct_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ),
inference(cnfConj,[status(thm)],[1894]) ).
thf(843,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(5643,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(3712,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(9167,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(5370,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ k1_zfmisc_1 @ ( I @ m1_subset_1 ) )
& ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).
thf(10238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ k1_zfmisc_1 @ ( I @ m1_subset_1 ) )
& ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) )
=> ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( B @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1874]) ).
thf(1886,plain,
! [B: $i,A: $i] :
( ( B @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1880]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(7336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(864,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_1) ).
thf(5772,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(3036,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(4364,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(4087,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).
thf(10273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(432,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t188_relat_1) ).
thf(3676,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(874,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( ( A @ ( A @ k1_sysrel @ k2_relat_1 @ k8_relat_1 ) )
= ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ ( A @ k1_sysrel @ k1_relat_1 @ k8_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ) )
& ( ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_sysrel) ).
thf(5846,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( ( A @ ( A @ k1_sysrel @ k2_relat_1 @ k8_relat_1 ) )
= ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ ( A @ k1_sysrel @ k1_relat_1 @ k8_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ) )
& ( ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( ( A @ k1_sysrel @ k2_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k1_sysrel @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(5897,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = I ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_mcart_1) ).
thf(6772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = I ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(4825,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(601,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(4536,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(491,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(3955,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(346,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
thf(3243,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(247,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2809,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(10574,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(11483,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,9230]) ).
thf(11484,plain,
( ( sk593 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11483]) ).
thf(11505,plain,
sk593 != sk378,
inference(simp,[status(thm)],[11484]) ).
thf(1446,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(8939,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(4707,plain,
sk149 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[4706]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_pboole) ).
thf(4379,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1459,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(9007,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(15314,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,6953]) ).
thf(15315,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15314]) ).
thf(15321,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk397 ),
inference(simp,[status(thm)],[15315]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_relset_1) ).
thf(4285,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1643,axiom,
! [A: $i] :
( ( a_0_3_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_3_domain_1) ).
thf(9923,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_3_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_3_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p2_s10_domain_1 )
& ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(1226,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_2) ).
thf(7688,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ r2_hidden ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_pua2mss1) ).
thf(2392,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ r2_hidden ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1784,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k1_relset_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relset_2) ).
thf(10933,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k1_relset_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) )
& ( D @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_5) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) )
& ( D @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1506,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
<=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(9272,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(7460,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1289,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(8033,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
thf(2718,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_partfun1) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_partfun1) ).
thf(4082,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(509,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(4065,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(7408,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(6474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1749,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(10690,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(1352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(8421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_partfun1) ).
thf(3378,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(7952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(276,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
thf(2922,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(8508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1304,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(8170,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(10941,plain,
( ( ( sk27 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,7814]) ).
thf(10942,plain,
( ( sk27 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10941]) ).
thf(10943,plain,
sk27 != k4_numbers,
inference(simp,[status(thm)],[10942]) ).
thf(1523,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
<=> ( B
= ( A @ k1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(9340,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B
= ( A @ k1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(2574,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(493,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(3984,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(404,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(3531,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k5_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_relat_1) ).
thf(3186,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k5_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relset_2) ).
thf(7859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1674,axiom,
( ! [A: $i] :
~ ( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_pboole) ).
thf(10162,plain,
( ! [A: $i] :
~ ( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(10163,plain,
( ~ ? [A: $i] :
( ( ( A @ f2_s1_pboole )
= k1_xboole_0 )
& ( f1_s1_pboole @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_pboole @ ( B @ r2_hidden ) )
=> ( B @ f2_s1_pboole @ ( B @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( f1_s1_pboole @ ( A @ m1_pboole ) ) ) ),
inference(miniscope,[status(thm)],[10162]) ).
thf(10164,plain,
! [A: $i] :
( ( ( A @ f2_s1_pboole @ ( A @ ( sk690 @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( f1_s1_pboole @ ( A @ r2_hidden ) )
| ( ( sk689 @ f2_s1_pboole )
= k1_xboole_0 ) )
& ( ( f1_s1_pboole @ ( sk690 @ m1_pboole ) )
| ( ( sk689 @ f2_s1_pboole )
= k1_xboole_0 ) )
& ( ( A @ f2_s1_pboole @ ( A @ ( sk690 @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( f1_s1_pboole @ ( A @ r2_hidden ) )
| ( f1_s1_pboole @ ( sk689 @ r2_hidden ) ) )
& ( ( f1_s1_pboole @ ( sk690 @ m1_pboole ) )
| ( f1_s1_pboole @ ( sk689 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[10163]) ).
thf(10165,plain,
( ( f1_s1_pboole @ ( sk690 @ m1_pboole ) )
| ( f1_s1_pboole @ ( sk689 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[10164]) ).
thf(1775,axiom,
! [A: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( A @ m2_relset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( B @ m2_relset_1 ) ) )
=> ( ( ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) )
& ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_pua2mss1) ).
thf(10855,plain,
! [A: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( A @ m2_relset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_pua2mss1 @ ( f1_s2_pua2mss1 @ ( B @ m2_relset_1 ) ) )
=> ( ( ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ p1_s2_pua2mss1 ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) )
& ! [C: $i] :
( ( f1_s2_pua2mss1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s2_pua2mss1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ p1_s2_pua2mss1 ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ p1_s2_pua2mss1 ) ) ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(4853,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1604,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(9720,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(6760,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1597,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(9682,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(1771,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_subset_1) ).
thf(10811,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ k2_enumset1 ) ) ) @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(680,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_sysrel) ).
thf(4893,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(415,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(3587,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(3588,plain,
( ( sk81 @ v2_funct_1 )
& ( sk81 @ v1_funct_1 )
& ( sk81 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3587]) ).
thf(3591,plain,
sk81 @ v2_funct_1,
inference(cnfConj,[status(thm)],[3588]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7148,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[7147]) ).
thf(7149,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[7148]) ).
thf(28457,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,7149]) ).
thf(28458,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[28457]) ).
thf(28473,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk384 ),
inference(simp,[status(thm)],[28458]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( C @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_tarski ) @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_5) ).
thf(4753,plain,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( C @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_tarski ) @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_mcart_1) ).
thf(6020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = G ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_relat_1) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1721,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(10506,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(1424,axiom,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(8820,plain,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(8821,plain,
! [A: $i] :
( ( ( ( A @ ( sk540 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk538 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk540 @ m2_relset_1 ) ) )
| ~ sk538 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk540 @ v1_funct_2 ) ) )
| ~ sk538 )
& ( ( sk540 @ v1_funct_1 )
| ~ sk538 )
& ( sk538
| ~ ( f2_s13_funct_2 @ ( sk539 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk538
| ( f1_s13_funct_2 @ ( sk539 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[8820]) ).
thf(8827,plain,
( sk538
| ( f1_s13_funct_2 @ ( sk539 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[8821]) ).
thf(11660,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,8244]) ).
thf(11661,plain,
( ( sk470 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11660]) ).
thf(11672,plain,
sk470 != sk397,
inference(simp,[status(thm)],[11661]) ).
thf(1575,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_setfam_1) ).
thf(9588,plain,
! [A: $i] : ( A @ ( A @ r1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(1195,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(7518,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1914]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_mcart_1) ).
thf(7410,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(7005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(2232,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1428,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
= ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_mcart_1) ).
thf(8842,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
= ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_relat_1) ).
thf(5519,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1612,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(9773,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(9774,plain,
! [A: $i] :
( ( ( ( A @ ( sk650 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f7_s11_funct_2 ) )
| ( A = f4_s11_funct_2 )
| ( A = f3_s11_funct_2 )
| ~ ( f1_s11_funct_2 @ ( A @ m1_subset_1 ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( ( f4_s11_funct_2 @ ( sk650 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( ( f3_s11_funct_2 @ ( sk650 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( sk650 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
inference(cnf,[status(esa)],[9773]) ).
thf(9780,plain,
( ( sk650 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[9774]) ).
thf(9785,plain,
( ( sk650 @ v1_funct_1 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[9780]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(4100,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(2496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_pboole) ).
thf(3550,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
& ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(523,axiom,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k2_relat_1 )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(4172,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k2_relat_1 )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(25265,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7517,1899]) ).
thf(25266,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25265]) ).
thf(25267,plain,
sk378 @ k1_relat_1 @ ( sk378 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25266:[bind(A,$thf( sk378 ))]]) ).
thf(1489,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
thf(9175,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(25286,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2437,1899]) ).
thf(25287,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25286]) ).
thf(25288,plain,
sk27 @ k1_relat_1 @ ( sk27 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25287:[bind(A,$thf( sk27 ))]]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ~ ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(10345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(24032,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk455 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,8147]) ).
thf(24033,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk455 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24032]) ).
thf(24038,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk455 ),
inference(simp,[status(thm)],[24033]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).
thf(6122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(419,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v3_relat_1 )
<=> ( k1_xboole_0 @ k1_tarski @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_relat_1) ).
thf(3603,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ k1_tarski @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( A @ v3_relat_1 ) )
& ( ( A @ v3_relat_1 )
=> ( k1_xboole_0 @ k1_tarski @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1709,axiom,
? [A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ( B @ p1_s1_int_1 ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_int_1) ).
thf(10424,plain,
? [A: $i] :
( ! [B: $i] :
( ( B @ v1_int_1 )
=> ( ( ( B @ p1_s1_int_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_int_1 ) ) ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(10425,plain,
! [A: $i] :
( ( ( sk715 @ ( A @ r2_hidden ) )
| ~ ( A @ p1_s1_int_1 )
| ~ ( A @ v1_int_1 ) )
& ( ( A @ p1_s1_int_1 )
| ~ ( sk715 @ ( A @ r2_hidden ) )
| ~ ( A @ v1_int_1 ) )
& ( k4_numbers @ k1_zfmisc_1 @ ( sk715 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[10424]) ).
thf(10426,plain,
k4_numbers @ k1_zfmisc_1 @ ( sk715 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[10425]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(2969,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(25704,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9271,1900]) ).
thf(25705,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25704]) ).
thf(25706,plain,
sk594 @ k2_relat_1 @ ( sk594 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25705:[bind(A,$thf( sk594 ))]]) ).
thf(1815,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
| ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1815]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) @ m2_finseq_1 ) )
| ( B @ ( A @ ( B @ sk5 ) @ r2_hidden ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(simp,[status(thm)],[1823]) ).
thf(11210,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,8147]) ).
thf(11211,plain,
( ( sk455 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11210]) ).
thf(11212,plain,
sk455 != sk149,
inference(simp,[status(thm)],[11211]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(5206,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(8343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(147,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_partfun1) ).
thf(2409,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(4712,plain,
sk149 @ v1_finset_1,
inference(cnfConj,[status(thm)],[4706]) ).
thf(7989,plain,
sk431 @ v1_funct_1,
inference(cnfConj,[status(thm)],[7986]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relset_2) ).
thf(5670,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_2) ).
thf(2560,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1675,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(10171,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(1457,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(8994,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2541,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D
= ( C @ ( B @ ( A @ k9_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_2) ).
thf(9412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D
= ( C @ ( B @ ( A @ k9_funct_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_mcart_1) ).
thf(5002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(8476,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1253,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(7827,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k5_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_sysrel) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_pboole) ).
thf(6264,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) )
=> ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_funct_2) ).
thf(4878,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(5579,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1284,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(7994,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2133,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_funct_1) ).
thf(3022,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ? [I: $i] :
( ? [J: $i] :
( ~ ( ( ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k11_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k10_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k9_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k8_mcart_1 ) ) ) ) ) ) )
& ( I = J )
& ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( J @ m1_subset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) ) )
& ( H != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_mcart_1) ).
thf(5956,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ? [I: $i] :
( ? [J: $i] :
( ~ ( ( ( I @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k11_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k10_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k9_mcart_1 ) ) ) ) ) )
& ( ( I @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( J @ ( H @ ( G @ ( F @ ( E @ k8_mcart_1 ) ) ) ) ) ) )
& ( I = J )
& ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( J @ m1_subset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( I @ m1_subset_1 ) ) )
& ( H != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1773,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(10843,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(11200,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,9226]) ).
thf(11201,plain,
( ( sk592 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11200]) ).
thf(11217,plain,
sk592 != sk149,
inference(simp,[status(thm)],[11201]) ).
thf(1742,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(10657,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(1493,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ v3_ordinal1 ) ) )
=> ( A @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(9207,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ v3_ordinal1 ) ) )
=> ( A @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(25998,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7988,1901]) ).
thf(25999,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25998]) ).
thf(26000,plain,
sk431 @ k1_relat_1 @ ( sk431 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25999:[bind(A,$thf( sk431 ))]]) ).
thf(1384,axiom,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(8608,plain,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(451,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(3752,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(11612,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,9270]) ).
thf(11613,plain,
( ( sk594 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11612]) ).
thf(11634,plain,
sk594 != sk384,
inference(simp,[status(thm)],[11613]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3989,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(345,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(3239,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(8550,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1118,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s8_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s8_funct_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s8_funct_2 ) ) ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_funct_2) ).
thf(7082,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s8_funct_2 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s8_funct_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s8_funct_2 ) ) ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(7083,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( A @ k4_tarski ) @ ( sk328 @ k1_funct_1 ) )
= ( B @ ( A @ f4_s8_funct_2 ) ) )
| ~ ( f2_s8_funct_2 @ ( B @ m1_subset_1 ) )
| ~ ( f1_s8_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( sk328 @ m2_relset_1 ) ) )
& ( f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( sk328 @ v1_funct_2 ) ) )
& ( sk328 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[7082]) ).
thf(7084,plain,
sk328 @ v1_funct_1,
inference(cnfConj,[status(thm)],[7083]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(5470,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(12597,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk431 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,7987]) ).
thf(12598,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk431 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12597]) ).
thf(12608,plain,
sk595 != sk431,
inference(simp,[status(thm)],[12598]) ).
thf(720,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(5085,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_partfun1) ).
thf(2032,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(5507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(627,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(4661,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2528,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_finset_1) ).
thf(8878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ~ ( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_mcart_1) ).
thf(3207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ~ ( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_5) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(3339,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
thf(2015,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(5924,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(354,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(3286,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(15568,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,7933]) ).
thf(15569,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15568]) ).
thf(15595,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk595 ),
inference(simp,[status(thm)],[15569]) ).
thf(1409,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relset_1) ).
thf(8746,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(1920,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) )
| ~ ( A @ ( B @ m2_pua2mss1 ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1919]) ).
thf(612,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(4585,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(741,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
thf(5177,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1516,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(9301,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(1449,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(8964,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(10235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(4708,plain,
sk149 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4706]) ).
thf(25974,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4708,1901]) ).
thf(25975,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25974]) ).
thf(25976,plain,
sk149 @ k1_relat_1 @ ( sk149 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25975:[bind(A,$thf( sk149 ))]]) ).
thf(1504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(9264,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(1757,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(10721,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(330,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(3166,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B
= ( A @ ( C @ k7_relat_1 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
thf(2445,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) )
=> ( B
= ( A @ ( C @ k7_relat_1 ) ) ) )
& ( ( B
= ( A @ ( C @ k7_relat_1 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).
thf(7308,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(6646,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(2464,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_5) ).
thf(1938,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(238,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(2758,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(882,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k3_tarski @ r1_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal2) ).
thf(5879,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ ( A @ k3_tarski @ r1_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(10634,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[10633]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k4_relat_1 @ k9_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t163_relat_1) ).
thf(1837,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k4_relat_1 @ k9_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(422,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3618,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(6629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_card_1) ).
thf(5983,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k2_card_1 )
= ( B @ k2_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1720,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(10502,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3403,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k4_relat_1 @ k3_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_relat_1) ).
thf(1968,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k4_relat_1 @ k3_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1114,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_realset1) ).
thf(7063,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(1447,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(8942,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(923,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(6043,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1667,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(10116,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k4_relat_1 @ ( B @ k2_xboole_0 ) @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_sysrel) ).
thf(1951,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k4_relat_1 @ ( B @ k2_xboole_0 ) @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( E @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_2) ).
thf(6708,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( E @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_sysrel) ).
thf(1842,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ k6_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1842]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(1839,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1840,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(cnf,[status(esa)],[1839]) ).
thf(1841,plain,
! [A: $i] :
( ( A @ k6_relat_1 )
= ( A @ k6_partfun1 ) ),
inference(lifteq,[status(thm)],[1840]) ).
thf(13686,plain,
! [B: $i,A: $i] :
( ( B @ k4_relat_1 @ ( A @ k6_partfun1 @ r1_tarski ) )
| ~ ( B @ ( A @ k6_partfun1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(rewrite,[status(thm)],[1843,1841]) ).
thf(656,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(4776,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(3600,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(5779,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1589,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).
thf(9626,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3546,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1659,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_4_domain_1) ).
thf(10067,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_4_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p2_s5_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1834]) ).
thf(1704,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_pboole) ).
thf(10367,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ! [C: $i] :
( ( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(4942,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(986,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(6392,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(11664,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,8147]) ).
thf(11665,plain,
( ( sk455 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11664]) ).
thf(11670,plain,
sk455 != sk397,
inference(simp,[status(thm)],[11665]) ).
thf(1429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
<=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(8847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(12590,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,7497]) ).
thf(12591,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12590]) ).
thf(12603,plain,
sk595 != sk376,
inference(simp,[status(thm)],[12591]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relset_2) ).
thf(6168,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3050,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_relset_1) ).
thf(2547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( B @ ( C @ ( D @ ( B @ ( A @ ( C @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(5858,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(15243,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,6422]) ).
thf(15244,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk595 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15243]) ).
thf(15279,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk595 ),
inference(simp,[status(thm)],[15244]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_2) ).
thf(3727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_relat_1) ).
thf(2741,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(25707,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9314,1900]) ).
thf(25708,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25707]) ).
thf(25709,plain,
sk595 @ k2_relat_1 @ ( sk595 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25708:[bind(A,$thf( sk595 ))]]) ).
thf(1637,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(9885,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k4_xboole_0 ) ) )
& ( ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k3_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_sysrel) ).
thf(4461,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k4_xboole_0 ) ) )
& ( ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k3_xboole_0 ) ) )
& ( ( B @ ( A @ k2_xboole_0 ) @ k6_relat_1 )
= ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(3931,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(13151,plain,
! [A: $i] :
( ( A != sk594 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11235]) ).
thf(13152,plain,
! [A: $i] :
( ( A != sk594 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[13151]) ).
thf(13153,plain,
( ~ ( sk2 @ ( sk594 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[13152:[bind(A,$thf( sk594 ))]]) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k2_funct_1 @ v1_funct_1 )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1909]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m4_realset1 ) )
& ~ ( A @ v1_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_realset1) ).
thf(5330,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m4_realset1 ) )
& ~ ( A @ v1_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1592,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(9641,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(3595,plain,
! [A: $i] : ( A @ sk82 @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[3593]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_pboole) ).
thf(2769,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(11499,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,7987]) ).
thf(11500,plain,
( ( sk431 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11499]) ).
thf(11503,plain,
sk431 != sk378,
inference(simp,[status(thm)],[11500]) ).
thf(1120,axiom,
( a_0_3_domain_1
= ( a_0_5_domain_1 @ ( a_0_4_domain_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s10_domain_1) ).
thf(7094,plain,
( a_0_3_domain_1
= ( a_0_5_domain_1 @ ( a_0_4_domain_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(7095,plain,
( ( a_0_5_domain_1 @ ( a_0_4_domain_1 @ k3_xboole_0 ) )
= a_0_3_domain_1 ),
inference(lifteq,[status(thm)],[7094]) ).
thf(1902,plain,
! [A: $i] :
( ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1898]) ).
thf(26364,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3830,1902]) ).
thf(26365,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26364]) ).
thf(26366,plain,
sk95 @ k2_relat_1 @ ( sk95 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26365:[bind(A,$thf( sk95 ))]]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_card_1) ).
thf(6888,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(1474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(9095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(25672,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9011,1900]) ).
thf(25673,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25672]) ).
thf(25674,plain,
sk567 @ k2_relat_1 @ ( sk567 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25673:[bind(A,$thf( sk567 ))]]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(9804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).
thf(1802,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1803,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) )
& ( ( B @ v1_relat_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ) ),
inference(cnf,[status(esa)],[1802]) ).
thf(1804,plain,
! [B: $i,A: $i] :
( ( B @ v1_relat_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ),
inference(cnfConj,[status(thm)],[1803]) ).
thf(228,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( D @ ( A @ ( B @ k5_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(2726,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( D @ ( A @ ( B @ k5_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(8149,plain,
sk455 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[8146]) ).
thf(15584,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,7933]) ).
thf(15585,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15584]) ).
thf(15599,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk378 ),
inference(simp,[status(thm)],[15585]) ).
thf(1670,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(10131,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(1325,axiom,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(8297,plain,
! [A: $i] :
( ( A @ ( A @ k5_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_partfun1) ).
thf(6215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1341,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(8354,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(5313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_vectsp_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_vectsp_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_vectsp_1) ).
thf(6075,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_vectsp_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_vectsp_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1558,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(9493,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(457,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3782,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(3615,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(1491,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_card_1) ).
thf(9196,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_partfun1) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1359,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_mcart_1) ).
thf(8446,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(1243,axiom,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_card_1) ).
thf(7777,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(6677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1331,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relset_1) ).
thf(8314,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(3831,plain,
sk95 @ v3_relat_1,
inference(cnfConj,[status(thm)],[3829]) ).
thf(11128,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,9226]) ).
thf(11129,plain,
( ( sk592 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11128]) ).
thf(11133,plain,
sk592 != sk27,
inference(simp,[status(thm)],[11129]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( A @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_5) ).
thf(2115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( A @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3482,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(5053,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_domain_1) ).
thf(8677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_mcart_1) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(5238,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1787,plain,
( ~ sk3
| ( sk4 != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(1794,plain,
( ~ sk3
| ( sk4 != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1787]) ).
thf(1694,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_subset_1) ).
thf(10295,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(6995,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(845,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(5673,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(599,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k1_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(4512,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k1_relat_1 ) ) )
& ( ( B
= ( A @ k1_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_pua2mss1) ).
thf(6691,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_partfun1) ).
thf(2895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_partfun1) ).
thf(2359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1337,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(8339,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1499,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(9245,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(5577,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(5502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1727,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mssubfam) ).
thf(10566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(341,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ k5_funcop_1 ) ) @ k5_relat_1 ) )
= ( B @ ( D @ ( A @ ( C @ k5_relat_1 ) @ k5_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(3218,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ k5_funcop_1 ) ) @ k5_relat_1 ) )
= ( B @ ( D @ ( A @ ( C @ k5_relat_1 ) @ k5_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(660,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_pboole) ).
thf(4789,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1332,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_setfam_1) ).
thf(8319,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( A != k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1850]) ).
thf(1853,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( A != k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1851]) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1853]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(simp,[status(thm)],[1855]) ).
thf(625,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k5_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(4636,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r5_pboole) ).
thf(2692,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2694,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(4845,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(791,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_1) ).
thf(5428,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(1286,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(8014,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_relat_1) ).
thf(5362,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
<=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(5583,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1209,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( F @ ( E @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(7593,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( F @ ( E @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(2724,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1714,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(10445,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5978,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1695,axiom,
( ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_ordinal1 ) ) )
=> ( A @ p1_s2_ordinal1 ) ) )
=> ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ p1_s2_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_ordinal1) ).
thf(10298,plain,
( ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s2_ordinal1 ) ) )
=> ( A @ p1_s2_ordinal1 ) ) )
=> ! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ p1_s2_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(886,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( D @ k3_funcop_1 ) ) @ ( C @ k5_relat_1 ) )
= ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ ( D @ k3_funcop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(5889,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( D @ k3_funcop_1 ) ) @ ( C @ k5_relat_1 ) )
= ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ ( D @ k3_funcop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(7513,plain,
sk378 @ v1_finset_1,
inference(cnfConj,[status(thm)],[7512]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_partfun1) ).
thf(5811,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(450,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
<=> ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_funct_1) ).
thf(3746,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_relat_1 ) )
& ( ( A @ v2_relat_1 )
=> ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_relat_1) ).
thf(4840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(25920,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3830,1901]) ).
thf(25921,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25920]) ).
thf(25922,plain,
sk95 @ k1_relat_1 @ ( sk95 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25921:[bind(A,$thf( sk95 ))]]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(3650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1418,axiom,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(8796,plain,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(8797,plain,
! [A: $i] :
( ( ( ( A @ ( sk537 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk535 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk537 @ m2_relset_1 ) ) )
| ~ sk535 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk537 @ v1_funct_2 ) ) )
| ~ sk535 )
& ( ( sk537 @ v1_funct_1 )
| ~ sk535 )
& ( sk535
| ~ ( f2_s12_funct_2 @ ( sk536 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk535
| ( f1_s12_funct_2 @ ( sk536 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[8796]) ).
thf(8800,plain,
( sk535
| ( f1_s12_funct_2 @ ( sk536 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[8797]) ).
thf(1376,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relset_1) ).
thf(8567,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(24014,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,7497]) ).
thf(24015,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24014]) ).
thf(24044,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk376 ),
inference(simp,[status(thm)],[24015]) ).
thf(1377,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(8572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3941,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_sysrel) ).
thf(2268,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(15275,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,6422]) ).
thf(15276,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15275]) ).
thf(15281,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk397 ),
inference(simp,[status(thm)],[15276]) ).
thf(1422,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(8815,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(4219,plain,
sk119 @ v3_relat_1,
inference(cnfConj,[status(thm)],[4217]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(7116,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_partfun1) ).
thf(5497,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(312,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_1) ).
thf(3060,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_pboole) ).
thf(4263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(7101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ k1_card_1 )
= ( D @ k1_card_1 ) )
& ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_5) ).
thf(3952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ k1_card_1 )
= ( D @ k1_card_1 ) )
& ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ k1_card_1 )
= ( D @ ( B @ k1_funct_2 ) @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k10_relat_1 ) @ ( B @ k4_relat_1 @ k10_relat_1 ) @ ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t183_relat_1) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k10_relat_1 ) @ ( B @ k4_relat_1 @ k10_relat_1 ) @ ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1257,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(7846,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_tarski ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(6363,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( C
= ( B @ ( A @ k2_tarski ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1175,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_orders_1) ).
thf(7404,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1426,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(8835,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ k2_tarski ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_mssubfam) ).
thf(7189,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ k2_tarski ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( A @ k3_pua2mss1 @ ( B @ m2_finseq_1 ) )
=> ? [C: $i] :
( ( ( B @ k4_card_3 )
= ( C @ k1_tarski ) )
& ( A @ ( C @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pua2mss1) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( A @ k3_pua2mss1 @ ( B @ m2_finseq_1 ) )
=> ? [C: $i] :
( ( ( B @ k4_card_3 )
= ( C @ k1_tarski ) )
& ( A @ ( C @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_2) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(10944,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,7987]) ).
thf(10945,plain,
( ( sk431 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10944]) ).
thf(10946,plain,
sk431 != sk27,
inference(simp,[status(thm)],[10945]) ).
thf(1755,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(10708,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(7774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(719,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(5075,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1203,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
<=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_card_1) ).
thf(7559,plain,
! [A: $i] :
( ( A @ v1_card_1 )
=> ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( ~ ( A @ ( B @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1676,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(10185,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(1111,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(7054,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(805,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pboole) ).
thf(5491,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(5492,plain,
! [A: $i] :
( ( A @ sk181 @ v1_funct_1 )
& ( A @ sk181 @ v2_relat_1 )
& ( A @ sk181 @ v1_relat_1 )
& ( A @ ( A @ sk181 @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[5491]) ).
thf(5496,plain,
! [A: $i] : ( A @ sk181 @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[5492]) ).
thf(1074,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(6844,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(7629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(6593,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1280,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(7981,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(579,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(4425,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(3596,plain,
! [A: $i] : ( A @ sk82 @ v3_relat_1 ),
inference(cnfConj,[status(thm)],[3593]) ).
thf(1398,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_tarski ) @ ( C @ r1_setfam_1 ) )
=> ! [D: $i] :
~ ( ~ ( B @ ( D @ r1_tarski ) )
& ~ ( A @ ( D @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_setfam_1) ).
thf(8687,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_tarski ) @ ( C @ r1_setfam_1 ) )
=> ! [D: $i] :
~ ( ~ ( B @ ( D @ r1_tarski ) )
& ~ ( A @ ( D @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(10337,plain,
( ! [A: $i] :
( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( ( A @ k3_pua2mss1 )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[10336]) ).
thf(10338,plain,
! [B: $i,A: $i] :
( ( ( B = k1_xboole_0 )
| ( ( B @ k3_pua2mss1 )
!= k1_xboole_0 ) )
& ( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[10337]) ).
thf(10339,plain,
! [A: $i] :
( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[10338]) ).
thf(10341,plain,
! [A: $i] :
( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[10339]) ).
thf(10342,plain,
( ( k1_xboole_0 @ k3_pua2mss1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[10341]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_setfam_1) ).
thf(4389,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_setfam_1 )
& ( A @ v1_setfam_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_funct_1) ).
thf(2419,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1316,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( A @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(8258,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ~ ( A @ ( D @ r2_hidden ) ) )
& ( ~ ( A @ ( D @ r2_hidden ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) ) )
=> ( A
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(1646,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(9957,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ k5_funct_5 @ k2_relat_1 @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( B @ k1_funct_2 ) @ ( C @ k3_funct_5 @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_5) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ k5_funct_5 @ k2_relat_1 @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( B @ k1_funct_2 ) @ ( C @ k3_funct_5 @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k2_relat_1 @ k8_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_relat_1) ).
thf(4545,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k2_relat_1 @ k8_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_pboole) ).
thf(5253,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_xboole_1) ).
thf(5337,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1582,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(9609,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(11632,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,8147]) ).
thf(11633,plain,
( ( sk455 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11632]) ).
thf(11642,plain,
sk455 != sk384,
inference(simp,[status(thm)],[11633]) ).
thf(1553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(9477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_sysrel) ).
thf(4406,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(948,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_ordinal1) ).
thf(6164,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_relat_1) ).
thf(2613,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1025,axiom,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(6573,plain,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(6256,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1680,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_8_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_domain_1) ).
thf(10195,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_8_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(24988,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk384 ) ),
inference(paramod_ordered,[status(thm)],[9625,15600]) ).
thf(24989,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk384 ),
inference(pattern_uni,[status(thm)],[24988:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(11644,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,9270]) ).
thf(11645,plain,
( ( sk594 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11644]) ).
thf(11666,plain,
sk594 != sk397,
inference(simp,[status(thm)],[11645]) ).
thf(1450,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ ( A @ k4_zfmisc_1 ) ) ) )
= ( B @ ( B @ ( B @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_mcart_1) ).
thf(8968,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ ( A @ k4_zfmisc_1 ) ) ) )
= ( B @ ( B @ ( B @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(5865,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_pboole) ).
thf(3194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1748,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_setfam_1) ).
thf(10688,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(6395,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(6501,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_relat_1) ).
thf(2108,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( B @ ( A @ k8_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_relat_1) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( B @ ( A @ k8_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1113,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(7059,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ k1_relat_1 @ ( A @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1888]) ).
thf(1207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(7572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1265,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_orders_1) ).
thf(7895,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(294,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(2978,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(6935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(4180,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(969,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(6271,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1663,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(10094,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1251,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_relat_1) ).
thf(7821,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1560,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(9513,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(645,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relset_1) ).
thf(4736,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_domain_1) ).
thf(7293,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k6_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1220,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(7668,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(2504,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(9012,plain,
sk567 @ v1_funct_1,
inference(cnfConj,[status(thm)],[9010]) ).
thf(1743,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(10666,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(3409,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(10513,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(1445,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(8935,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(5317,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1393,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(8673,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(6134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( A = C ) )
=> ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_relset_1) ).
thf(2932,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1212,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(7609,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(8442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(5481,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(26026,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9271,1901]) ).
thf(26027,plain,
! [A: $i] :
( ( ( sk594 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26026]) ).
thf(26028,plain,
sk594 @ k1_relat_1 @ ( sk594 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26027:[bind(A,$thf( sk594 ))]]) ).
thf(732,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(5149,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1340,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(8351,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(25663,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4218,1900]) ).
thf(25664,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25663]) ).
thf(25665,plain,
sk119 @ k2_relat_1 @ ( sk119 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25664:[bind(A,$thf( sk119 ))]]) ).
thf(25939,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10850,1901]) ).
thf(25940,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25939]) ).
thf(25941,plain,
sk777 @ k1_relat_1 @ ( sk777 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25940:[bind(A,$thf( sk777 ))]]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(2836,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2598,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1768,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(10787,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(9316,plain,
sk595 @ v1_funct_1,
inference(cnfConj,[status(thm)],[9313]) ).
thf(15304,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,6953]) ).
thf(15305,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15304]) ).
thf(15322,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk384 ),
inference(simp,[status(thm)],[15305]) ).
thf(1193,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(7508,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(5639,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) ) )
=> ( ( B @ k3_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_orders_1) ).
thf(3743,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) ) )
=> ( ( B @ k3_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(3770,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1640,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(9893,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(1656,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(10026,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(5900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(6207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pboole) ).
thf(5973,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1324,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(8294,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(592,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_partfun1) ).
thf(4482,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_partfun1) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_relat_1) ).
thf(2581,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1399,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).
thf(8690,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A
= ( C @ k1_tarski ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(1692,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(10285,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(539,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4237,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_funct_1) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(3540,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( B @ ( A @ ( D @ k5_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_finseq_2) ).
thf(2566,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( B @ ( A @ ( D @ k5_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(25654,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4708,1900]) ).
thf(25655,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25654]) ).
thf(25656,plain,
sk149 @ k2_relat_1 @ ( sk149 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25655:[bind(A,$thf( sk149 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_2) ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ v2_funct_1 )
| ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
!= ( A @ k6_partfun1 ) )
| ~ ( A @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1797]) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ v2_funct_1 )
| ~ ( A @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
!= ( A @ k6_partfun1 ) )
| ( B = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1798]) ).
thf(1466,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
=> ~ ( A @ v1_realset1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_realset1) ).
thf(9053,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
=> ~ ( A @ v1_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1551,axiom,
( ! [A: $i] :
~ ( ! [B: $i] :
~ ( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_2) ).
thf(9461,plain,
( ! [A: $i] :
~ ( ! [B: $i] :
~ ( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(1440,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8896,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) )
<=> ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_mcart_1) ).
thf(7027,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) )
=> ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) ) )
& ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) )
=> ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(4347,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(7086,plain,
f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( sk328 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[7083]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_domain_1) ).
thf(2766,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1378,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_domain_1) ).
thf(8576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1627,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(9846,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(682,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(4902,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1127,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(7123,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1328,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(8307,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_pboole) ).
thf(5026,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k5_relset_2 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
thf(3005,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) )
=> ( C
= ( B @ ( A @ k5_relset_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_relset_2 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(576,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_relat_1 @ ( B @ k7_relat_1 ) @ k1_relat_1 @ ( A @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t189_relat_1) ).
thf(4416,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_relat_1 @ ( B @ k7_relat_1 ) @ k1_relat_1 @ ( A @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(371,axiom,
! [A: $i,B: $i] : ( B @ ( B @ r2_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_setfam_1) ).
thf(3364,plain,
! [A: $i] : ( A @ ( A @ r2_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1161,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(7333,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(237,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(2756,plain,
! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(536,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(4223,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(15306,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,6953]) ).
thf(15307,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15306]) ).
thf(15317,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk378 ),
inference(simp,[status(thm)],[15307]) ).
thf(11020,plain,
( ( ( k4_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,7814]) ).
thf(11021,plain,
( ( k4_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11020]) ).
thf(11031,plain,
k4_numbers != k1_xboole_0,
inference(simp,[status(thm)],[11021]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( A @ k1_tarski @ ( B @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_setfam_1) ).
thf(6533,plain,
! [A: $i,B: $i] :
( ( A @ k1_tarski @ ( B @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(2761,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1441,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(8923,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(2074,plain,
( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2073]) ).
thf(2076,plain,
( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2074]) ).
thf(1487,axiom,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(9170,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(9171,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9170]) ).
thf(1272,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(7941,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(921,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(6038,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1402,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_finset_1) ).
thf(8708,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_relat_1) ).
thf(5170,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(522,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
<=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(4163,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_pboole) ).
thf(3147,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r4_pboole ) ) ) )
=> ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( A @ v3_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(6171,plain,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( A @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1599,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(9699,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(1708,axiom,
( ( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_card_1 ) ) )
& ( A @ v2_card_1 ) )
=> ( ( A @ p1_s1_card_1 )
| ( A = k1_xboole_0 ) ) ) )
& ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( A @ p1_s1_card_1 )
=> ( A @ k2_card_1 @ p1_s1_card_1 ) ) )
& ( k1_xboole_0 @ p1_s1_card_1 ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_card_1) ).
thf(10406,plain,
( ( ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( ! [B: $i] :
( ( B @ v1_card_1 )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s1_card_1 ) ) )
& ( A @ v2_card_1 ) )
=> ( ( A @ p1_s1_card_1 )
| ( A = k1_xboole_0 ) ) ) )
& ! [A: $i] :
( ( A @ v1_card_1 )
=> ( ( A @ p1_s1_card_1 )
=> ( A @ k2_card_1 @ p1_s1_card_1 ) ) )
& ( k1_xboole_0 @ p1_s1_card_1 ) )
=> ! [A: $i] :
( ( A @ v1_card_1 )
=> ( A @ p1_s1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(7193,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(3824,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relset_1) ).
thf(2634,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(15576,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,7933]) ).
thf(15577,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15576]) ).
thf(15597,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15577]) ).
thf(24652,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[9625,15597]) ).
thf(24653,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[24652:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(24688,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_zfmisc_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,24653]) ).
thf(24689,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_zfmisc_1 ) )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[24688]) ).
thf(24690,plain,
( ~ ( sk2 @ ( k1_xboole_0 @ k1_zfmisc_1 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[24689:[bind(A,$thf( k1_xboole_0 @ k1_zfmisc_1 ))]]) ).
thf(11662,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,7987]) ).
thf(11663,plain,
( ( sk431 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11662]) ).
thf(11673,plain,
sk431 != sk397,
inference(simp,[status(thm)],[11663]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(7150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(825,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( ( A @ ( C @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(5557,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( ( A @ ( C @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(4184,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1104,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(7020,plain,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(11196,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,8985]) ).
thf(11197,plain,
( ( sk561 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11196]) ).
thf(11216,plain,
sk561 != sk149,
inference(simp,[status(thm)],[11197]) ).
thf(734,axiom,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(5153,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_relat_1) ).
thf(2926,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(9462,plain,
( ~ ? [A: $i] :
( ~ ? [B: $i] :
( ( B @ ( A @ p1_s1_funct_2 ) )
& ( f2_s1_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s1_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(miniscope,[status(thm)],[9461]) ).
thf(9463,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk612 @ k1_funct_1 ) @ ( B @ p1_s1_funct_2 ) )
| ~ ( f1_s1_funct_2 @ ( B @ r2_hidden ) )
| ~ sk610 )
& ( ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( sk612 @ m2_relset_1 ) ) )
| ~ sk610 )
& ( ( f2_s1_funct_2 @ ( f1_s1_funct_2 @ ( sk612 @ v1_funct_2 ) ) )
| ~ sk610 )
& ( ( sk612 @ v1_funct_1 )
| ~ sk610 )
& ( sk610
| ~ ( A @ ( sk611 @ p1_s1_funct_2 ) )
| ~ ( f2_s1_funct_2 @ ( A @ r2_hidden ) ) )
& ( sk610
| ( f1_s1_funct_2 @ ( sk611 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[9462]) ).
thf(9468,plain,
( sk610
| ( f1_s1_funct_2 @ ( sk611 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[9463]) ).
thf(1641,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(9913,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(18182,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1929,6953]) ).
thf(18183,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[18182]) ).
thf(18196,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[18183]) ).
thf(29569,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[18196,10644]) ).
thf(1093,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_domain_1) ).
thf(6963,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(8482,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4625,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(6160,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(4567,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(11120,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,8985]) ).
thf(11121,plain,
( ( sk561 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11120]) ).
thf(11125,plain,
sk561 != sk27,
inference(simp,[status(thm)],[11121]) ).
thf(1370,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(8512,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(4782,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1456,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(8989,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(4966,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_realset1 ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_realset1) ).
thf(9436,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_realset1 ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(1602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(9716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(10689,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_setfam_1 ) ),
inference(cnf,[status(esa)],[10688]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_orders_1) ).
thf(3306,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(23507,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk595 ) ),
inference(paramod_ordered,[status(thm)],[9625,15595]) ).
thf(23508,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk595 ),
inference(pattern_uni,[status(thm)],[23507:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_2) ).
thf(1846,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25259,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3830,1899]) ).
thf(25260,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25259]) ).
thf(25261,plain,
sk95 @ k1_relat_1 @ ( sk95 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25260:[bind(A,$thf( sk95 ))]]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(6279,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
thf(3999,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1737,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_relset_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_relset_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ ( B @ p1_s2_relset_1 ) ) ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_relset_1) ).
thf(10635,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_relset_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_relset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s2_relset_1 ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( B @ p1_s2_relset_1 ) ) ) ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ~ ( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_mcart_1) ).
thf(5209,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ~ ( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(5930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(10960,plain,
! [A: $i] :
( ( A != sk70 )
| ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,3407]) ).
thf(10961,plain,
( ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( sk70 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[10960:[bind(A,$thf( sk70 ))]]) ).
thf(11064,plain,
( ~ $true
| ~ ( sk2 @ ( sk70 @ r2_hidden ) )
| sk3 ),
inference(rewrite,[status(thm)],[10961,3611]) ).
thf(11065,plain,
( ~ ( sk2 @ ( sk70 @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11064]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(7476,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_pboole) ).
thf(5887,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_pboole ) )
=> ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
& ( E @ ( D @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) )
=> ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1895,plain,
! [B: $i,A: $i] :
( ( B @ v2_relat_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ),
inference(cnfConj,[status(thm)],[1894]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(6311,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1678,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(10190,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( D
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_mcart_1) ).
thf(5126,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( D
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ k3_mcart_1 ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_mcart_1) ).
thf(5840,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_relat_1) ).
thf(1996,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(5872,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(7817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(3660,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(980,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(6314,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_relat_1) ).
thf(5359,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(2428,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk26 @ r1_ordinal1 ) )
| ( A @ ( B @ r2_hidden ) )
| ~ ( B @ v3_ordinal1 ) )
& ~ ( A @ ( A @ sk26 @ r2_hidden ) )
& ( A @ sk26 @ v3_ordinal1 ) ),
inference(cnf,[status(esa)],[2427]) ).
thf(2430,plain,
! [A: $i] :
~ ( A @ ( A @ sk26 @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2428]) ).
thf(26243,plain,
! [A: $i] :
( ( ( A @ ( A @ sk26 @ r2_hidden ) )
!= ( sk2 @ ( sk4 @ r2_hidden ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[1788,2430]) ).
thf(26244,plain,
! [A: $i] :
( ( ( A @ ( A @ sk26 @ r2_hidden ) )
!= ( sk2 @ ( sk4 @ r2_hidden ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[26243]) ).
thf(26293,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk26 )
!= sk4 )
| ~ sk3 ),
inference(simp,[status(thm)],[26244]) ).
thf(26310,plain,
( ( ( sk2 @ sk26 )
!= sk4 )
| ~ sk3 ),
inference(simp,[status(thm)],[26293]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
<=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
thf(4562,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) ) )
& ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(6524,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(956,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_domain_1) ).
thf(6192,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k7_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(4921,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(6901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(12578,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk593 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,9230]) ).
thf(12579,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk593 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12578]) ).
thf(12609,plain,
sk595 != sk593,
inference(simp,[status(thm)],[12579]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_2) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1464,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(9040,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(11491,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,9226]) ).
thf(11492,plain,
( ( sk592 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11491]) ).
thf(11506,plain,
sk592 != sk378,
inference(simp,[status(thm)],[11492]) ).
thf(1010,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(6507,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2677,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
thf(4685,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1664,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(10101,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_sysrel) ).
thf(2292,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel )
= ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).
thf(9765,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(4872,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(3003,plain,
sk44 @ v2_relat_1,
inference(cnfConj,[status(thm)],[3001]) ).
thf(10970,plain,
! [A: $i] :
( ( A != sk44 )
| ( k1_xboole_0 @ v2_relat_1 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,3003]) ).
thf(10971,plain,
( ( k1_xboole_0 @ v2_relat_1 )
| ~ ( sk2 @ ( sk44 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[10970:[bind(A,$thf( sk44 ))]]) ).
thf(1498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
<=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_mcart_1) ).
thf(9231,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 )
=> ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) )
& ( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(11622,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,9226]) ).
thf(11623,plain,
( ( sk592 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11622]) ).
thf(11638,plain,
sk592 != sk384,
inference(simp,[status(thm)],[11623]) ).
thf(869,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(5808,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(40,axiom,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_relat_1) ).
thf(1958,plain,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1959,plain,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1958]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pboole) ).
thf(2556,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
=> ( ( D @ ( B @ ( A @ r2_pboole ) ) )
& ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(558,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(4354,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(350,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
& ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_pboole) ).
thf(3257,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
& ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r4_pboole) ).
thf(3607,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r4_pboole ) ) )
=> ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3890,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_partfun1) ).
thf(7010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_2) ).
thf(3079,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(4412,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(2570,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_mcart_1) ).
thf(9122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(1406,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
<=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_2) ).
thf(8728,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 ) )
& ( ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(6578,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1299,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B
= ( A @ k2_card_1 ) )
<=> ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_card_1) ).
thf(8112,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) )
=> ( B
= ( A @ k2_card_1 ) ) )
& ( ( B
= ( A @ k2_card_1 ) )
=> ( ! [C: $i] :
( ( C @ v1_card_1 )
=> ( ( C @ ( A @ k1_card_1 @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) ) )
& ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(7599,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(6001,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( E
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_mcart_1) ).
thf(3289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( E
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ k4_mcart_1 ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1630,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_mcart_1) ).
thf(9853,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(1590,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( C @ k9_relat_1 ) )
= ( C @ ( B @ ( A @ a_3_0_relset_2 ) ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_2) ).
thf(9635,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( C @ k9_relat_1 ) )
= ( C @ ( B @ ( A @ a_3_0_relset_2 ) ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( D @ ( G @ ( F @ k4_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_finseq_2) ).
thf(2028,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( D @ ( G @ ( F @ k4_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_mcart_1) ).
thf(7636,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(3839,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_partfun1) ).
thf(3523,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_relat_1) ).
thf(5928,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1431,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(8859,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(1269,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(7920,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(4269,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_2) ).
thf(7785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(435,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(3686,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ? [D: $i] :
( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_mcart_1) ).
thf(4017,plain,
! [A: $i,B: $i,C: $i] :
~ ( ? [D: $i] :
( ? [E: $i,F: $i,G: $i] :
( ~ ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= G )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= F )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= E ) )
& ( D
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1330,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(8311,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(4489,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(6052,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1170,axiom,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(7372,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(4453,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(712,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_sysrel) ).
thf(5043,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(5241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1420,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(8807,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(1367,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(8495,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(4786,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3319,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(3589,plain,
sk81 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3588]) ).
thf(25339,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3589,1899]) ).
thf(25340,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25339]) ).
thf(25341,plain,
sk81 @ k1_relat_1 @ ( sk81 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25340:[bind(A,$thf( sk81 ))]]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3900,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_subset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(6407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1543,axiom,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(9418,plain,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(4998,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(5933,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1278,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(7968,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_partfun1) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(7938,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(1469,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_pboole ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_pboole) ).
thf(9062,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( B @ ( A @ k10_pboole ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_pboole ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_finseq_2) ).
thf(1916,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(25948,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2437,1901]) ).
thf(25949,plain,
! [A: $i] :
( ( ( sk27 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25948]) ).
thf(25950,plain,
sk27 @ k1_relat_1 @ ( sk27 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25949:[bind(A,$thf( sk27 ))]]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_orders_1) ).
thf(3768,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(3636,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(281,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_pua2mss1) ).
thf(2938,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1483,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k13_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ~ ( ( B @ v1_xboole_0 )
& ( ( B @ k1_relat_1 )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_unialg_1) ).
thf(9142,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k13_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ~ ( ( B @ v1_xboole_0 )
& ( ( B @ k1_relat_1 )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_funct_1) ).
thf(5488,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(4077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(12214,plain,
! [A: $i] :
( ( A != sk592 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11132]) ).
thf(12215,plain,
! [A: $i] :
( ( A != sk592 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[12214]) ).
thf(12216,plain,
( ~ ( sk2 @ ( sk592 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[12215:[bind(A,$thf( sk592 ))]]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_rlvect_1 ) ) )
= ( F @ ( E @ ( D @ g1_rlvect_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_rlvect_1) ).
thf(7736,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_rlvect_1 ) ) )
= ( F @ ( E @ ( D @ g1_rlvect_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1147,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(7233,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(11118,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,8985]) ).
thf(11119,plain,
( ( sk561 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11118]) ).
thf(11124,plain,
sk561 != k1_xboole_0,
inference(simp,[status(thm)],[11119]) ).
thf(12168,plain,
! [A: $i] :
( ( A != sk561 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11124]) ).
thf(12169,plain,
! [A: $i] :
( ( A != sk561 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[12168]) ).
thf(12170,plain,
( ~ ( sk2 @ ( sk561 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[12169:[bind(A,$thf( sk561 ))]]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_pboole) ).
thf(2525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(716,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v3_ordinal1 )
=> ( A @ k2_relat_1 @ ( A @ m1_ordinal1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
thf(5065,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v3_ordinal1 )
=> ( A @ k2_relat_1 @ ( A @ m1_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1350,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_pboole) ).
thf(8404,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_pboole) ).
thf(2981,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( A @ ( B @ r1_ordinal1 ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(5067,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( A @ ( B @ r1_ordinal1 ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(317,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_partfun1) ).
thf(3086,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(15308,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,6953]) ).
thf(15309,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15308]) ).
thf(15320,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk149 ),
inference(simp,[status(thm)],[15309]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_card_1) ).
thf(4677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_2) ).
thf(3266,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1552,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
<=> ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_1) ).
thf(9471,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(519,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(4122,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(9295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(4709,plain,
sk149 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4706]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(7704,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(5876,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1562,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).
thf(9521,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m3_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3458,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(6898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1467,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(9057,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(1726,axiom,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(10544,plain,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(10545,plain,
( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk735 @ r2_hidden ) )
| ~ ( sk735 @ p1_s4_subset_1 )
| sk733 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk735 @ p1_s4_subset_1 )
| ~ ( sk735 @ p1_s4_subset_1 )
| sk733 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk735 @ r2_hidden ) )
| ( f3_s4_subset_1 @ ( sk735 @ r2_hidden ) )
| sk733 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk735 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk735 @ r2_hidden ) )
| sk733 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk735 @ m1_subset_1 ) )
| sk733 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk733
| ~ ( f2_s4_subset_1 @ ( sk734 @ r2_hidden ) )
| ~ ( sk734 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk733
| ( sk734 @ p1_s4_subset_1 )
| ~ ( sk734 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk733
| ~ ( f2_s4_subset_1 @ ( sk734 @ r2_hidden ) )
| ( f2_s4_subset_1 @ ( sk734 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk733
| ( sk734 @ p1_s4_subset_1 )
| ( f2_s4_subset_1 @ ( sk734 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk733
| ( f1_s4_subset_1 @ ( sk734 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[10544]) ).
thf(10551,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk735 @ m1_subset_1 ) )
| sk733 ),
inference(cnfConj,[status(thm)],[10545]) ).
thf(10557,plain,
( ( f1_s4_subset_1 @ ( sk735 @ m1_subset_1 ) )
| sk733
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[10551]) ).
thf(1408,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(8740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(3590,plain,
sk81 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3588]) ).
thf(1380,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_pboole) ).
thf(8581,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k11_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(224,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k3_setfam_1 ) @ r1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_setfam_1) ).
thf(2716,plain,
! [A: $i] : ( A @ ( A @ ( A @ k3_setfam_1 ) @ r1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_2) ).
thf(4381,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(4590,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(4975,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(653,axiom,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_1) ).
thf(4769,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(7815,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(6705,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
= ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B
= ( A @ k1_card_1 ) )
<=> ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_card_1) ).
thf(4505,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( ( B @ ( A @ r2_wellord2 ) )
=> ( B
= ( A @ k1_card_1 ) ) )
& ( ( B
= ( A @ k1_card_1 ) )
=> ( B @ ( A @ r2_wellord2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_2) ).
thf(7218,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k9_funct_2 ) ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1479,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(9125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(1427,axiom,
? [A: $i] : ( A @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_card_1) ).
thf(8840,plain,
? [A: $i] : ( A @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(8841,plain,
sk541 @ v1_card_1,
inference(cnf,[status(esa)],[8840]) ).
thf(3002,plain,
sk44 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3001]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(6091,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( B @ r1_xboole_0 ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1616,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(9802,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(9803,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m1_ordinal1 ) ),
inference(cnf,[status(esa)],[9802]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(7865,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(1658,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(10056,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(1349,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_domain_1) ).
thf(8381,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) )
& ( ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_relat_1) ).
thf(3223,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(8767,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(5546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(11646,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,9230]) ).
thf(11647,plain,
( ( sk593 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11646]) ).
thf(11671,plain,
sk593 != sk397,
inference(simp,[status(thm)],[11647]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_2) ).
thf(4978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1734,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(10611,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1591,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_domain_1) ).
thf(9638,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_domain_1) ).
thf(7201,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k5_mcart_1 ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
=> ( A = F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(6937,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(1309,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r3_relat_2 ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).
thf(8188,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r3_relat_2 ) ) )
& ( ( B @ ( A @ r3_relat_2 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(7270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1302,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_setfam_1) ).
thf(8152,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_setfam_1 ) ) )
& ( ( B @ ( A @ r1_setfam_1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(668,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ a_3_0_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_domain_1) ).
thf(4837,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ a_3_0_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1281,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(7983,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1042,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(6673,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1738,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(10640,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_1) ).
thf(2738,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(8665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_1) ).
thf(3663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_sysrel) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25306,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3615,1899]) ).
thf(25307,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25306]) ).
thf(25308,plain,
k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25307:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2816,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2815]) ).
thf(2818,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2816]) ).
thf(27649,plain,
k1_xboole_0 @ ( k1_xboole_0 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(rewrite,[status(thm)],[25308,2818]) ).
thf(1326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(8300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1566,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pboole) ).
thf(9538,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k3_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(651,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( A @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( B @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funcop_1) ).
thf(4764,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( A @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( B @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(320,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_orders_1) ).
thf(3123,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(25324,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3002,1899]) ).
thf(25325,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25324]) ).
thf(25326,plain,
sk44 @ k1_relat_1 @ ( sk44 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25325:[bind(A,$thf( sk44 ))]]) ).
thf(1760,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_2) ).
thf(10728,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(236,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_realset1 ) ) )
= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_realset1) ).
thf(2753,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_realset1 ) ) )
= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(15578,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,7933]) ).
thf(15579,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15578]) ).
thf(15594,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk27 ),
inference(simp,[status(thm)],[15579]) ).
thf(396,axiom,
! [A: $i] :
( ( A @ k1_pboole @ v1_funct_1 )
& ( A @ k1_pboole @ v3_relat_1 )
& ( A @ k1_pboole @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pboole) ).
thf(3487,plain,
! [A: $i] :
( ( A @ k1_pboole @ v1_funct_1 )
& ( A @ k1_pboole @ v3_relat_1 )
& ( A @ k1_pboole @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_partfun1) ).
thf(9555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(25971,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5475,1901]) ).
thf(25972,plain,
! [A: $i] :
( ( ( sk180 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25971]) ).
thf(25973,plain,
sk180 @ k1_relat_1 @ ( sk180 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25972:[bind(A,$thf( sk180 ))]]) ).
thf(1221,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(7671,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(851,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( k1_xboole_0 @ k8_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_relat_1) ).
thf(5703,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( k1_xboole_0 @ k8_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_sysrel) ).
thf(5449,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(464,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ r1_tarski ) )
=> ( A
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_sysrel) ).
thf(3832,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ r1_tarski ) )
=> ( A
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(820,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(5539,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(7536,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1219,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_domain_1) ).
thf(7658,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(150,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(2425,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1655,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(10024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(5158,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(6248,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(11233,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,9270]) ).
thf(11234,plain,
( ( sk594 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11233]) ).
thf(11237,plain,
sk594 != sk149,
inference(simp,[status(thm)],[11234]) ).
thf(1526,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(9354,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(8202,plain,
sk462 @ v1_funct_1,
inference(cnfConj,[status(thm)],[8201]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_funct_1) ).
thf(3719,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(9258,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(1347,axiom,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(8376,plain,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(6016,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1500,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(9248,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(1624,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(9835,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(1536,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(9390,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(6048,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_relat_1) ).
thf(2510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(24073,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk149 ) ),
inference(paramod_ordered,[status(thm)],[9625,15596]) ).
thf(24074,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk149 ),
inference(pattern_uni,[status(thm)],[24073:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_2) ).
thf(3251,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(9614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(4914,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(116,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2284,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
& ( B
!= ( A @ k1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_pboole) ).
thf(2943,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
& ( B
!= ( A @ k1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1557,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(9491,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(840,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(5616,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k3_funct_5 @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_5) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k3_funct_5 @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_mcart_1) ).
thf(6144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(132,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(2346,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(2721,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1058,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_orders_1) ).
thf(6742,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(10368,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_pboole @ ( B @ r2_hidden ) )
=> ( ! [C: $i] :
( ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s2_pboole ) )
& ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
inference(miniscope,[status(thm)],[10367]) ).
thf(10369,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk708 @ k1_funct_1 ) @ ( C @ r2_hidden ) )
| ~ ( C @ ( A @ p1_s2_pboole ) )
| ~ ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ p1_s2_pboole ) )
| ~ ( A @ ( sk708 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( A @ ( sk708 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
| ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
& ( f1_s2_pboole @ ( sk708 @ m1_pboole ) ) ),
inference(cnf,[status(esa)],[10368]) ).
thf(10370,plain,
f1_s2_pboole @ ( sk708 @ m1_pboole ),
inference(cnfConj,[status(thm)],[10369]) ).
thf(1573,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(9575,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(12599,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk455 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,8147]) ).
thf(12600,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk455 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12599]) ).
thf(12604,plain,
sk595 != sk455,
inference(simp,[status(thm)],[12600]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(4228,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(2538,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(7514,plain,
sk378 @ v1_funct_1,
inference(cnfConj,[status(thm)],[7512]) ).
thf(1710,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(10429,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3155,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1548,axiom,
( ! [A: $i,B: $i] :
( ( ( f2_s6_funct_2 @ ( B @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( A @ r2_hidden ) ) )
=> ( f3_s6_funct_2 @ ( B @ ( A @ f4_s6_funct_2 ) @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s6_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s6_funct_2 ) ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s6_funct_2) ).
thf(9446,plain,
( ! [A: $i,B: $i] :
( ( ( f2_s6_funct_2 @ ( B @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( A @ r2_hidden ) ) )
=> ( f3_s6_funct_2 @ ( B @ ( A @ f4_s6_funct_2 ) @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s6_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s6_funct_2 @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ f4_s6_funct_2 ) ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(9447,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( A @ k4_tarski ) @ ( sk609 @ k1_funct_1 ) )
= ( B @ ( A @ f4_s6_funct_2 ) ) )
| ~ ( f2_s6_funct_2 @ ( B @ r2_hidden ) )
| ~ ( f1_s6_funct_2 @ ( A @ r2_hidden ) )
| ~ sk606 )
& ( ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( sk609 @ m2_relset_1 ) ) )
| ~ sk606 )
& ( ( f3_s6_funct_2 @ ( f2_s6_funct_2 @ ( f1_s6_funct_2 @ k2_zfmisc_1 ) @ ( sk609 @ v1_funct_2 ) ) )
| ~ sk606 )
& ( ( sk609 @ v1_funct_1 )
| ~ sk606 )
& ( sk606
| ~ ( f3_s6_funct_2 @ ( sk608 @ ( sk607 @ f4_s6_funct_2 ) @ r2_hidden ) ) )
& ( sk606
| ( f2_s6_funct_2 @ ( sk608 @ r2_hidden ) ) )
& ( sk606
| ( f1_s6_funct_2 @ ( sk607 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[9446]) ).
thf(9454,plain,
( sk606
| ( f2_s6_funct_2 @ ( sk608 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[9447]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(2084,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(6920,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(8715,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(11501,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,8147]) ).
thf(11502,plain,
( ( sk455 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11501]) ).
thf(11508,plain,
sk455 != sk378,
inference(simp,[status(thm)],[11502]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(6179,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(5244,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(307,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(3038,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1531,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(9377,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(15298,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,6953]) ).
thf(15299,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15298]) ).
thf(15316,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15299]) ).
thf(24022,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk594 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,9270]) ).
thf(24023,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk594 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24022]) ).
thf(24043,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk594 ),
inference(simp,[status(thm)],[24023]) ).
thf(944,axiom,
! [A: $i] :
( ~ ( ( A @ v1_realset1 )
& ? [B: $i,C: $i] :
( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) )
& ~ ( ! [B: $i,C: $i] :
~ ( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ~ ( A @ v1_realset1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_realset1) ).
thf(6147,plain,
! [A: $i] :
( ~ ( ( A @ v1_realset1 )
& ? [B: $i,C: $i] :
( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) )
& ~ ( ! [B: $i,C: $i] :
~ ( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ~ ( A @ v1_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(244,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_funcop_1 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ k10_relat_1 ) @ k2_funcop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(2774,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_funcop_1 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ k10_relat_1 ) @ k2_funcop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t186_partfun1) ).
thf(4828,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1625,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s3_subset_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ( B @ p1_s3_subset_1 ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1) ).
thf(9838,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s3_subset_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p1_s3_subset_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s3_subset_1 ) ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(9839,plain,
! [A: $i] :
( ( ( sk654 @ ( A @ r2_hidden ) )
| ~ ( A @ p1_s3_subset_1 )
| ~ ( f1_s3_subset_1 @ ( A @ m1_subset_1 ) ) )
& ( ( A @ p1_s3_subset_1 )
| ~ ( sk654 @ ( A @ r2_hidden ) )
| ~ ( f1_s3_subset_1 @ ( A @ m1_subset_1 ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( sk654 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[9838]) ).
thf(9840,plain,
f1_s3_subset_1 @ k1_zfmisc_1 @ ( sk654 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[9839]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_xboole_1) ).
thf(3779,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k5_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( B @ v3_relat_1 )
& ~ ( A @ ( B @ k7_relat_1 ) @ v3_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t190_relat_1) ).
thf(2906,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( B @ v3_relat_1 )
& ~ ( A @ ( B @ k7_relat_1 ) @ v3_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1611,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(9771,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(25268,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8150,1899]) ).
thf(25269,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25268]) ).
thf(25270,plain,
sk455 @ k1_relat_1 @ ( sk455 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25269:[bind(A,$thf( sk455 ))]]) ).
thf(8171,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8170]) ).
thf(1477,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k1_setfam_1 @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_ordinal2) ).
thf(9118,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) )
=> ( A @ k1_setfam_1 @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(1642,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(9920,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(7330,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1294,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_tarski ) )
<=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( D = F )
<=> ( E = G ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).
thf(8047,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) )
=> ( B @ ( A @ r2_tarski ) ) )
& ( ( B @ ( A @ r2_tarski ) )
=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2839,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(838,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v2_relat_1 )
<=> ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_1) ).
thf(5610,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v2_relat_1 ) )
& ( ( A @ v2_relat_1 )
=> ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(617,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4616,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1801,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
| ~ ( B @ ( C @ m2_finseq_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1800]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ( A @ ( C @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pboole) ).
thf(5531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_pboole ) ) )
=> ( A @ ( C @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(8986,plain,
sk561 @ v1_realset1,
inference(cnfConj,[status(thm)],[8984]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(5346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_1) ).
thf(6289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k1_relset_2 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).
thf(10019,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k1_relset_2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_partfun1) ).
thf(4300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(789,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_pboole) ).
thf(5381,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(7362,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(4374,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1614,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(9789,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) )
& ( A @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_sysrel) ).
thf(2197,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_sysrel @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) )
& ( A @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1601,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(9713,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(710,axiom,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(5035,plain,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(11656,plain,
( ( ( sk397 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,7497]) ).
thf(11657,plain,
( ( sk397 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11656]) ).
thf(11669,plain,
sk397 != sk376,
inference(simp,[status(thm)],[11657]) ).
thf(1225,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(7685,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1650,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
<=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(10004,plain,
! [A: $i] :
( ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v1_setfam_1 ) )
& ( ( A @ v1_setfam_1 )
=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(2923,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(cnf,[status(esa)],[2922]) ).
thf(18277,plain,
! [A: $i] : ( A @ k6_partfun1 @ v2_funct_1 ),
inference(rewrite,[status(thm)],[2923,1841]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(3456,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(827,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(5563,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(6834,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(4203,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_partfun1) ).
thf(5114,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1444,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_7_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_domain_1) ).
thf(8932,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_7_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(1740,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_subset_1) ).
thf(10645,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ~ ( ( B @ ( A @ r2_hidden ) )
<=> ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(9042,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) )
=> ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
=> ~ ( ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
=> ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(811,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k7_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(5511,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k7_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1407,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8735,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(581,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ v1_realset1 )
<=> ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_realset1) ).
thf(4430,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
=> ~ ( A @ v1_realset1 ) )
& ( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_card_1) ).
thf(5920,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_mcart_1) ).
thf(7275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ! [E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( F = J ) ) ) ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1707,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( B
= ( F @ ( E @ ( D @ ( C @ k4_mcart_1 ) ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_mcart_1) ).
thf(10397,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( B
= ( F @ ( E @ ( D @ ( C @ k4_mcart_1 ) ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1705,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(10375,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(15263,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,6422]) ).
thf(15264,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15263]) ).
thf(15280,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk384 ),
inference(simp,[status(thm)],[15264]) ).
thf(1638,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(9888,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
thf(2343,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1481,axiom,
? [A: $i] : ( A @ v1_int_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_int_1) ).
thf(9133,plain,
? [A: $i] : ( A @ v1_int_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(9134,plain,
sk578 @ v1_int_1,
inference(cnf,[status(esa)],[9133]) ).
thf(12476,plain,
! [A: $i] :
( ( A != sk578 )
| ( k1_xboole_0 @ v1_int_1 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,9134]) ).
thf(12477,plain,
( ( k1_xboole_0 @ v1_int_1 )
| ~ ( sk2 @ ( sk578 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[12476:[bind(A,$thf( sk578 ))]]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_0_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_domain_1) ).
thf(9079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_0_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_0_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1388,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(8661,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel )
= ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_sysrel) ).
thf(1993,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_sysrel )
= ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(26902,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,5034]) ).
thf(26903,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26902]) ).
thf(26918,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk149 ),
inference(simp,[status(thm)],[26903]) ).
thf(1859,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) )
| ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1858]) ).
thf(1861,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ m2_finseq_1 ) )
| ~ ( A @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( D @ v1_finseq_1 )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) )
| ( D
!= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
| ( ( F @ k3_finseq_1 )
!= ( G @ k3_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1859]) ).
thf(1862,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ m2_finseq_1 ) )
| ~ ( A @ ( E @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_finseq_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_funct_1 )
| ~ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ v1_relat_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ k3_finseq_1 )
= ( E @ k3_finseq_1 ) )
| ( ( E @ k3_finseq_1 )
!= ( F @ k3_finseq_1 ) ) ),
inference(simp,[status(thm)],[1861]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(7551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1761,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(10732,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(335,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3192,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(12435,plain,
( ( ( sk592 @ v1_realset1 )
!= ( sk561 @ v1_realset1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8986,9227]) ).
thf(12436,plain,
( ( sk592 @ v1_realset1 )
!= ( sk561 @ v1_realset1 ) ),
inference(simp,[status(thm)],[12435]) ).
thf(12438,plain,
sk592 != sk561,
inference(simp,[status(thm)],[12436]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(9280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k9_relat_1 ) @ ( B @ k4_relat_1 @ k9_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1837]) ).
thf(3614,plain,
k1_xboole_0 @ v1_finseq_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(7778,plain,
( ( k1_xboole_0 @ k1_card_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[7777]) ).
thf(4850,plain,
sk153 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4849]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_finseq_2) ).
thf(3451,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( A @ k3_pua2mss1 @ ( C @ k9_relat_1 ) @ ( A @ k3_pua2mss1 @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) @ ( A @ k3_pua2mss1 @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_2) ).
thf(7141,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( A @ k3_pua2mss1 @ ( C @ k9_relat_1 ) @ ( A @ k3_pua2mss1 @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) @ ( A @ k3_pua2mss1 @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1346,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(8372,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_card_1) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(11620,plain,
( ( ( sk384 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,3407]) ).
thf(11621,plain,
( ( sk384 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11620]) ).
thf(11640,plain,
sk384 != sk70,
inference(simp,[status(thm)],[11621]) ).
thf(1458,axiom,
( ! [A: $i] :
( ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
=> ( f2_s2_funct_2 @ ( A @ f3_s2_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_funct_2 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s2_funct_2 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_2) ).
thf(8998,plain,
( ! [A: $i] :
( ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
=> ( f2_s2_funct_2 @ ( A @ f3_s2_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s2_funct_2 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) )
= ( B @ f3_s2_funct_2 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(1719,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).
thf(10489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_mcart_1) ).
thf(8473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(2289,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(5180,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1075,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(6847,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(4726,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1564,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(9528,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(703,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_finseq_2) ).
thf(4993,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(7021,plain,
~ ? [A: $i] :
! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[7020]) ).
thf(7022,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk324 @ r2_hidden ) )
& ( A @ sk324 @ v3_ordinal1 ) ),
inference(cnf,[status(esa)],[7021]) ).
thf(7023,plain,
! [A: $i] : ( A @ sk324 @ v3_ordinal1 ),
inference(cnfConj,[status(thm)],[7022]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k4_relat_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k4_relat_1 @ k1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(2329,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k4_relat_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k4_relat_1 @ k1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(2842,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_mcart_1) ).
thf(5838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(478,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(3893,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(4554,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(4990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2578,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1189,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ m1_orders_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_orders_1) ).
thf(7479,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( A @ ( B @ m1_orders_1 ) ) )
& ( ( A @ ( B @ m1_orders_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(5575,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(8541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) )
=> ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_mcart_1) ).
thf(2967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_funct_1) ).
thf(8280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(11614,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,9230]) ).
thf(11615,plain,
( ( sk593 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11614]) ).
thf(11643,plain,
sk593 != sk384,
inference(simp,[status(thm)],[11615]) ).
thf(1634,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(9873,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(11168,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,9230]) ).
thf(11169,plain,
( ( sk593 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11168]) ).
thf(11173,plain,
sk593 != sk27,
inference(simp,[status(thm)],[11169]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v3_relat_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(4933,plain,
! [A: $i,B: $i] :
( ( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v3_relat_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(780,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
thf(5340,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(8440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(2439,plain,
sk27 @ v2_funct_1,
inference(cnfConj,[status(thm)],[2436]) ).
thf(11208,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,7987]) ).
thf(11209,plain,
( ( sk431 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11208]) ).
thf(11220,plain,
sk431 != sk149,
inference(simp,[status(thm)],[11209]) ).
thf(289,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_partfun1) ).
thf(2962,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_card_1) ).
thf(5775,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(26367,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7517,1902]) ).
thf(26368,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26367]) ).
thf(26369,plain,
sk378 @ k2_relat_1 @ ( sk378 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26368:[bind(A,$thf( sk378 ))]]) ).
thf(1586,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(9619,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(6907,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_2) ).
thf(2051,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(8719,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(2620,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1660,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(10076,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(7469,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(959,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_6_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_domain_1) ).
thf(6223,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_6_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1683,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(10208,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(90,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B
= ( C @ ( A @ k5_relat_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_finseq_2) ).
thf(2139,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B
= ( C @ ( A @ k5_relat_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1533,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(9381,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ k7_relat_1 ) @ k2_relat_1 @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
thf(4085,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ k7_relat_1 ) @ k2_relat_1 @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(327,axiom,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(3159,plain,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_relat_1) ).
thf(4918,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1530,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_domain_1) ).
thf(9366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(1783,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(10930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(440,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_domain_1) ).
thf(3706,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(3142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(178,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
thf(2535,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(7024,plain,
! [A: $i] :
~ ( A @ ( A @ sk324 @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[7022]) ).
thf(27803,plain,
! [A: $i] :
( ( ( A @ ( A @ sk324 @ r2_hidden ) )
!= ( sk2 @ ( sk4 @ r2_hidden ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[1788,7024]) ).
thf(27804,plain,
! [A: $i] :
( ( ( A @ ( A @ sk324 @ r2_hidden ) )
!= ( sk2 @ ( sk4 @ r2_hidden ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[27803]) ).
thf(27844,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ sk324 )
!= sk4 )
| ~ sk3 ),
inference(simp,[status(thm)],[27804]) ).
thf(27858,plain,
( ( ( sk2 @ sk324 )
!= sk4 )
| ~ sk3 ),
inference(simp,[status(thm)],[27844]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ? [G: $i] :
( ? [H: $i] :
( ~ ( ( ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k7_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k6_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k5_mcart_1 ) ) ) ) ) )
& ( G = H )
& ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( H @ m1_subset_1 ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_mcart_1) ).
thf(5299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ? [G: $i] :
( ? [H: $i] :
( ~ ( ( ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k7_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k6_mcart_1 ) ) ) ) )
& ( ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( H @ ( F @ ( E @ ( D @ k5_mcart_1 ) ) ) ) ) )
& ( G = H )
& ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( H @ m1_subset_1 ) ) )
& ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( F @ ( D @ ( B @ k3_mcart_1 ) ) @ ( F @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( F @ ( D @ ( A @ k3_mcart_1 ) ) @ ( F @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k6_enumset1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_mcart_1) ).
thf(7339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( F @ ( D @ ( B @ k3_mcart_1 ) ) @ ( F @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( F @ ( D @ ( A @ k3_mcart_1 ) ) @ ( F @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k6_enumset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(4497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(4282,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(367,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(3348,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(5495,plain,
! [A: $i] : ( A @ sk181 @ v2_relat_1 ),
inference(cnfConj,[status(thm)],[5492]) ).
thf(510,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v3_relat_1 )
<=> ! [B: $i] :
( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t184_relat_1) ).
thf(4067,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ! [B: $i] :
( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B = k1_xboole_0 ) )
=> ( A @ v3_relat_1 ) )
& ( ( A @ v3_relat_1 )
=> ! [B: $i] :
( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_domain_1) ).
thf(7916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(11487,plain,
( ( ( sk561 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,8985]) ).
thf(11488,plain,
( ( sk561 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11487]) ).
thf(11507,plain,
sk561 != sk378,
inference(simp,[status(thm)],[11488]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_partfun1) ).
thf(5326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(3876,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(1290,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_eqrel_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ a_4_0_pua2mss1 ) ) ) @ m1_eqrel_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_pua2mss1) ).
thf(8035,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_eqrel_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ a_4_0_pua2mss1 ) ) ) @ m1_eqrel_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(4158,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1805,plain,
! [B: $i,A: $i] :
( ( B @ v1_funct_1 )
| ~ ( A @ ( B @ m2_pua2mss1 ) ) ),
inference(cnfConj,[status(thm)],[1803]) ).
thf(73,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( B @ ( A @ k7_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funcop_1) ).
thf(2069,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( B @ ( A @ k7_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1054,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(6730,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(2867,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1750,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(10692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(3488,plain,
( ! [A: $i] : ( A @ k1_pboole @ v1_funct_1 )
& ! [A: $i] : ( A @ k1_pboole @ v3_relat_1 )
& ! [A: $i] : ( A @ k1_pboole @ v1_relat_1 ) ),
inference(miniscope,[status(thm)],[3487]) ).
thf(3489,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k1_pboole @ v1_funct_1 )
& ( B @ k1_pboole @ v3_relat_1 )
& ( A @ k1_pboole @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3488]) ).
thf(3490,plain,
! [A: $i] : ( A @ k1_pboole @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[3489]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( C @ k2_relat_1 )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_2) ).
thf(3380,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
=> ( ( C @ k2_relat_1 )
= B ) )
& ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(7154,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(3444,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1809,plain,
! [A: $i] :
( ( A @ k3_funct_5 @ v1_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1807]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(6540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(2878,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(11016,plain,
( ( ( sk70 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,3407]) ).
thf(11017,plain,
( ( sk70 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11016]) ).
thf(11030,plain,
sk70 != k1_xboole_0,
inference(simp,[status(thm)],[11017]) ).
thf(1351,axiom,
! [A: $i] :
( ( A @ v1_funct_1 )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(8409,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
=> ( A @ v1_funct_1 ) )
& ( ( A @ v1_funct_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
thf(7070,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k4_card_3 )
= ( B @ k4_card_3 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_pua2mss1) ).
thf(2005,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k4_card_3 )
= ( B @ k4_card_3 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24936,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk378 ) ),
inference(paramod_ordered,[status(thm)],[9625,15599]) ).
thf(24937,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk378 ),
inference(pattern_uni,[status(thm)],[24936:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relset_2 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relset_2 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(2054,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relset_2 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relset_2 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(4207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_partfun1) ).
thf(1948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(6890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1699,axiom,
! [A: $i] :
( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(10322,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_2_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( ( ( C @ k5_funct_5 @ k1_relat_1 )
= B )
& ( ( C @ k3_funct_5 @ k1_relat_1 )
= A ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_5) ).
thf(2096,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( ( ( C @ k5_funct_5 @ k1_relat_1 )
= B )
& ( ( C @ k3_funct_5 @ k1_relat_1 )
= A ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1539,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( E @ ( F @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(9403,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( E @ ( F @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(7485,plain,
( ~ ? [A: $i] :
( ? [B: $i] :
( ~ ? [C: $i] :
( ( C @ ( B @ ( A @ p1_s5_funct_2 ) ) )
& ( f3_s5_funct_2 @ ( C @ r2_hidden ) ) )
& ( f2_s5_funct_2 @ ( B @ r2_hidden ) ) )
& ( f1_s5_funct_2 @ ( A @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( f2_s5_funct_2 @ ( C @ r2_hidden ) )
& ( f1_s5_funct_2 @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) @ ( C @ ( B @ p1_s5_funct_2 ) ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(miniscope,[status(thm)],[7484]) ).
thf(7486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ k4_tarski ) @ ( sk375 @ k1_funct_1 ) @ ( C @ ( B @ p1_s5_funct_2 ) ) )
| ~ ( f2_s5_funct_2 @ ( C @ r2_hidden ) )
| ~ ( f1_s5_funct_2 @ ( B @ r2_hidden ) )
| ~ sk372 )
& ( ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( sk375 @ m2_relset_1 ) ) )
| ~ sk372 )
& ( ( f3_s5_funct_2 @ ( f2_s5_funct_2 @ ( f1_s5_funct_2 @ k2_zfmisc_1 ) @ ( sk375 @ v1_funct_2 ) ) )
| ~ sk372 )
& ( ( sk375 @ v1_funct_1 )
| ~ sk372 )
& ( sk372
| ~ ( A @ ( sk374 @ ( sk373 @ p1_s5_funct_2 ) ) )
| ~ ( f3_s5_funct_2 @ ( A @ r2_hidden ) ) )
& ( sk372
| ( f2_s5_funct_2 @ ( sk374 @ r2_hidden ) ) )
& ( sk372
| ( f1_s5_funct_2 @ ( sk373 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[7485]) ).
thf(7490,plain,
( sk372
| ( f2_s5_funct_2 @ ( sk374 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[7486]) ).
thf(816,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_2) ).
thf(5528,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(589,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(4458,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(883,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_relat_1) ).
thf(5881,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_partfun1) ).
thf(2665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_vectsp_1 ) ) )
= ( F @ ( E @ ( D @ g1_vectsp_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_vectsp_1) ).
thf(7650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_vectsp_1 ) ) )
= ( F @ ( E @ ( D @ g1_vectsp_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(679,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k1_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(4886,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k1_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(125,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ v1_funct_1 )
& ( A @ k5_funct_5 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_funct_5) ).
thf(2318,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ v1_funct_1 )
& ( A @ k5_funct_5 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1570,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(9563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(4456,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(3293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1593,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
thf(9651,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(25648,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3615,1900]) ).
thf(25649,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25648]) ).
thf(25650,plain,
k1_xboole_0 @ k2_relat_1 @ ( k1_xboole_0 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25649:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(30136,plain,
k1_xboole_0 @ ( k1_xboole_0 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(rewrite,[status(thm)],[25650,2819]) ).
thf(161,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2471,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(328,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3161,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_5) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ k3_funct_5 )
!= ( D @ k3_funct_5 ) )
| ( ( D @ k1_relat_1 )
!= ( B @ ( A @ k2_zfmisc_1 ) ) )
| ( ( C @ k1_relat_1 )
!= ( B @ ( A @ k2_zfmisc_1 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1903]) ).
thf(1905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( C = D )
| ( ( C @ k3_funct_5 )
!= ( D @ k3_funct_5 ) )
| ( ( D @ k1_relat_1 )
!= ( B @ ( A @ k2_zfmisc_1 ) ) )
| ( ( C @ k1_relat_1 )
!= ( B @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1904]) ).
thf(25327,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4850,1899]) ).
thf(25328,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25327]) ).
thf(25329,plain,
sk153 @ k1_relat_1 @ ( sk153 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25328:[bind(A,$thf( sk153 ))]]) ).
thf(26898,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,5034]) ).
thf(26899,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26898]) ).
thf(26914,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk384 ),
inference(simp,[status(thm)],[26899]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ r1_tarski ) )
& ( A @ ( A @ k1_sysrel @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_sysrel) ).
thf(2234,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ r1_tarski ) )
& ( A @ ( A @ k1_sysrel @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1715,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(10449,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(8505,plain,
( sk495
| ( f1_s7_funct_2 @ ( sk496 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[8499]) ).
thf(8789,plain,
( sk530
| ( sk533 @ ( sk531 @ p1_s1_funct_1 ) ) ),
inference(cnfConj,[status(thm)],[8785]) ).
thf(1645,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(9943,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1772,axiom,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ~ ( B @ ( C @ p1_s1_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) ) ) )
& ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( B @ ( C @ p1_s1_orders_1 ) )
& ~ ( C @ ( B @ p1_s1_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s1_orders_1 @ ( A @ r1_tarski ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s1_orders_1 ) )
& ( B @ ( A @ p1_s1_orders_1 ) ) )
=> ( C @ ( A @ p1_s1_orders_1 ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ p1_s1_orders_1 ) )
& ( B @ ( A @ p1_s1_orders_1 ) ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s1_orders_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ p1_s1_orders_1 ) )
& ( A != B ) ) )
& ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_orders_1) ).
thf(10814,plain,
( ( ! [A: $i] :
~ ( ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ~ ( B @ ( C @ p1_s1_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) ) ) )
& ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ~ ( B @ ( C @ p1_s1_orders_1 ) )
& ~ ( C @ ( B @ p1_s1_orders_1 ) )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s1_orders_1 @ ( A @ r1_tarski ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_orders_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s1_orders_1 ) )
& ( B @ ( A @ p1_s1_orders_1 ) ) )
=> ( C @ ( A @ p1_s1_orders_1 ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ p1_s1_orders_1 ) )
& ( B @ ( A @ p1_s1_orders_1 ) ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s1_orders_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_orders_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ p1_s1_orders_1 ) )
& ( A != B ) ) )
& ( f1_s1_orders_1 @ ( A @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2629,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1632,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(9858,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_relat_1) ).
thf(4859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(5165,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(7679,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(4688,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(893,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relset_1) ).
thf(5916,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1068,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( B @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(6806,plain,
! [A: $i] :
~ ! [B: $i] :
( ( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(7013,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(9777,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[9774]) ).
thf(9783,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ v1_funct_2 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[9777]) ).
thf(1507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ r1_tarski ) )
& ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( H @ ( F @ ( D @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ ( E @ ( C @ ( A @ k4_zfmisc_1 ) ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_mcart_1) ).
thf(9276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ r1_tarski ) )
& ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( H @ ( F @ ( D @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ ( E @ ( C @ ( A @ k4_zfmisc_1 ) ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(1432,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) )
= ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k8_setfam_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relset_2) ).
thf(8863,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) )
= ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k8_setfam_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_setfam_1 ) )
& ( B @ ( A @ r1_setfam_1 ) ) )
=> ( C @ ( A @ r1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_setfam_1) ).
thf(6115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_setfam_1 ) )
& ( B @ ( A @ r1_setfam_1 ) ) )
=> ( C @ ( A @ r1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(271,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t195_orders_1) ).
thf(2899,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1762,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(10736,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(1521,axiom,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(9317,plain,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r1_tarski ) )
=> ( ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_sysrel) ).
thf(4045,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r1_tarski ) )
=> ( ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(7085,plain,
f3_s8_funct_2 @ ( f2_s8_funct_2 @ ( f1_s8_funct_2 @ k2_zfmisc_1 ) @ ( sk328 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[7083]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2863,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k3_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(5514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k3_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(724,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(5111,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(628,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
& ( B @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_card_1) ).
thf(4671,plain,
! [A: $i] :
? [B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
& ( B @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(4672,plain,
! [A: $i] :
( ( A @ sk148 @ ( A @ r2_wellord2 ) )
& ( A @ sk148 @ v3_ordinal1 ) ),
inference(cnf,[status(esa)],[4671]) ).
thf(4673,plain,
! [A: $i] : ( A @ sk148 @ v3_ordinal1 ),
inference(cnfConj,[status(thm)],[4672]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_card_1) ).
thf(5748,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( B @ k1_tarski @ ( A @ r2_wellord2 ) ) )
& ( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1753,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(10704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(1574,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_mcart_1) ).
thf(9578,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = G ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(563,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(4377,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(622,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4630,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_relat_1) ).
thf(5446,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(2513,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( D @ ( E @ k5_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_finseq_2) ).
thf(1844,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( D @ ( E @ k5_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1845,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( D @ ( E @ k5_funcop_1 ) ) @ m2_finseq_1 ) )
| ~ ( B @ ( F @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1844]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ ( C @ k1_sysrel @ ( C @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k2_relat_1 @ k4_xboole_0 ) @ ( B @ r2_hidden ) ) )
| ( A = B ) ) )
& ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ k1_sysrel @ ( C @ k4_xboole_0 ) @ ( C @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_sysrel) ).
thf(5452,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ ( C @ k1_sysrel @ ( C @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k2_relat_1 @ k4_xboole_0 ) @ ( B @ r2_hidden ) ) )
| ( A = B ) ) )
& ( ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( C @ k1_sysrel @ ( C @ k4_xboole_0 ) @ ( C @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( C @ ( C @ k5_relat_1 ) )
= C ) )
=> ( ( ( C @ k1_sysrel @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_sysrel @ k1_relat_1 @ ( C @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1382,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_ordinal1) ).
thf(8593,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v3_ordinal1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_partfun1) ).
thf(5229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1636,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(9879,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(855,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(5716,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(373,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_partfun1) ).
thf(3376,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1693,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_subset_1) ).
thf(10287,plain,
? [A: $i] :
( ! [B: $i] :
( ( ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(10288,plain,
? [A: $i] :
( ! [B: $i] :
( ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(miniscope,[status(thm)],[10287]) ).
thf(10289,plain,
! [B: $i,A: $i] :
( ( ( sk702 @ ( B @ r2_hidden ) )
| ~ ( B @ p1_s1_subset_1 )
| ~ ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) )
& ( ( A @ p1_s1_subset_1 )
| ~ ( sk702 @ ( A @ r2_hidden ) ) )
& ( ( f1_s1_subset_1 @ ( A @ r2_hidden ) )
| ~ ( sk702 @ ( A @ r2_hidden ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( sk702 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[10288]) ).
thf(10290,plain,
f1_s1_subset_1 @ k1_zfmisc_1 @ ( sk702 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[10289]) ).
thf(1046,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r2_relat_2 ) )
<=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_2) ).
thf(6683,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r2_relat_2 ) ) )
& ( ( B @ ( A @ r2_relat_2 ) )
=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(6472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1581,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(9606,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_relat_1 @ ( C @ m1_eqrel_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_pua2mss1) ).
thf(4864,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_relat_1 @ ( C @ m1_eqrel_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) )
=> ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(5250,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(3842,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(25681,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3589,1900]) ).
thf(25682,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25681]) ).
thf(25683,plain,
sk81 @ k2_relat_1 @ ( sk81 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25682:[bind(A,$thf( sk81 ))]]) ).
thf(1077,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(6885,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(690,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4939,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(5478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_5) ).
thf(2060,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(545,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(4272,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(1438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_mcart_1) ).
thf(8890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(91,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_1 ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2143,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B
= ( A @ k2_funct_1 ) ) )
& ( ( B
= ( A @ k2_funct_1 ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_2) ).
thf(2012,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(5499,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1139,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(7196,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(230,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_partfun1) ).
thf(2732,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
~ ( A @ k1_relat_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k5_funct_5 )
= k1_xboole_0 )
& ( ( A @ k3_funct_5 )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_5) ).
thf(1941,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
~ ( A @ k1_relat_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k5_funct_5 )
= k1_xboole_0 )
& ( ( A @ k3_funct_5 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1747,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(10684,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1729,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(10572,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(4200,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(26029,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9314,1901]) ).
thf(26030,plain,
! [A: $i] :
( ( ( sk595 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26029]) ).
thf(26031,plain,
sk595 @ k1_relat_1 @ ( sk595 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26030:[bind(A,$thf( sk595 ))]]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(3949,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_mcart_1) ).
thf(7045,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relset_1) ).
thf(2518,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(25929,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8150,1901]) ).
thf(25930,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25929]) ).
thf(25931,plain,
sk455 @ k1_relat_1 @ ( sk455 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25930:[bind(A,$thf( sk455 ))]]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_ordinal1) ).
thf(4961,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_ordinal1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_sysrel) ).
thf(2386,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k1_sysrel @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1700,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_1_domain_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_domain_1) ).
thf(10333,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_1_domain_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(1673,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(10159,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_relset_2) ).
thf(7724,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) )
=> ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(2888,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(25666,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3002,1900]) ).
thf(25667,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25666]) ).
thf(25668,plain,
sk44 @ k2_relat_1 @ ( sk44 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25667:[bind(A,$thf( sk44 ))]]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(7832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(1145,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_5_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_domain_1) ).
thf(7228,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_5_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_mcart_1) ).
thf(2831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) )
=> ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1292,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(8039,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(2747,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(5235,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(4190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_pboole) ).
thf(3691,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1205,axiom,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_card_1) ).
thf(7568,plain,
! [A: $i] : ( A @ k2_card_1 @ ( k1_xboole_0 @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(411,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3554,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k13_finseq_1 ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1817]) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
| ~ ( A @ k13_finseq_1 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[1829]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pboole) ).
thf(5186,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1697,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(10307,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(3246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(583,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( B @ k1_sysrel @ ( A @ k1_sysrel @ r1_tarski ) ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( B @ k1_sysrel @ ( A @ k1_sysrel @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_sysrel) ).
thf(4437,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( B @ k1_sysrel @ ( A @ k1_sysrel @ r1_tarski ) ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( B @ k1_sysrel @ ( A @ k1_sysrel @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(8609,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk512 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk510 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk512 @ m2_relset_1 ) ) )
| ~ sk510 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk512 @ v1_funct_2 ) ) )
| ~ sk510 )
& ( ( sk512 @ v1_funct_1 )
| ~ sk510 )
& ( sk510
| ~ ( A @ ( sk511 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk510
| ( f1_s14_funct_2 @ ( sk511 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[8608]) ).
thf(8612,plain,
( sk510
| ( f1_s14_funct_2 @ ( sk511 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[8609]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 ) ) )
& ( ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( A @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_sysrel) ).
thf(3642,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 ) ) )
& ( ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( A @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_mcart_1) ).
thf(6762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1495,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(9214,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v1_relat_1 ) )
& ( ( A @ v1_relat_1 )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_5) ).
thf(2092,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k4_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_2) ).
thf(4905,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k4_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1579,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k13_finseq_1 @ ( A @ k13_finseq_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_finseq_1) ).
thf(9599,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k13_finseq_1 @ ( A @ k13_finseq_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_mcart_1) ).
thf(7971,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) )
=> ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) ) )
& ( ( E
= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( E = H ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(445,axiom,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pboole) ).
thf(3722,plain,
! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(8873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(1182,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_card_1) ).
thf(7443,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k2_card_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1868,plain,
! [A: $i] :
( ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1867]) ).
thf(1869,plain,
! [A: $i] :
( ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[1868]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_relset_1) ).
thf(5276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(3475,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1684,axiom,
! [A: $i] :
( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(10211,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_1_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(3026,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(2429,plain,
! [A: $i] : ( A @ sk26 @ v3_ordinal1 ),
inference(cnfConj,[status(thm)],[2428]) ).
thf(826,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t187_relat_1) ).
thf(5560,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(9815,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_mcart_1) ).
thf(6298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(11652,plain,
( ( ( sk397 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,3407]) ).
thf(11653,plain,
( ( sk397 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11652]) ).
thf(11674,plain,
sk397 != sk70,
inference(simp,[status(thm)],[11653]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1980,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(5203,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(940,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).
thf(6125,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(557,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_relat_1) ).
thf(4351,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(11206,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,8244]) ).
thf(11207,plain,
( ( sk470 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11206]) ).
thf(11213,plain,
sk470 != sk149,
inference(simp,[status(thm)],[11207]) ).
thf(1335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) ) ) )
& ( ( ( A @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_sysrel) ).
thf(8327,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( ( ( A @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) ) ) )
& ( ( ( A @ ( C @ r2_hidden ) )
& ( E @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ ( E @ r1_tarski ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ~ ( A @ ( D @ r2_hidden ) )
& ~ ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(1040,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(6653,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( B @ k9_relset_1 ) ) ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( D @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_partfun1) ).
thf(2322,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( B @ k9_relset_1 ) ) ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( D @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(8148,plain,
sk455 @ v1_finset_1,
inference(cnfConj,[status(thm)],[8146]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(7351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(9666,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(996,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(6436,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ m1_eqrel_1 ) )
& ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).
thf(8248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ m1_eqrel_1 ) )
& ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2545,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1652,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(10012,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(11624,plain,
( ( ( sk384 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,7497]) ).
thf(11625,plain,
( ( sk384 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11624]) ).
thf(11637,plain,
sk384 != sk376,
inference(simp,[status(thm)],[11625]) ).
thf(370,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v3_relat_1 )
<=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_funct_1) ).
thf(3359,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 ) )
=> ( A @ v3_relat_1 ) )
& ( ( A @ v3_relat_1 )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
<=> ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_card_1) ).
thf(3174,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
=> ? [C: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_pua2mss1) ).
thf(2044,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1411,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(8757,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1722,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_orders_1) ).
thf(10509,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
thf(4875,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(10608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(3715,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(135,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(2354,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1036,axiom,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(6632,plain,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(6633,plain,
! [A: $i] : ( A @ k1_card_1 @ v1_card_1 ),
inference(cnf,[status(esa)],[6632]) ).
thf(752,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(5223,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(841,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_sysrel) ).
thf(5633,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1728,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(10568,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(537,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ ( B @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k3_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(4225,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ ( B @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k3_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(11628,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,8244]) ).
thf(11629,plain,
( ( sk470 @ v1_xboole_0 )
!= ( sk384 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11628]) ).
thf(11636,plain,
sk470 != sk384,
inference(simp,[status(thm)],[11629]) ).
thf(1232,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(7720,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1610,axiom,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).
thf(9770,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(1396,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(8679,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(8464,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(5319,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1439,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(8893,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_5) ).
thf(2247,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(5147,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(284,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2948,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).
thf(6746,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) )
=> ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(9891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(439,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_partfun1) ).
thf(3697,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ k1_tarski @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_mcart_1) ).
thf(7466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ k1_tarski @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1555,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(9486,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_partfun1) ).
thf(5902,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k9_relset_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ r1_tarski ) )
=> ( ~ ( B @ ( A @ r2_wellord2 ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_card_1) ).
thf(7456,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ r1_tarski ) )
=> ( ~ ( B @ ( A @ r2_wellord2 ) )
& ( B @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1045,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(6679,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ~ ( C @ v2_funct_1 )
| ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
!= ( A @ k6_partfun1 ) )
| ( ( C @ k2_relat_1 )
!= B )
| ~ ( A @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1846]) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ v2_funct_1 )
| ~ ( A @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
!= ( A @ k6_partfun1 ) )
| ( ( C @ k2_relat_1 )
!= B ) ),
inference(lifteq,[status(thm)],[1847]) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ v2_funct_1 )
| ~ ( A @ ( B @ k2_relat_1 @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ k2_relat_1 @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( C
= ( B @ k2_funct_1 ) )
| ( ( B @ k2_relat_1 )
= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( C @ ( B @ ( A @ ( B @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_partfun1 ) ) ) ) ) )
!= ( A @ k6_partfun1 ) ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_partfun1) ).
thf(7779,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1654,axiom,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).
thf(10023,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ( C @ ( D @ ( F @ ( E @ k4_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_finseq_2) ).
thf(2113,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ( C @ ( D @ ( F @ ( E @ k4_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_pboole) ).
thf(6073,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1777,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(10885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(3491,plain,
! [A: $i] : ( A @ k1_pboole @ v3_relat_1 ),
inference(cnfConj,[status(thm)],[3489]) ).
thf(3493,plain,
! [A: $i] : ( A @ k1_pboole @ v3_relat_1 ),
inference(simp,[status(thm)],[3491]) ).
thf(1596,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(9675,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(967,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(6262,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1669,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(10128,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1164,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_realset1 ) ) )
<=> ( ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_realset1) ).
thf(7342,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) )
=> ( C @ ( B @ ( A @ r2_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_realset1 ) ) )
=> ( ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ m2_relset_1 ) ) )
& ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_2 ) ) )
& ( C @ k1_tarski @ ( A @ ( B @ k1_realset1 ) @ k4_xboole_0 ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ m1_realset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(1629,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_1_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_2) ).
thf(9851,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_1_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(2543,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(5998,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_relat_1) ).
thf(3356,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1115,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ k6_finseq_1 @ ( E @ k4_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_finseq_2) ).
thf(7067,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ k6_finseq_1 @ ( E @ k4_funcop_1 ) ) )
= ( C @ k6_finseq_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1016,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_domain_1) ).
thf(6526,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1529,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(9363,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2357,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(39,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 )
= ( A @ k2_funct_4 @ k3_funct_5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_5) ).
thf(1955,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 )
= ( A @ k2_funct_4 @ k3_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i,G: $i] :
~ ( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_mcart_1) ).
thf(7374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i,G: $i] :
~ ( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_partfun1) ).
thf(4538,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(25604,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7517,1900]) ).
thf(25605,plain,
! [A: $i] :
( ( ( sk378 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25604]) ).
thf(25606,plain,
sk378 @ k2_relat_1 @ ( sk378 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25605:[bind(A,$thf( sk378 ))]]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(4634,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( C @ ( B @ ( A @ k2_tarski ) @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_relat_1) ).
thf(5226,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1213,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(7612,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_mcart_1) ).
thf(5685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ? [E: $i] :
( ? [F: $i,G: $i,H: $i,I: $i] :
( ~ ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) )
= I )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k10_mcart_1 ) ) ) ) )
= H )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) )
= G )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_mcart_1 ) ) ) ) )
= F ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) ) )
& ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( E @ m1_subset_1 ) ) )
& ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(319,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(3117,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(259,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ v3_binop_1 ) )
=> ( ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(2860,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ v3_binop_1 ) )
=> ( ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(492,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3961,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(6467,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(983,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(6358,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(2892,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1879,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk7 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1874]) ).
thf(1881,plain,
! [B: $i,A: $i] :
( ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) )
!= ( A @ ( B @ sk7 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk7 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1879]) ).
thf(1092,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(6960,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(3914,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(7498,plain,
sk376 @ v1_finset_1,
inference(cnfConj,[status(thm)],[7496]) ).
thf(1594,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(9654,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( C @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( ( C @ ( D @ k5_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_5) ).
thf(4795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( C @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( ( C @ ( D @ k5_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(8151,plain,
sk455 @ v1_funct_1,
inference(cnfConj,[status(thm)],[8146]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(5596,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(3366,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_relat_1) ).
thf(2584,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(15300,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,6953]) ).
thf(15301,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15300]) ).
thf(15319,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk27 ),
inference(simp,[status(thm)],[15301]) ).
thf(10674,plain,
( sk745
| ( sk747 @ ( sk746 @ p1_s1_tarski ) ) ),
inference(cnfConj,[status(thm)],[10673]) ).
thf(11054,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,8244]) ).
thf(11055,plain,
( ( sk470 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11054]) ).
thf(11059,plain,
sk470 != sk27,
inference(simp,[status(thm)],[11055]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6992,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(1580,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(9601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(4414,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(434,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3684,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1648,axiom,
? [A: $i] :
! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0) ).
thf(9995,plain,
? [A: $i] :
! [B: $i] :
( ( ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_xboole_0 )
& ( f1_s1_xboole_0 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(15267,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,6422]) ).
thf(15268,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15267]) ).
thf(15283,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= sk149 ),
inference(simp,[status(thm)],[15268]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(6301,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1354,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(8431,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(1455,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_realset1) ).
thf(8987,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(3533,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1101,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(7007,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( ( B @ ( A @ k2_tarski ) @ ( C @ k1_funct_2 ) @ k1_card_1 )
= ( C @ k1_zfmisc_1 @ k1_card_1 ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( A @ k2_tarski ) @ ( C @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_5) ).
thf(3665,plain,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( ( B @ ( A @ k2_tarski ) @ ( C @ k1_funct_2 ) @ k1_card_1 )
= ( C @ k1_zfmisc_1 @ k1_card_1 ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( A @ k2_tarski ) @ ( C @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(6711,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1343,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(8360,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(1397,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_pboole) ).
thf(8681,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(1421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).
thf(8812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(25619,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10850,1900]) ).
thf(25620,plain,
! [A: $i] :
( ( ( sk777 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25619]) ).
thf(25621,plain,
sk777 @ k2_relat_1 @ ( sk777 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25620:[bind(A,$thf( sk777 ))]]) ).
thf(1119,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(7089,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
=> ~ ( B @ v3_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pboole) ).
thf(2924,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
=> ~ ( B @ v3_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(3478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(3956,plain,
( ! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 )
& ! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(miniscope,[status(thm)],[3955]) ).
thf(3957,plain,
! [B: $i,A: $i] :
( ( B @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3956]) ).
thf(3959,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[3957]) ).
thf(3960,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_funct_1 ),
inference(simp,[status(thm)],[3959]) ).
thf(20996,plain,
! [A: $i] : ( A @ k6_partfun1 @ v1_funct_1 ),
inference(rewrite,[status(thm)],[3960,1841]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(5939,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( D @ ( C @ k8_relat_1 ) )
= ( C @ ( A @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) )
& ( ( ( A @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_sysrel) ).
thf(4548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( D @ ( C @ k8_relat_1 ) )
= ( C @ ( A @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) )
& ( ( ( A @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1451,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(8973,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(23159,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk27 ) ),
inference(paramod_ordered,[status(thm)],[9625,15594]) ).
thf(23160,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= sk27 ),
inference(pattern_uni,[status(thm)],[23159:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_pboole ) )
= ( B @ ( A @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_pboole) ).
thf(3139,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_pboole ) )
= ( B @ ( A @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1765,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
<=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(10754,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k7_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ k5_relset_2 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( D @ ( B @ k5_relset_2 ) @ k1_funct_1 ) )
= ( A @ ( D @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_2) ).
thf(2626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ k5_relset_2 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( D @ ( B @ k5_relset_2 ) @ k1_funct_1 ) )
= ( A @ ( D @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1400,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(8698,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(636,axiom,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(4698,plain,
! [A: $i,B: $i] :
~ ( ( ( B @ ( A @ k2_xboole_0 ) @ k1_setfam_1 )
!= ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(7676,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(995,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(6425,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(10082,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(4851,plain,
sk153 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4849]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(6758,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(692,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_orders_1) ).
thf(4945,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(10364,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_partfun1) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1239,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_card_1) ).
thf(7764,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( A @ k2_card_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(9306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(2885,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(221,axiom,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(2696,plain,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(6041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1606,axiom,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).
thf(9760,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(3039,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(cnf,[status(esa)],[3038]) ).
thf(18811,plain,
! [A: $i] : ( A @ k6_partfun1 @ v1_relat_1 ),
inference(rewrite,[status(thm)],[3039,1841]) ).
thf(10507,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[10506]) ).
thf(10508,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[10507]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_sysrel) ).
thf(3171,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_relat_1) ).
thf(5777,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(7606,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_5) ).
thf(2078,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(577,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_domain_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_domain_1) ).
thf(4419,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_domain_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_partfun1) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1913,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 )
| ~ ( C @ v2_funct_1 )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1912]) ).
thf(22742,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_card_1 )
!= ( A @ k1_card_1 ) )
| ( k1_xboole_0 @ v1_card_1 ) ),
inference(paramod_ordered,[status(thm)],[7778,6633]) ).
thf(22743,plain,
k1_xboole_0 @ v1_card_1,
inference(pattern_uni,[status(thm)],[22742:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(6390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(3548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2194,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(11044,plain,
( ( ( sk455 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,8147]) ).
thf(11045,plain,
( ( sk455 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11044]) ).
thf(11050,plain,
sk455 != k1_xboole_0,
inference(simp,[status(thm)],[11045]) ).
thf(11679,plain,
! [A: $i] :
( ( A != sk455 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11050]) ).
thf(11680,plain,
! [A: $i] :
( ( A != sk455 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11679]) ).
thf(11681,plain,
( ~ ( sk2 @ ( sk455 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[11680:[bind(A,$thf( sk455 ))]]) ).
thf(1672,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_subset_1) ).
thf(10156,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2611,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2325,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1679,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(10193,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(1094,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r7_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_2) ).
thf(6980,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r7_relat_2 ) ) )
& ( ( B @ ( A @ r7_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_2) ).
thf(2209,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(6674,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[6673]) ).
thf(10636,plain,
! [B: $i,A: $i] :
( ( ( sk741 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
| ~ ( B @ ( A @ p1_s2_relset_1 ) )
| ~ ( f2_s2_relset_1 @ ( B @ m1_subset_1 ) )
| ~ ( f1_s2_relset_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ ( A @ p1_s2_relset_1 ) )
| ~ ( sk741 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
| ~ ( f2_s2_relset_1 @ ( B @ m1_subset_1 ) )
| ~ ( f1_s2_relset_1 @ ( A @ m1_subset_1 ) ) )
& ( f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( sk741 @ m2_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[10635]) ).
thf(10637,plain,
f2_s2_relset_1 @ ( f1_s2_relset_1 @ ( sk741 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[10636]) ).
thf(1321,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(8285,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(1780,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(10905,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(15257,plain,
! [A: $i] :
( ( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,6422]) ).
thf(15258,plain,
! [A: $i] :
( ( A @ k13_finseq_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[15257]) ).
thf(15277,plain,
! [A: $i] :
( ( A @ k13_finseq_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15258]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_domain_1) ).
thf(2997,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_5) ).
thf(5485,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(5332,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(1866,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1865]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ k1_card_1 ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_5) ).
thf(2658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ k1_card_1 ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(3929,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_relat_1) ).
thf(5258,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(3613,plain,
k1_xboole_0 @ v2_funct_1,
inference(cnfConj,[status(thm)],[3610]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ~ ( ! [D: $i] :
( ( D @ v3_ordinal1 )
=> ( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_ordinal1 ) ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ( A != k1_xboole_0 )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(6030,plain,
! [A: $i,B: $i] :
( ( B @ v3_ordinal1 )
=> ~ ( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ~ ( ! [D: $i] :
( ( D @ v3_ordinal1 )
=> ( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_ordinal1 ) ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ( A != k1_xboole_0 )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(5351,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(25362,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7649,1899]) ).
thf(25363,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25362]) ).
thf(25364,plain,
sk397 @ k1_relat_1 @ ( sk397 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25363:[bind(A,$thf( sk397 ))]]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_partfun1) ).
thf(2608,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_mcart_1) ).
thf(8337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(3911,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(11616,plain,
( ( ( sk384 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7571,7814]) ).
thf(11617,plain,
( ( sk384 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11616]) ).
thf(11639,plain,
sk384 != k4_numbers,
inference(simp,[status(thm)],[11617]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funct_2) ).
thf(2273,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10167,plain,
( ( f1_s1_pboole @ ( sk690 @ m1_pboole ) )
| ( ( sk689 @ f2_s1_pboole )
= k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[10164]) ).
thf(10169,plain,
( ( f1_s1_pboole @ ( sk690 @ m1_pboole ) )
| ( ( sk689 @ f2_s1_pboole )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[10167]) ).
thf(441,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( A @ ( B @ k5_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(3709,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( A @ ( B @ k5_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(6489,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B
= ( A @ k4_relat_1 ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(2251,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k4_relat_1 ) ) )
& ( ( B
= ( A @ k4_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1167,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(7359,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_sysrel) ).
thf(2406,plain,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(25598,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3830,1900]) ).
thf(25599,plain,
! [A: $i] :
( ( ( sk95 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25598]) ).
thf(25600,plain,
sk95 @ k2_relat_1 @ ( sk95 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25599:[bind(A,$thf( sk95 ))]]) ).
thf(746,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ ( A @ k3_xboole_0 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_2) ).
thf(5191,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ ( A @ k3_xboole_0 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( B @ ( A @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_relat_1) ).
thf(2811,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( B @ ( A @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1644,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_5_domain_1) ).
thf(9934,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_5_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(661,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_relat_1) ).
thf(4791,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(6003,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1064,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(6770,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(787,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(5368,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1550,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(9459,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(1741,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_6_domain_1) ).
thf(10648,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_6_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p2_s6_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(1852,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1851]) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( B = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1852]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_mcart_1) ).
thf(6910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(24024,plain,
! [B: $i,A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,6953]) ).
thf(24025,plain,
! [B: $i,A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24024]) ).
thf(24042,plain,
! [B: $i,A: $i] :
( ( A @ sk649 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[24025]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(5756,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1818,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k13_finseq_1 ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) ) ),
inference(cnfConj,[status(thm)],[1814]) ).
thf(1821,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(lifteq,[status(thm)],[1818]) ).
thf(1822,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk6 ) @ r2_hidden ) )
| ~ ( A @ ( A @ ( B @ sk5 ) @ m2_finseq_1 ) )
| ( B
= ( A @ k13_finseq_1 ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1621,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(9824,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( C = k1_xboole_0 ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(5087,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( ( C = k1_xboole_0 )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( C = k1_xboole_0 ) ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(88,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
& ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_finseq_2) ).
thf(2130,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
& ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(23996,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk593 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,9230]) ).
thf(23997,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk593 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[23996]) ).
thf(24048,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk593 ),
inference(simp,[status(thm)],[23997]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4495,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1416,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
thf(8781,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( C @ ( E @ r2_hidden ) )
<=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(10254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(9449,plain,
( sk606
| ( f1_s6_funct_2 @ ( sk607 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[9447]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(6694,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(5505,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k3_pboole ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_pboole) ).
thf(4969,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( B @ ( B @ ( A @ k3_pboole ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1385,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(8617,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(148,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ ( C @ k4_funcop_1 ) ) @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ ( C @ k5_relat_1 ) @ k4_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(2416,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ ( C @ k4_funcop_1 ) ) @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ ( C @ k5_relat_1 ) @ k4_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1490,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_domain_1) ).
thf(9179,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) )
=> ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) ) )
& ( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ k9_mcart_1 ) ) ) ) ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( D @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( E @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(1419,axiom,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_ordinal1) ).
thf(8805,plain,
! [A: $i] :
( ( A @ v3_ordinal1 )
=> ( A @ k3_tarski @ v3_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(4451,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pboole) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(7327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1600,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(9701,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ k4_card_3 @ r1_tarski ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pua2mss1) ).
thf(2399,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ k4_card_3 @ r1_tarski ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(7399,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1671,axiom,
( ( ! [A: $i] :
( ( f2_s2_xboole_0 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s2_xboole_0 ) )
& ! [A: $i] :
( ( f1_s2_xboole_0 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s2_xboole_0 ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_xboole_0) ).
thf(10137,plain,
( ( ! [A: $i] :
( ( ( A @ p1_s2_xboole_0 )
=> ( f2_s2_xboole_0 @ ( A @ r2_hidden ) ) )
& ( ( f2_s2_xboole_0 @ ( A @ r2_hidden ) )
=> ( A @ p1_s2_xboole_0 ) ) )
& ! [A: $i] :
( ( ( A @ p1_s2_xboole_0 )
=> ( f1_s2_xboole_0 @ ( A @ r2_hidden ) ) )
& ( ( f1_s2_xboole_0 @ ( A @ r2_hidden ) )
=> ( A @ p1_s2_xboole_0 ) ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(1298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(8102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(12584,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk561 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,8985]) ).
thf(12585,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk561 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12584]) ).
thf(12601,plain,
sk595 != sk561,
inference(simp,[status(thm)],[12585]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_mcart_1) ).
thf(9289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_relat_1) ).
thf(4619,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(10935,plain,
( ( ( sk70 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,3407]) ).
thf(10936,plain,
( ( sk70 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10935]) ).
thf(10937,plain,
sk70 != sk27,
inference(simp,[status(thm)],[10936]) ).
thf(1305,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(8172,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_2) ).
thf(2956,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1603,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(9718,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_partfun1) ).
thf(2081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( C @ ( B @ ( A @ ( D @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ ( D @ ( C @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_mcart_1) ).
thf(7256,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( C @ ( B @ ( A @ ( D @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ ( D @ ( C @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_pboole) ).
thf(3694,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k5_pboole ) ) )
= ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1345,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(8369,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(6305,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(25989,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4850,1901]) ).
thf(25990,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25989]) ).
thf(25991,plain,
sk153 @ k1_relat_1 @ ( sk153 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25990:[bind(A,$thf( sk153 ))]]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(5162,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3497,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1647,axiom,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(9962,plain,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(1559,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_0_relset_2 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_2) ).
thf(9510,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_0_relset_2 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(210,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(2648,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(25312,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4708,1899]) ).
thf(25313,plain,
! [A: $i] :
( ( ( sk149 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25312]) ).
thf(25314,plain,
sk149 @ k1_relat_1 @ ( sk149 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25313:[bind(A,$thf( sk149 ))]]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(3585,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1537,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(9393,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setfam_1) ).
thf(6018,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_setfam_1 ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1615,axiom,
! [A: $i] :
( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(9792,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(8203,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk462 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[8201]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(3598,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1545,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(9434,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(723,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ v3_relat_1 ) )
=> ( C @ v3_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_pboole) ).
thf(5109,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
& ( B @ v3_relat_1 ) )
=> ( C @ v3_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_realset1) ).
thf(2462,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m4_realset1 ) )
=> ~ ( B @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(711,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_relat_1) ).
thf(5040,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1763,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(10738,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(1327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(8304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(7039,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_mcart_1) ).
thf(7747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_partfun1) ).
thf(3149,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(3529,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(6521,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(7157,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_sysrel) ).
thf(2362,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) )
& ( ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_sysrel @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( B @ ( A @ r1_ordinal1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(5549,plain,
! [A: $i,B: $i] :
( ( ( B @ v3_ordinal1 )
& ( A @ v3_ordinal1 ) )
=> ( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_ordinal1 ) ) )
& ( ( B @ ( A @ r1_ordinal1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(11166,plain,
( ( ( sk593 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,9230]) ).
thf(11167,plain,
( ( sk593 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11166]) ).
thf(11172,plain,
sk593 != k1_xboole_0,
inference(simp,[status(thm)],[11167]) ).
thf(26908,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,5034]) ).
thf(26909,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26908]) ).
thf(26917,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk397 ),
inference(simp,[status(thm)],[26909]) ).
thf(218,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(2680,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(9419,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk604 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
| ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk602 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk604 @ m2_relset_1 ) ) )
| ~ sk602 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk604 @ v1_funct_2 ) ) )
| ~ sk602 )
& ( ( sk604 @ v1_funct_1 )
| ~ sk602 )
& ( sk602
| ~ ( A @ ( sk603 @ p1_s3_funct_2 ) )
| ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk602
| ( f1_s3_funct_2 @ ( sk603 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[9418]) ).
thf(9421,plain,
( sk602
| ( f1_s3_funct_2 @ ( sk603 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[9419]) ).
thf(25986,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3002,1901]) ).
thf(25987,plain,
! [A: $i] :
( ( ( sk44 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25986]) ).
thf(25988,plain,
sk44 @ k1_relat_1 @ ( sk44 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25987:[bind(A,$thf( sk44 ))]]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(3351,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(26894,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,5034]) ).
thf(26895,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26894]) ).
thf(26912,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk27 ),
inference(simp,[status(thm)],[26895]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(7520,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k4_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k4_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_finseq_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_finseq_2) ).
thf(4446,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_finseq_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1494,axiom,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_orders_1) ).
thf(9211,plain,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(26001,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3589,1901]) ).
thf(26002,plain,
! [A: $i] :
( ( ( sk81 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[26001]) ).
thf(26003,plain,
sk81 @ k1_relat_1 @ ( sk81 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26002:[bind(A,$thf( sk81 ))]]) ).
thf(1405,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(8721,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(813,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(5517,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(2494,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1176,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(7406,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(4570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(748,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(5196,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relset_1) ).
thf(2917,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1613,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(9787,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(205,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_1) ).
thf(2623,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1485,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(9162,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(1544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(9427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(1532,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_2) ).
thf(9378,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(381,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v3_relat_1 )
<=> ( ( ( A @ k2_relat_1 )
= ( k1_xboole_0 @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_pboole) ).
thf(3420,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( ( A @ k2_relat_1 )
= ( k1_xboole_0 @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( A @ v3_relat_1 ) )
& ( ( A @ v3_relat_1 )
=> ( ( ( A @ k2_relat_1 )
= ( k1_xboole_0 @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(8209,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pboole) ).
thf(3987,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( G @ ( D @ ( F @ k5_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_finseq_2) ).
thf(2008,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( G @ ( D @ ( F @ k5_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(884,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(5884,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1329,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k3_tarski @ ( C @ k9_relat_1 ) @ ( A @ ( C @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k5_setfam_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_2) ).
thf(8309,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k3_tarski @ ( C @ k9_relat_1 ) @ ( A @ ( C @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k5_setfam_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(7955,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(25321,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4218,1899]) ).
thf(25322,plain,
! [A: $i] :
( ( ( sk119 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25321]) ).
thf(25323,plain,
sk119 @ k1_relat_1 @ ( sk119 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25322:[bind(A,$thf( sk119 ))]]) ).
thf(1049,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(6703,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_2) ).
thf(3992,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(6924,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(86,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2123,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(4125,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1338,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(8341,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2374,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(7048,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1274,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(7946,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1142,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(7216,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(117,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2287,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= B )
& ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ k1_sysrel )
= ( B @ k1_sysrel ) ) )
& ( ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= B )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( A @ k1_sysrel )
= ( B @ k1_sysrel ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_sysrel) ).
thf(2102,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= B )
& ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ k1_sysrel )
= ( B @ k1_sysrel ) ) )
& ( ( ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= B )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( A @ k1_sysrel )
= ( B @ k1_sysrel ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(6055,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(17067,plain,
! [A: $i] :
( ( ( sk2 @ ( sk4 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( A @ r2_hidden ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[1788,10469]) ).
thf(17068,plain,
! [A: $i] :
( ( ( sk2 @ ( sk4 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( A @ r2_hidden ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[17067]) ).
thf(17086,plain,
! [A: $i] :
( ( sk2 != k1_xboole_0 )
| ( sk4 != A )
| ~ sk3 ),
inference(simp,[status(thm)],[17068]) ).
thf(17091,plain,
( ( sk2 != k1_xboole_0 )
| ~ sk3 ),
inference(simp,[status(thm)],[17086]) ).
thf(1283,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(7991,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(1463,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(9034,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(7126,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(4792,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4791]) ).
thf(14030,plain,
( ( k1_xboole_0 @ k6_partfun1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[4792,1841]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(4014,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(4472,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1437,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(8886,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(3860,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1618,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(9806,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(5971,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_2) ).
thf(6997,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(6007,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_2) ).
thf(7868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B @ v1_setfam_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_eqrel_1) ).
thf(6439,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1066,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ p1_s6_domain_1 )
<=> ( B @ p2_s6_domain_1 ) ) )
=> ( ( A @ a_1_5_domain_1 )
= ( A @ a_1_6_domain_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s6_domain_1) ).
thf(6786,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p2_s6_domain_1 )
=> ( B @ p1_s6_domain_1 ) )
& ( ( B @ p1_s6_domain_1 )
=> ( B @ p2_s6_domain_1 ) ) ) )
=> ( ( A @ a_1_5_domain_1 )
= ( A @ a_1_6_domain_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(664,axiom,
! [A: $i] :
( ( A @ v1_card_1 )
<=> ? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ( B @ ( C @ r2_wellord2 ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ( A = B )
& ( B @ v3_ordinal1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_card_1) ).
thf(4809,plain,
! [A: $i] :
( ( ? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ( B @ ( C @ r2_wellord2 ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ( A = B )
& ( B @ v3_ordinal1 ) )
=> ( A @ v1_card_1 ) )
& ( ( A @ v1_card_1 )
=> ? [B: $i] :
( ! [C: $i] :
( ( C @ v3_ordinal1 )
=> ( ( B @ ( C @ r2_wellord2 ) )
=> ( C @ ( B @ r1_ordinal1 ) ) ) )
& ( A = B )
& ( B @ v3_ordinal1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
<=> ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_card_1) ).
thf(2983,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) ) )
& ( ( B @ k1_card_1 @ ( A @ k1_card_1 @ r1_tarski ) )
=> ? [C: $i] :
( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= B )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(25669,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4850,1900]) ).
thf(25670,plain,
! [A: $i] :
( ( ( sk153 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25669]) ).
thf(25671,plain,
sk153 @ k2_relat_1 @ ( sk153 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25670:[bind(A,$thf( sk153 ))]]) ).
thf(24030,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk431 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,7987]) ).
thf(24031,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk431 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24030]) ).
thf(24039,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk431 ),
inference(simp,[status(thm)],[24031]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k7_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(5004,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k7_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(7231,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(2587,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1237,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(7744,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(765,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_card_1) ).
thf(5268,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) )
& ( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(9318,plain,
! [A: $i] : ( A @ k2_card_1 @ v1_card_1 ),
inference(cnf,[status(esa)],[9317]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_2) ).
thf(4596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ~ ( B @ v2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_pboole) ).
thf(3264,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v3_relat_1 )
=> ~ ( B @ v2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r2_wellord2 ) )
& ( C @ ( A @ r2_wellord2 ) )
& ( D @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_card_1) ).
thf(5537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r2_wellord2 ) )
& ( C @ ( A @ r2_wellord2 ) )
& ( D @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1713,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(10443,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_partfun1) ).
thf(6050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(2522,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_partfun1) ).
thf(5430,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(11198,plain,
( ( ( sk149 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,3407]) ).
thf(11199,plain,
( ( sk149 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11198]) ).
thf(11219,plain,
sk149 != sk70,
inference(simp,[status(thm)],[11199]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(5764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_pboole) ).
thf(4843,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(24018,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk470 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,8244]) ).
thf(24019,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk470 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24018]) ).
thf(24046,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk470 ),
inference(simp,[status(thm)],[24019]) ).
thf(5477,plain,
sk180 @ v1_funct_1,
inference(cnfConj,[status(thm)],[5474]) ).
thf(1724,axiom,
! [A: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ( C @ p1_s2_subset_1 ) ) )
& ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
<=> ( C @ p1_s2_subset_1 ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_subset_1) ).
thf(10515,plain,
! [A: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ p1_s2_subset_1 )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C @ p1_s2_subset_1 ) ) ) )
& ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ p1_s2_subset_1 )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( C @ p1_s2_subset_1 ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(25992,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9011,1901]) ).
thf(25993,plain,
! [A: $i] :
( ( ( sk567 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25992]) ).
thf(25994,plain,
sk567 @ k1_relat_1 @ ( sk567 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25993:[bind(A,$thf( sk567 ))]]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(6226,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1028,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_pboole) ).
thf(6580,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(9070,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(5247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1578,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).
thf(9596,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(25336,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7988,1899]) ).
thf(25337,plain,
! [A: $i] :
( ( ( sk431 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k1_relat_1 @ ( A @ k1_sysrel @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25336]) ).
thf(25338,plain,
sk431 @ k1_relat_1 @ ( sk431 @ k1_sysrel @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25337:[bind(A,$thf( sk431 ))]]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_2) ).
thf(4367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(896,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(5926,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
<=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_card_1) ).
thf(3062,plain,
! [A: $i,B: $i] :
( ( ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) )
=> ( B @ ( A @ r2_wellord2 ) ) )
& ( ( B @ ( A @ r2_wellord2 ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_card_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_funct_2) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1287,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(8019,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(1353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_2) ).
thf(8424,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funct_2) ).
thf(6590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( E @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( E @ ( D @ ( B @ ( A @ k9_relset_1 ) ) ) @ k1_funct_1 ) )
= ( C @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1317,axiom,
k1_xboole_0 @ v3_ordinal1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_ordinal1) ).
thf(8277,plain,
k1_xboole_0 @ v3_ordinal1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g3_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g3_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_vectsp_1) ).
thf(8002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g3_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g3_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) @ m1_pboole ) )
& ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) @ v2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_pboole) ).
thf(2040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( D @ v2_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) @ m1_pboole ) )
& ( D @ ( C @ ( B @ ( A @ k8_pboole ) ) ) @ v2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(7772,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(850,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ k1_relat_1 )
= ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(5700,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ k1_relat_1 )
= ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(7323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k3_mcart_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_mcart_1) ).
thf(6535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k3_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(7433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ ( D @ k4_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_finseq_2) ).
thf(4029,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ ( D @ k4_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1258,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(7851,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(6627,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( B @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( C @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( C @ ( D @ k3_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( A @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_5) ).
thf(4051,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( B @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( C @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( C @ ( D @ k3_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( A @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1770,axiom,
! [A: $i] : ( A @ k13_finseq_1 @ ( k1_xboole_0 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_finseq_1) ).
thf(10809,plain,
! [A: $i] : ( A @ k13_finseq_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1387,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(8653,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(25701,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7649,1900]) ).
thf(25702,plain,
! [A: $i] :
( ( ( sk397 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25701]) ).
thf(25703,plain,
sk397 @ k2_relat_1 @ ( sk397 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25702:[bind(A,$thf( sk397 ))]]) ).
thf(11202,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4710,7497]) ).
thf(11203,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk149 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11202]) ).
thf(11214,plain,
sk376 != sk149,
inference(simp,[status(thm)],[11203]) ).
thf(1136,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
<=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_2) ).
thf(7184,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) )
=> ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) ) )
& ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1311,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( C @ ( B @ ( A @ k3_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_domain_1) ).
thf(8207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( C @ ( B @ ( A @ k3_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funcop_1) ).
thf(5709,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1364,axiom,
! [A: $i] :
( ( A @ v1_int_1 )
<=> ( k4_numbers @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_int_1) ).
thf(8484,plain,
! [A: $i] :
( ( ( k4_numbers @ ( A @ r2_hidden ) )
=> ( A @ v1_int_1 ) )
& ( ( A @ v1_int_1 )
=> ( k4_numbers @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(12576,plain,
( ( ( sk595 @ v1_xboole_0 )
!= ( sk594 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9315,9270]) ).
thf(12577,plain,
( ( sk595 @ v1_xboole_0 )
!= ( sk594 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12576]) ).
thf(12605,plain,
sk595 != sk594,
inference(simp,[status(thm)],[12577]) ).
thf(768,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(5290,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(533,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_sysrel) ).
thf(4210,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(580,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(4427,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(6735,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(722,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(5105,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(8999,plain,
! [A: $i] :
( ( ( ( A @ ( sk566 @ k1_funct_1 ) )
= ( A @ f3_s2_funct_2 ) )
| ~ ( f1_s2_funct_2 @ ( A @ r2_hidden ) )
| ~ sk564 )
& ( ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( sk566 @ m2_relset_1 ) ) )
| ~ sk564 )
& ( ( f2_s2_funct_2 @ ( f1_s2_funct_2 @ ( sk566 @ v1_funct_2 ) ) )
| ~ sk564 )
& ( ( sk566 @ v1_funct_1 )
| ~ sk564 )
& ( sk564
| ~ ( f2_s2_funct_2 @ ( sk565 @ f3_s2_funct_2 @ r2_hidden ) ) )
& ( sk564
| ( f1_s2_funct_2 @ ( sk565 @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[8998]) ).
thf(9002,plain,
( sk564
| ( f1_s2_funct_2 @ ( sk565 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[8999]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(5462,plain,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(11006,plain,
! [A: $i] :
( ( A != k4_numbers )
| ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,7814]) ).
thf(11007,plain,
( ~ ( k1_xboole_0 @ v1_xboole_0 )
| ~ ( sk2 @ ( k4_numbers @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[11006:[bind(A,$thf( k4_numbers ))]]) ).
thf(11521,plain,
( ~ $true
| ~ ( sk2 @ ( k4_numbers @ r2_hidden ) )
| sk3 ),
inference(rewrite,[status(thm)],[11007,3611]) ).
thf(11522,plain,
( ~ ( sk2 @ ( k4_numbers @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11521]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( D
!= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_mcart_1) ).
thf(2704,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ! [D: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_subset_1 ) )
=> ( ( D
!= ( D @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
& ( D
!= ( D @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) ) ) ) )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(10472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(1789,plain,
sk1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( sk2 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1786]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(5867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(337,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(3196,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1888]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(3030,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(11654,plain,
( ( ( sk592 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,9226]) ).
thf(11655,plain,
( ( sk592 @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11654]) ).
thf(11668,plain,
sk592 != sk397,
inference(simp,[status(thm)],[11655]) ).
thf(1273,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_4_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_domain_1) ).
thf(7943,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_4_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(6398,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(11018,plain,
( ( ( sk431 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3611,7987]) ).
thf(11019,plain,
( ( sk431 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11018]) ).
thf(11028,plain,
sk431 != k1_xboole_0,
inference(simp,[status(thm)],[11019]) ).
thf(1033,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(6612,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(11497,plain,
( ( ( sk470 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,8244]) ).
thf(11498,plain,
( ( sk470 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11497]) ).
thf(11509,plain,
sk470 != sk378,
inference(simp,[status(thm)],[11498]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(2668,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(3045,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(8706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(1540,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(9409,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_partfun1) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_setfam_1) ).
thf(6273,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(5322,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(5440,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ m1_pboole ) )
<=> ( ( B @ k1_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pboole) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= A )
=> ( A @ ( B @ m1_pboole ) ) )
& ( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1686,axiom,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).
thf(10224,plain,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).
thf(7525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(26900,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,5034]) ).
thf(26901,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[26900]) ).
thf(26913,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk378 ),
inference(simp,[status(thm)],[26901]) ).
thf(1250,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pua2mss1 ) ) @ m1_eqrel_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_pua2mss1) ).
thf(7819,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pua2mss1 ) ) @ m1_eqrel_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(6503,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_card_1) ).
thf(2549,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(10086,plain,
? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_relset_1 ) )
& ( f2_s1_relset_1 @ ( C @ r2_hidden ) )
& ( f1_s1_relset_1 @ ( B @ r2_hidden ) ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( A @ m2_relset_1 ) ) ) ),
inference(miniscope,[status(thm)],[10085]) ).
thf(10087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk679 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
| ~ ( D @ ( C @ p1_s1_relset_1 ) )
| ~ ( f2_s1_relset_1 @ ( D @ r2_hidden ) )
| ~ ( f1_s1_relset_1 @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ p1_s1_relset_1 ) )
| ~ ( sk679 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f2_s1_relset_1 @ ( B @ r2_hidden ) )
| ~ ( sk679 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( f1_s1_relset_1 @ ( A @ r2_hidden ) )
| ~ ( sk679 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( sk679 @ m2_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[10086]) ).
thf(10092,plain,
f2_s1_relset_1 @ ( f1_s1_relset_1 @ ( sk679 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[10087]) ).
thf(474,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_partfun1) ).
thf(3869,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_relat_1) ).
thf(5581,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k8_relat_1 ) @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_relat_1) ).
thf(4395,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k8_relat_1 ) @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(7694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(9441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(5269,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) )
& ! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[5268]) ).
thf(5270,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( B @ r2_wellord2 ) )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) ) ),
inference(cnf,[status(esa)],[5269]) ).
thf(5272,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[5270]) ).
thf(5274,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[5272]) ).
thf(5275,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r2_wellord2 ),
inference(simp,[status(thm)],[5274]) ).
thf(1394,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(8675,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_mcart_1) ).
thf(6874,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1567,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(9547,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(11229,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2440,9270]) ).
thf(11230,plain,
( ( sk594 @ v1_xboole_0 )
!= ( sk27 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11229]) ).
thf(11236,plain,
sk594 != sk27,
inference(simp,[status(thm)],[11230]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
<=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_1) ).
thf(5945,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(6190,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(87,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( A @ k1_card_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_finseq_1) ).
thf(2127,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( A @ k1_card_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(9357,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(25607,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8150,1900]) ).
thf(25608,plain,
! [A: $i] :
( ( ( sk455 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( A @ k2_relat_1 @ ( A @ k1_sysrel @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25607]) ).
thf(25609,plain,
sk455 @ k2_relat_1 @ ( sk455 @ k1_sysrel @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[25608:[bind(A,$thf( sk455 ))]]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(3543,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1358,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(8444,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(5151,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ r2_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_pboole) ).
thf(5806,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
& ( D @ ( C @ ( A @ r2_pboole ) ) )
& ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_relat_1) ).
thf(3411,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_funcop_1) ).
thf(3772,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_partfun1) ).
thf(5061,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(908,axiom,
! [A: $i] :
( ( A @ k1_pboole )
= ( k1_xboole_0 @ ( A @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pboole) ).
thf(5975,plain,
! [A: $i] :
( ( A @ k1_pboole )
= ( k1_xboole_0 @ ( A @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(4987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1254,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(7829,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3817,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(3020,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k8_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(4239,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k8_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k8_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(7493,plain,
( sk372
| ( f1_s5_funct_2 @ ( sk373 @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[7486]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = G ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_mcart_1) ).
thf(7708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
=> ( D = G ) ) ) ) )
=> ( ( D
= ( E @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(18178,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1929,7933]) ).
thf(18179,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[18178]) ).
thf(18200,plain,
! [B: $i,A: $i] :
( ( A @ k6_finseq_1 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[18179]) ).
thf(29596,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[18200,10644]) ).
thf(1476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
<=> ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_mcart_1) ).
thf(9110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
=> ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) ) )
& ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
=> ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(863,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( B @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funcop_1) ).
thf(5768,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( B @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_domain_1) ).
thf(7025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
<=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_mcart_1) ).
thf(6595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) )
& ( ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(11475,plain,
! [A: $i] :
( ( A != sk376 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11029]) ).
thf(11476,plain,
! [A: $i] :
( ( A != sk376 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[11475]) ).
thf(11477,plain,
( ~ ( sk2 @ ( sk376 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[11476:[bind(A,$thf( sk376 ))]]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(4659,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
=> ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(1924,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) )
| ~ ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1923]) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) ) ),
inference(lifteq,[status(thm)],[1924]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( F @ ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ r2_hidden ) )
& ( E @ ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ r2_hidden ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_mcart_1) ).
thf(4713,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( G @ r2_hidden ) )
=> ( ( F @ ( G @ ( C @ ( B @ ( A @ k7_mcart_1 ) ) ) @ r2_hidden ) )
& ( E @ ( G @ ( C @ ( B @ ( A @ k6_mcart_1 ) ) ) @ r2_hidden ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ k5_mcart_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(5468,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(487,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] : ( A @ ( B @ m4_realset1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m4_realset1) ).
thf(3939,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] : ( A @ ( B @ m4_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(3740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1628,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(9848,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(3076,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1556,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(9489,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(1876,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( A @ k1_relat_1 @ ( A @ ( B @ sk7 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1874]) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( A @ k1_relat_1 @ ( A @ ( B @ sk7 ) @ r2_hidden ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1876]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( A @ ( B @ k1_tarski @ k1_funct_2 ) @ k1_card_1 ) )
& ( A @ ( B @ k1_tarski @ k1_funct_2 ) @ ( A @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_5) ).
thf(4691,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( A @ ( B @ k1_tarski @ k1_funct_2 ) @ k1_card_1 ) )
& ( A @ ( B @ k1_tarski @ k1_funct_2 ) @ ( A @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(3492,plain,
! [A: $i] : ( A @ k1_pboole @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[3489]) ).
thf(3494,plain,
! [A: $i] : ( A @ k1_pboole @ v1_funct_1 ),
inference(simp,[status(thm)],[3492]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_relat_1) ).
thf(4345,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1204,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ r5_pboole ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_pboole) ).
thf(7563,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) )
=> ( C @ ( B @ ( A @ r5_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r5_pboole ) ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1430,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ a_3_8_domain_1 ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_domain_1) ).
thf(8857,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ a_3_8_domain_1 ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(6658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1173,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
<=> ( B
= ( A @ k2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(7392,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k2_subset_1 ) )
=> ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) )
& ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B
= ( A @ k2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( C @ ( B @ k4_tarski ) @ ( D @ ( A @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_mcart_1) ).
thf(8978,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( C @ ( B @ k4_tarski ) @ ( D @ ( A @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(1691,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
~ ( ( B
= ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_mcart_1) ).
thf(10276,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
~ ( ( B
= ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_relat_1) ).
thf(4221,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1366,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_relset_2 ) ) @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_relset_2) ).
thf(8493,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_relset_2 ) ) @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(6423,plain,
! [A: $i] : ( A @ k13_finseq_1 @ v1_fraenkel ),
inference(cnfConj,[status(thm)],[6421]) ).
thf(6424,plain,
! [A: $i] : ( A @ k13_finseq_1 @ v1_fraenkel ),
inference(simp,[status(thm)],[6423]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(7367,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(8245,plain,
sk470 @ v1_setfam_1,
inference(cnfConj,[status(thm)],[8243]) ).
thf(743,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ k1_realset1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_realset1) ).
thf(5183,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ k1_realset1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(28467,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,7149]) ).
thf(28468,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk397 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[28467]) ).
thf(28472,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk397 ),
inference(simp,[status(thm)],[28468]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(4533,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(3526,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1754,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(10706,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(1307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_domain_1) ).
thf(8184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2640,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = H ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_mcart_1) ).
thf(8950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = H ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k9_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(11648,plain,
( ( ( sk397 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7648,7814]) ).
thf(11649,plain,
( ( sk397 @ v1_xboole_0 )
!= ( k4_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11648]) ).
thf(11675,plain,
sk397 != k4_numbers,
inference(simp,[status(thm)],[11649]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(6173,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(1758,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_realset1) ).
thf(10723,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(7531,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(4702,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(821,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m4_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_realset1) ).
thf(5542,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m4_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1668,axiom,
! [A: $i] :
( ( a_0_4_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_4_domain_1) ).
thf(10118,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_4_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_4_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s10_domain_1 )
& ( A = B )
& ( f1_s10_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_5) ).
thf(4627,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1375,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = J ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_mcart_1) ).
thf(8553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( D @ ( J @ m1_subset_1 ) )
=> ( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
=> ( E = J ) ) ) ) ) )
=> ( ( E
= ( F @ ( D @ ( C @ ( B @ ( A @ k11_mcart_1 ) ) ) ) ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(10187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ k5_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(2563,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(266,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( E @ ( A @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( E @ ( B @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funcop_1) ).
thf(2881,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( E @ ( A @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( E @ ( B @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(911,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r5_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_2) ).
thf(5986,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r5_relat_2 ) ) )
& ( ( B @ ( A @ r5_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(5494,plain,
! [A: $i] : ( A @ sk181 @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[5492]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_funct_5) ).
thf(3299,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k1_funct_2 ) @ k1_card_1 )
= ( C @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ k1_card_1 ) )
& ( C @ ( B @ k1_funct_2 ) @ ( C @ ( A @ k1_funct_2 ) @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k1_funct_2 ) @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1565,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(9536,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pboole) ).
thf(6842,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ k4_relat_1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_relat_1) ).
thf(2206,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k4_relat_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(6733,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( B @ ( A @ k2_enumset1 ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(652,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4767,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(7056,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(9775,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[9774]) ).
thf(9784,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk650 @ m2_relset_1 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[9775]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1778,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(10900,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(1425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(8829,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(7861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(12486,plain,
! [A: $i] :
( ( A != sk593 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[1795,11172]) ).
thf(12487,plain,
! [A: $i] :
( ( A != sk593 )
| ~ ( sk2 @ ( A @ r2_hidden ) )
| sk3 ),
inference(simp,[status(thm)],[12486]) ).
thf(12488,plain,
( ~ ( sk2 @ ( sk593 @ r2_hidden ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[12487:[bind(A,$thf( sk593 ))]]) ).
thf(1535,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ r1_xboole_0 ) )
=> ( ~ ( F @ ( C @ r1_xboole_0 ) )
& ~ ( E @ ( B @ r1_xboole_0 ) )
& ~ ( D @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_mcart_1) ).
thf(9385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ r1_xboole_0 ) )
=> ( ~ ( F @ ( C @ r1_xboole_0 ) )
& ~ ( E @ ( B @ r1_xboole_0 ) )
& ~ ( D @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(4742,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(762,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( E @ ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( E @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(5255,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( E @ ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( E @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(2438,plain,
sk27 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2436]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2238,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).
thf(6575,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(684,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= B ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(4908,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= B ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1917,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ m2_finseq_1 ) )
| ~ ( B @ ( F @ m2_finseq_1 ) )
| ~ ( A @ ( E @ m2_finseq_1 ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( C @ v1_xboole_0 )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1916]) ).
thf(1764,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(10745,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_mcart_1) ).
thf(6404,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(361,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3316,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_relat_1) ).
thf(2351,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1511,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(9286,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(338,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
<=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(3200,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v1_finset_1 )
=> ( A @ k1_relat_1 @ v1_finset_1 ) )
& ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_2) ).
thf(2191,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1649,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(10002,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(11481,plain,
( ( ( sk594 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7515,9270]) ).
thf(11482,plain,
( ( sk594 @ v1_xboole_0 )
!= ( sk378 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11481]) ).
thf(11511,plain,
sk594 != sk378,
inference(simp,[status(thm)],[11482]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(6739,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3933,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_sysrel) ).
thf(5293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1423,axiom,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_card_1) ).
thf(8818,plain,
! [A: $i,B: $i] :
( ( B @ v1_card_1 )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_card_1 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(1179,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(7424,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(24008,plain,
! [A: $i] :
( ( ( A @ sk649 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9764,3407]) ).
thf(24009,plain,
! [A: $i] :
( ( A @ sk649 @ v1_xboole_0 )
!= ( sk70 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[24008]) ).
thf(24036,plain,
! [A: $i] :
( ( A @ sk649 )
!= sk70 ),
inference(simp,[status(thm)],[24009]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k2_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_domain_1) ).
thf(7003,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k2_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1622,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(9831,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(1744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(10669,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1725,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(10537,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( B @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_5) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( B @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(4002,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ ( B @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( B @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_relat_1) ).
thf(2771,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ ( B @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( B @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(44799,plain,
$false,
inference(e,[status(thm)],[8536,10319,4682,10790,8200,9032,2822,9131,6085,4188,25680,8930,7766,25985,6836,7427,25928,5365,8186,3883,5116,4835,12607,6355,2295,2306,3053,15278,2341,5593,7854,6231,8288,7691,2072,7445,8663,8097,4899,15596,9516,11504,5950,8514,2876,7673,11235,9833,8283,7798,1899,9731,3581,4852,7143,3863,9685,3830,5676,6317,7990,1850,6512,2427,9076,9864,7072,5028,4728,6954,7285,9091,6057,28977,1882,3460,6798,7253,9059,3680,2077,9621,4037,12602,10198,11635,7517,8044,5168,8434,10431,23095,5718,2231,6162,9351,6495,3858,9251,6106,9590,2381,5069,7958,2908,5842,10679,1808,9383,9456,24037,6813,3040,4391,2953,2590,6458,6441,5173,23455,2671,7198,4711,6830,1971,9572,7516,1793,4614,8928,4973,5348,5383,10463,10694,5614,9818,11881,8366,9135,6480,9268,6295,7813,4403,6939,4011,10881,6634,25279,3895,8752,3017,4543,1788,5120,24885,6278,10775,10484,8765,4090,9526,6505,3429,5565,6401,10433,25311,4739,8150,7697,11029,5906,3004,6675,10772,3648,11058,8981,6127,15600,1867,4220,9261,15282,3446,1999,7096,8667,8490,9565,10715,7484,6416,1872,3616,6515,4279,9855,10940,2476,7147,1988,3826,6241,3414,4294,10726,6117,8650,4435,8204,9278,9625,1835,2348,8578,8671,4198,9396,2516,2819,10336,6570,2972,3634,6251,2432,3994,1914,2491,9292,8086,24047,2763,24041,8325,10908,5123,4371,4079,23130,4266,7499,2020,7136,4679,15318,3088,3777,5476,6583,3308,1935,5723,8866,3809,2173,8025,9148,4963,2825,9013,6291,7918,4610,2531,6182,3597,11250,7311,10633,10584,25332,1887,5533,4386,6892,6538,3689,3612,1826,2466,5279,8178,5553,3248,3204,5953,10903,25367,3221,9172,8500,7914,10305,11667,9099,2735,2814,1985,4422,10587,7825,10997,8089,6547,9561,3342,6095,10053,8357,3495,4761,7528,7349,5188,3821,1907,6066,10382,3617,10221,2217,25630,7541,3485,4778,9360,4275,4349,2185,6713,10010,9315,5130,6113,3845,2488,1832,12606,5712,6519,9230,7000,11051,5706,4984,8242,3855,30910,10469,8880,2713,9612,9843,10206,8126,3866,4008,9768,8770,7835,5744,1922,6010,11641,1800,8278,1892,8590,2403,9480,24045,5521,10850,2049,11512,11510,1890,6951,5193,5604,4492,4622,8600,7857,2929,4675,3470,3312,11132,5942,26025,4632,3835,25370,2301,10702,4383,4793,8037,7633,4771,10682,8161,7112,7733,7226,8293,24040,5682,3431,7104,7317,2777,9319,6562,6259,2950,4205,9204,9304,7107,3322,9298,2616,9593,25653,7273,5892,9283,4583,8379,4443,1811,2090,5861,10623,2996,3724,1911,2782,26916,4297,2469,4733,6419,3163,5856,10918,6410,8791,12610,5680,3438,1864,26919,8321,11215,6176,10085,4724,1828,1978,5914,5032,9415,5311,2034,6559,1960,8246,7581,2335,8759,6157,2017,9309,2058,4718,9616,6755,6498,4924,10106,9347,2750,7722,10113,5572,2508,9875,2964,11218,2437,7036,6648,4033,2618,2833,3189,2281,1896,5643,3712,9167,5370,10238,1886,7336,7936,5772,1796,3036,4364,4087,10273,3676,5846,5897,6772,4825,4536,3955,3243,2809,10574,11505,8939,4707,9764,4379,9007,15321,4285,9923,7688,2392,10933,3906,9272,7460,8033,2718,1975,4082,4065,7408,6474,10690,8421,3378,7952,2922,8508,8170,10943,9340,2574,3984,3531,3186,7859,9009,10165,10855,4853,9720,6760,9682,10811,4216,4893,3591,2204,28473,4753,6020,2473,10506,7814,8827,11672,5034,9588,7518,1915,7410,7005,2232,8842,5519,9785,4100,2496,3550,4172,25267,9175,25288,10345,24038,5049,1900,8783,6122,3603,10426,2969,25706,1824,11212,2441,5206,8343,2409,3261,4712,7989,5670,2560,10171,8994,2541,4397,9412,5002,8476,7827,2277,6264,4878,5579,7994,2133,3022,5956,10843,11217,10657,9207,26000,8608,3752,11634,3989,3239,8550,7084,5470,12608,5085,2032,5507,4661,2528,8878,3207,2396,3339,2015,5924,3286,15595,8746,1920,4585,5177,9301,8964,10235,25976,9264,10721,3166,2445,7308,6646,2464,1938,2758,5879,10634,1837,3618,6629,5983,10502,3403,1968,7063,8145,8942,6043,2820,10116,1951,6708,13686,4776,3600,5779,9626,3546,10067,1836,10367,4942,6392,11670,8847,12603,6168,3050,2547,5858,15279,3727,2741,25709,9885,4461,3931,13153,1910,5330,9641,3595,2769,11503,7095,26366,6888,9095,25674,9804,1804,9773,2726,8149,15599,10131,8297,6215,8354,5313,6075,9493,3782,3615,9196,1983,8446,7777,6677,8314,3831,11133,2115,3482,5053,8677,2946,5238,1794,10295,6995,5673,4512,6691,2895,2359,8339,9245,5577,5502,10566,3218,4789,8319,1856,4636,2692,10644,2694,4845,5428,8014,9624,5362,5583,7593,2724,10445,5978,10298,5889,7513,5811,3746,4840,25922,3650,8800,8567,24044,8572,3941,2268,15281,8815,4219,7116,5497,5475,3060,4263,4291,7101,3952,1964,3000,7846,6363,7404,8835,7189,2023,3326,10946,10708,7774,5075,7559,10185,8985,7054,5496,3407,6844,7629,6593,7981,4425,3596,8687,10342,4389,2419,8258,9957,2312,4750,4545,5253,10671,5337,9609,11642,1842,9477,4406,6164,2613,6573,6256,1810,7930,10195,24989,11666,8968,5865,3194,10688,6395,6501,2108,2551,7059,1889,7572,7895,2978,6935,4180,6271,10094,7821,9513,4736,7293,8820,7668,2504,9012,10666,3409,10513,8935,5317,3611,8673,6134,2932,7609,8442,5481,26028,5149,2304,8351,25665,25941,2836,2598,10787,9316,15322,7508,5639,3743,3770,9893,10026,5900,6207,9761,5973,8294,4482,1932,2581,8690,10285,4237,7495,4540,3540,2566,25656,1799,9053,9461,8896,7027,4347,7086,2766,8576,9846,4902,7123,8307,5026,3005,4416,3364,7333,2756,4223,15317,11031,6533,2761,3587,8923,2076,9171,2440,7941,6038,8708,7646,5170,4163,3147,6171,9699,10406,7193,3824,8796,2634,24690,11673,1857,7150,5557,4184,7020,11216,5153,2926,9468,9913,29569,6963,3225,8482,4625,6160,4567,11125,8512,4782,8989,4966,9436,9716,10689,3306,23508,3592,1846,25261,6279,3999,10635,5209,5930,11065,7476,5887,1895,6311,10190,5126,5840,1996,5872,9226,7817,3660,6314,5359,26310,4562,6422,6524,7985,6192,4921,6901,1906,12609,2729,9040,11506,6507,2677,4708,4685,10101,2292,9765,4872,10971,9231,11638,5808,1959,2556,4354,3257,3607,3890,7010,3079,4412,2570,9122,8728,6578,8112,7599,6001,3289,9853,9635,2028,7636,3839,3523,5928,8859,7382,7920,4269,7785,3686,4017,8311,4489,6052,7372,4453,5043,5241,8807,8495,4786,5720,1833,3319,25341,3900,6407,9418,4998,5933,7968,3070,7938,9062,1916,25950,3768,3636,2938,9142,5488,4077,12216,7497,7736,3609,7233,12170,2525,5065,8404,2981,5067,3086,15320,4677,3266,2674,9471,4122,11124,9295,4709,7704,5876,9521,3458,6898,9057,10557,1795,8740,3590,8581,2716,4381,4590,4975,4769,2827,7815,6705,4505,7218,9125,8841,3002,6091,9803,7865,10056,8381,3223,8767,5546,11671,4978,10611,9638,7201,6937,8188,7270,8152,4837,7983,6673,10640,2738,8665,3663,1865,4218,27649,8300,9538,4764,7094,3123,25326,10728,2753,15594,3487,9555,25973,7671,5703,5449,3832,5539,7536,2457,1897,7658,2425,10024,5158,6248,11237,9354,8202,3719,9258,8376,6016,8244,9248,9835,9224,9390,6048,2510,24074,7933,3251,9614,4914,2284,2943,9491,5616,2065,6144,2346,2721,6742,10370,9575,12604,4228,2538,7514,10429,3155,9454,9312,2084,6920,8715,11508,6179,5244,3038,9377,15316,1806,24043,6147,2774,4828,9840,3779,2906,9771,25270,8171,5491,9118,9920,7330,8047,2839,5610,4616,1801,5531,8986,5346,6289,10019,3500,4300,5381,7362,4374,9789,2197,9713,5035,11669,8983,7685,3583,10004,18277,3456,5563,6834,4203,5114,8932,10645,9042,5511,8735,4430,5920,7275,10397,10375,15280,9888,2343,12477,9079,2111,8661,1993,26918,1862,7551,10732,3192,12438,9280,1838,3614,7778,4850,3451,7141,8372,2874,11640,8998,10489,8473,2289,5180,6847,4726,9528,4993,2553,7023,9228,2329,2842,5838,3893,4554,4990,2578,7479,10544,5575,8541,2967,8280,11643,9873,11173,4933,5340,8440,2439,1841,11220,1926,2962,5775,26369,9619,6907,2051,8719,2620,10076,7469,6223,10208,2139,9381,4085,3159,4918,9366,10930,3706,3142,10424,2535,9011,27858,5299,7339,4497,4282,8291,3348,5495,4067,7916,11507,5326,3876,9133,8035,4158,1805,2069,6730,2867,10692,3490,3380,7154,3444,1809,6540,2878,11030,8409,7070,2005,24937,2054,4207,1948,6890,2914,10322,9170,2096,1873,9403,7490,5528,9227,4458,5881,2665,7650,7571,4886,2994,2318,9563,4456,3293,9651,30136,2471,3161,1905,25329,26914,2234,10449,8505,8789,9943,10814,2629,9858,4859,5165,7679,4688,5916,6806,7013,1958,9783,9276,8863,6115,2899,10736,9317,4045,7085,2863,5514,5111,4673,5748,10704,9578,4377,4630,5446,2513,1845,5452,8593,5229,9879,5716,3376,10290,6683,6472,9606,4864,5250,3842,25683,6885,4939,5478,2060,4272,8890,2143,2012,5499,7196,2732,1941,10684,10572,4200,26031,3949,7045,2518,25931,4961,2386,10333,10159,7511,7724,9270,2888,25668,7832,7228,2831,8039,2747,5235,4190,3691,7568,3554,15598,1830,10846,5186,10307,3246,4437,8612,3642,6762,8498,9214,2092,4905,10162,9599,7971,3722,8873,7443,1869,5276,1785,3475,10211,7988,3026,2429,7149,5560,9815,6298,11674,1980,5203,6125,2219,4351,1901,11213,3828,8327,6653,8840,2322,8148,7351,9666,6436,8248,2545,10012,11637,3359,3174,2044,8757,10509,4875,10608,3715,2354,6633,5223,7391,5633,10568,4225,11636,7720,9770,8679,8464,5319,8893,2247,5147,2948,6746,9891,3697,7466,9486,5902,7456,6679,1849,7779,10023,2113,6073,1802,10885,3493,7515,9675,6262,10128,7342,9851,2543,5998,3356,7067,6526,9363,2357,1955,7374,4538,25606,4634,5226,7612,5685,1797,3117,2860,3961,6467,6358,2892,1881,6960,3914,7498,9654,4795,8151,5596,3366,2584,15319,10674,11059,4671,6992,9601,4414,3684,9995,15283,6301,8431,8987,3533,7007,3665,6711,8360,8681,8812,2435,25621,7089,2924,3478,20996,5939,4548,8973,23160,1839,3139,10754,2626,1918,8698,4698,7676,6425,10082,4851,7024,3589,6758,4945,2818,10364,1966,7764,9306,2885,2696,6041,9760,18811,10508,2870,3171,2960,5777,7606,2078,4419,1913,22743,1844,6390,3548,2194,11681,10156,2611,2325,10193,6980,2209,6674,10637,8285,10905,15277,2997,5485,7570,5332,1866,2658,3929,5258,3613,4710,6030,5351,24653,25364,7082,2608,8337,3911,11639,2273,10169,3709,9802,6489,2251,7359,1903,2406,6953,25600,5191,2811,9934,4791,6003,6770,5368,9459,10648,1854,6910,3003,24042,5756,1822,9824,5087,4705,2130,24048,4495,8781,10254,9449,6694,5505,4969,8617,2416,9179,8805,4451,4261,7327,9701,2399,7399,10137,8102,12601,9289,4619,10937,8172,2956,9718,2081,7256,3694,8369,6305,25991,5162,3497,9962,9510,2648,25314,3585,9393,6018,9792,8203,4774,3598,9434,5109,2462,5040,10738,8304,7039,7747,3149,3529,6521,7157,2362,6277,5549,11172,26917,2680,9421,25988,3351,26912,7520,4074,4446,9211,2230,1893,26003,8721,5517,2494,7406,4570,5196,2917,9787,2623,9162,9427,9378,3420,23076,8209,3987,2008,5884,8309,7955,25323,6703,3992,1908,6924,2123,4125,8341,2374,7048,7946,7216,2287,7649,2102,6055,17091,7991,9034,7126,14030,4014,4472,8886,3860,9806,5971,6997,6007,7868,6439,6786,4809,2983,25671,24039,5004,7231,2587,7744,5268,9318,4596,3264,5537,10443,6050,2522,5430,11219,5764,4843,3521,24046,5477,10515,25994,6226,6580,9070,5247,9596,25338,4367,5926,3062,3145,8019,8424,6590,8277,8002,2040,7772,5700,7323,6535,7433,4029,7851,6627,2201,4051,10809,8653,25703,11214,7184,8207,5709,8484,12605,5290,4210,9271,9134,4427,6735,5105,9002,5462,11522,2704,10472,1789,5867,3196,1891,3030,11668,7943,6398,11028,6612,11509,2668,3045,8706,9409,3673,6273,5322,5440,2651,7648,10224,7525,26913,7819,6503,2549,10092,11050,3869,5581,9314,4395,7694,9441,5275,8675,6874,9547,11236,2241,5945,6190,2127,4848,9357,25609,2430,3543,7987,8444,5151,5806,3411,3772,5061,5975,4987,7829,9446,3817,1923,3020,4239,7493,7708,29596,9110,5768,7025,6595,11477,4659,10287,1925,4713,10642,5468,3939,8147,3740,1902,9848,3076,9489,1885,4691,3494,4345,4501,15597,2270,7563,8857,5473,6658,7392,8978,10276,4221,8493,6424,7367,8245,5183,28472,4533,3526,10706,9838,8184,2640,8950,11675,6173,10723,7531,4702,5542,10118,4627,8553,10187,2563,2881,5986,5494,3299,9536,6842,2206,6733,4767,3405,7056,9784,5261,10900,8829,7861,12488,9385,4742,5255,2438,2238,6575,4908,1917,10745,6404,3316,6632,2351,9286,3200,2191,1812,10002,11511,6739,3933,5293,8818,7424,24036,7003,9831,10669,1912,10537,2177,4002,1870,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU430+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/5.41 % Computer : n014.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sat Sep 26 09:45:54 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/5.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.22/6.82 % [INFO] Parsing done (835ms).
% 4.22/6.83 % [INFO] Running in sequential loop mode.
% 5.09/7.20 % [INFO] eprover registered as external prover.
% 5.09/7.21 % [INFO] Scanning for conjecture ...
% 6.65/7.64 % [INFO] Found a conjecture (or negated_conjecture) and 4501 axioms. Running axiom selection ...
% 10.19/8.89 % [INFO] Axiom selection finished. Selected 1782 axioms (removed 2719 axioms).
% 13.98/9.94 % [INFO] Problem is first-order (TPTP FOF).
% 14.54/10.03 % [INFO] Type checking passed.
% 14.54/10.04 % [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 ...
% 143.44/46.45 % External prover 'e' found a proof!
% 143.44/46.45 % [INFO] Killing All external provers ...
% 143.44/46.45 % Time passed: 40893ms (effective reasoning time: 39609ms)
% 143.44/46.45 % 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)>
% 143.44/46.46 % Axioms used in derivation (1782): t106_xboole_1, t15_finset_1, t158_relat_1, t63_mcart_1, t44_xboole_1, redefinition_r1_ordinal1, t143_pboole, t119_funct_2, t60_mcart_1, t72_xboole_1, t189_relat_1, t86_partfun1, t62_partfun1, existence_m2_pboole, t23_funct_2, dt_m2_pua2mss1, t42_xboole_1, dt_k15_domain_1, t34_subset_1, t39_funct_5, t39_relset_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, d11_finseq_1, t79_mcart_1, dt_k11_pboole, t48_funcop_1, fraenkel_a_4_0_pua2mss1, t36_funcop_1, t177_relat_1, d6_pboole, free_g1_group_1, t25_mcart_1, t177_orders_1, d6_finseq_1, t109_pboole, fc1_zfmisc_1, t30_relat_1, t147_funct_1, d4_funct_1, t53_subset_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, t55_mcart_1, t43_subset_1, t86_funct_1, cc2_finset_1, t20_zfmisc_1, t54_relat_1, t35_subset_1, t66_finseq_1, d1_tarski, t101_relat_1, t135_zfmisc_1, t17_zfmisc_1, fc11_finseq_1, fc3_finset_1, t23_card_1, t25_relset_1, d3_mcart_1, t148_funct_1, t66_funct_2, t143_funct_1, t67_relat_1, t66_partfun1, t5_relset_2, t154_relat_1, t25_card_1, t60_funcop_1, t49_setfam_1, t70_funct_2, t6_setfam_1, t35_funct_2, t14_finset_1, dt_k9_domain_1, t105_zfmisc_1, t140_zfmisc_1, t63_funcop_1, t20_funct_2, dt_k8_funcop_1, redefinition_k8_relset_2, t73_xboole_1, dt_k5_relset_1, d5_relat_1, redefinition_k12_mcart_1, d9_setfam_1, t109_xboole_1, idempotence_k3_xboole_0, t77_partfun1, t67_funcop_1, rc4_finset_1, redefinition_k9_domain_1, t110_xboole_1, t57_funcop_1, t47_relset_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, dt_k8_pboole, s6_domain_1, t86_mcart_1, t38_mcart_1, t66_xboole_1, t23_xboole_1, t95_partfun1, t27_relset_2, 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, t180_orders_1, t97_xboole_1, t3_realset1, t137_funct_1, d3_subset_1, t40_funct_5, t12_pua2mss1, t183_relat_1, t98_relat_1, reflexivity_r2_pboole, dt_k4_relset_1, t1_pboole, t25_funct_1, d10_realset1, t18_funcop_1, dt_k7_domain_1, t113_xboole_1, t8_subset_1, d11_pboole, d12_relat_1, s3_funct_2, redefinition_k7_funct_2, t45_funcop_1, cc1_setfam_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, t42_sysrel, t44_pboole, t64_funct_5, t34_card_1, t25_setfam_1, t68_card_1, redefinition_k8_pboole, t81_partfun1, t56_partfun1, t38_funct_1, t3_relset_2, t53_funct_2, t76_mcart_1, d5_tarski, t83_mcart_1, t15_funct_1, dt_k11_domain_1, fc4_relat_1, fc4_setfam_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, redefinition_k3_finseq_1, t44_relat_1, fc4_funct_1, t1_subset, t147_relat_1, t10_partfun1, t10_mssubfam, t7_funct_2, t36_sysrel, t6_xboole_1, t25_sysrel, t158_partfun1, t39_ordinal1, d5_xboole_0, dt_k7_relset_1, t32_mcart_1, t29_subset_1, d10_mcart_1, t24_setfam_1, t151_funct_1, t52_zfmisc_1, t144_relat_1, t57_domain_1, t18_setfam_1, fc4_subset_1, t71_funct_1, fc3_realset1, t22_funct_1, t17_pboole, free_g3_vectsp_1, t79_funcop_1, dt_k3_funct_2, t74_funct_2, t168_funct_2, t43_xboole_1, fraenkel_a_8_0_domain_1, t54_partfun1, t81_zfmisc_1, d7_mcart_1, t10_relset_1, t135_partfun1, t55_domain_1, t5_ordinal2, t146_funct_2, fc3_setfam_1, t18_xboole_1, t4_funcop_1, t12_realset1, d5_relat_2, t3_mcart_1, t155_funct_1, fc3_relat_1, t96_zfmisc_1, t42_zfmisc_1, t85_funct_1, dt_k9_relset_1, dt_k1_subset_1, d5_pboole, 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, t33_mcart_1, t41_funct_2, t166_funct_2, t117_relat_1, t19_finset_1, t2_boole, t65_funct_5, t14_sysrel, t11_realset1, t73_funcop_1, t38_ordinal1, t47_relat_1, fc9_relat_1, t148_partfun1, t36_partfun1, fc5_finset_1, t68_xboole_1, t41_mcart_1, t25_xboole_1, t61_card_1, t35_zfmisc_1, t12_relset_2, d5_setfam_1, t46_ordinal1, fc2_finseq_1, t43_domain_1, t1_funcop_1, t11_pua2mss1, t82_relat_1, t117_zfmisc_1, t32_relat_1, t1_unialg_1, t65_partfun1, t186_partfun1, t44_funct_2, t14_card_1, t117_funct_1, dt_k4_realset1, t26_funct_5, t17_setfam_1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t108_pboole, t27_xboole_1, t122_zfmisc_1, t4_mcart_1, t139_relat_1, fc6_funcop_1, dt_m1_realset1, t110_zfmisc_1, fraenkel_a_1_4_domain_1, t24_relset_2, t64_domain_1, t32_ordinal1, t43_zfmisc_1, t1_pua2mss1, t30_ordinal1, t59_mcart_1, rc2_partfun1, t18_relat_1, t171_relat_1, t6_mssubfam, t162_partfun1, t64_funcop_1, dt_m3_pboole, dt_k6_partfun1, t70_zfmisc_1, t19_pboole, t103_zfmisc_1, t63_partfun1, t91_finseq_2, t153_funct_1, t95_zfmisc_1, t96_partfun1, t78_funcop_1, t15_relset_1, t45_ordinal1, t140_pboole, fraenkel_a_1_2_domain_1, t99_zfmisc_1, t44_mcart_1, d7_card_1, t97_orders_1, t61_subset_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, fraenkel_a_0_3_domain_1, t27_finseq_2, rc3_finseq_1, t7_orders_1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t81_mcart_1, rc1_finseq_1, t123_relat_1, t50_funct_2, t63_domain_1, s2_pboole, d8_pboole, t39_relat_1, t69_zfmisc_1, t56_relat_1, t84_funct_1, dt_k7_funct_2, t95_xboole_1, fc8_finset_1, t102_relat_1, dt_k14_domain_1, t29_relset_2, t41_relat_1, t21_pboole, t27_zfmisc_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, t40_domain_1, cc1_relat_1, fc9_funcop_1, dt_k5_funct_5, t131_zfmisc_1, t73_funct_5, redefinition_k2_funct_2, idempotence_k5_subset_1, t50_zfmisc_1, d7_partfun1, t112_pboole, t30_card_1, t2_funct_1, t36_subset_1, redefinition_k6_setfam_1, t142_pboole, t49_zfmisc_1, commutativity_k3_pboole, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t31_relset_1, t176_partfun1, fc2_pboole, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t6_relset_2, t70_partfun1, d9_mcart_1, t3_funcop_1, t138_funct_1, t3_setfam_1, t130_funct_2, t152_funct_2, t80_funcop_1, s13_funct_2, rc1_funct_1, t150_pboole, t97_finseq_2, t64_funct_2, symmetry_r5_pboole, t115_zfmisc_1, t52_funcop_1, t62_funct_1, t76_funct_2, t65_funct_2, t19_funct_1, t25_relset_2, t68_mcart_1, fc11_finset_1, dt_k14_mcart_1, dt_k8_relset_2, fraenkel_a_2_0_domain_1, t135_pboole, d2_tarski, 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, fc6_funct_1, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t51_mcart_1, t99_funct_1, t89_xboole_1, t83_funcop_1, s2_card_1, t25_funct_2, fc2_xboole_0, fraenkel_a_4_0_domain_1, t87_partfun1, t31_relat_1, d1_relset_2, dt_m2_realset1, t32_subset_1, t168_relat_1, t22_funcop_1, t46_sysrel, t29_funct_5, t76_partfun1, t108_xboole_1, t34_partfun1, dt_k9_funct_2, t44_card_1, 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, s1_orders_1, d1_xboole_0, t5_mssubfam, dt_m1_eqrel_1, t49_funct_1, d15_pboole, s2_relset_1, t40_funct_1, redefinition_k8_funcop_1, t138_zfmisc_1, t59_funct_5, rc6_finseq_1, t25_subset_1, fraenkel_a_1_5_domain_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, t2_pua2mss1, t165_funct_2, t15_funcop_1, t60_partfun1, t14_relset_1, t16_relset_1, rc3_relat_1, t47_funct_2, t27_relset_1, t52_domain_1, t52_relset_1, t34_funct_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, s4_subset_1, t8_funct_2, t29_funct_2, t122_pboole, dt_k6_finseq_1, fc10_finset_1, t118_funct_2, fc2_setfam_1, existence_m1_realset1, t26_finset_1, t92_finseq_2, t53_relset_1, t30_sysrel, t6_mcart_1, cc1_pboole, 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, s2_xboole_0, t56_zfmisc_1, t6_boole, t12_funct_1, dt_k1_card_1, t62_mcart_1, t4_orders_1, t3_funct_2, t18_subset_1, rc2_subset_1, fc9_finset_1, t46_mcart_1, t63_funct_1, t97_partfun1, t80_mcart_1, t38_sysrel, t50_xboole_1, dt_k6_subset_1, t10_relat_1, t59_setfam_1, d1_relat_1, existence_m2_pua2mss1, t33_card_1, dt_k3_relset_2, t185_partfun1, t29_relat_1, d6_mcart_1, t20_funct_1, t104_relat_1, t39_funcop_1, t3_partfun1, t75_xboole_1, t131_relat_1, commutativity_k2_xboole_0, t5_subset, d9_realset1, t57_mcart_1, t1_xboole_1, redefinition_k4_relset_2, t87_mcart_1, 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, t82_finseq_2, t70_funct_5, t12_sysrel, t60_card_1, t55_relat_1, t32_relset_1, t68_partfun1, t4_card_1, t17_domain_1, t7_setfam_1, t31_ordinal1, t4_setfam_1, t32_partfun1, t73_relat_1, t83_partfun1, redefinition_k4_funct_2, d6_tarski, t4_relat_1, t46_card_1, fc5_funcop_1, t28_subset_1, t52_xboole_1, t185_relat_1, t2_pboole, t116_relat_1, t21_finset_1, t160_funct_1, t28_relset_2, s5_domain_1, fc17_finset_1, redefinition_k13_mcart_1, t34_relat_1, t15_domain_1, t79_partfun1, fc3_subset_1, t128_zfmisc_1, d10_pboole, t39_partfun1, t149_funct_1, t75_zfmisc_1, t48_zfmisc_1, t7_mssubfam, t65_xboole_1, t163_relat_1, t6_pboole, t19_relset_1, t45_funct_2, t79_zfmisc_1, t128_relat_1, t25_zfmisc_1, d4_relat_1, t94_zfmisc_1, fc4_numbers, t4_xboole_0, t41_funcop_1, t65_finseq_1, d2_realset1, t32_sysrel, fc6_finset_1, t63_funct_5, d2_int_1, s1_xboole_0, fc17_finseq_1, d6_partfun1, t150_relat_1, existence_m1_relset_1, t20_finseq_1, d11_mcart_1, commutativity_k5_subset_1, t55_setfam_1, dt_k2_domain_1, t1_zfmisc_1, t77_mcart_1, s8_domain_1, t46_partfun1, t12_setfam_1, t5_setfam_1, t52_funct_1, t28_mcart_1, t4_pboole, dt_k1_sysrel, t123_zfmisc_1, fc2_subset_1, t5_funct_2, t176_relat_1, dt_k8_funct_2, d4_relset_2, t58_sysrel, t60_zfmisc_1, fc1_orders_1, t11_funct_2, d3_zfmisc_1, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t9_relat_1, t33_xboole_1, s9_domain_1, t2_zfmisc_1, fraenkel_a_1_6_domain_1, redefinition_k10_pboole, t167_funct_2, t53_partfun1, cc1_finseq_1, rc4_funct_1, t24_finset_1, t23_pboole, t97_zfmisc_1, redefinition_k7_domain_1, t28_partfun1, fc2_funct_1, t73_funct_1, dt_k3_realset1, t40_funct_2, t102_xboole_1, t49_sysrel, t28_relset_1, t24_domain_1, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, rc3_pboole, t72_mcart_1, t2_tarski, t56_mcart_1, t18_relset_2, t16_funct_1, t79_relat_1, t14_relat_1, t72_zfmisc_1, t142_funct_2, t17_ordinal2, t33_relat_1, t82_funct_2, fc6_subset_1, t28_zfmisc_1, t62_subset_1, t122_funct_1, t5_pboole, t53_sysrel, s1_pboole, 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, t49_card_1, t57_zfmisc_1, t4_subset, t30_xboole_1, dt_k2_funct_1, t74_zfmisc_1, t76_relat_1, t14_funct_1, t43_funct_1, d8_mcart_1, fc13_relat_1, t52_subset_1, t5_ordinal1, t4_boole, t36_funct_2, t53_xboole_1, t146_funct_1, d2_funct_2, cc2_eqrel_1, t84_xboole_1, dt_k9_mcart_1, fc16_finseq_1, 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, fraenkel_a_1_3_domain_1, t169_funct_2, t33_sysrel, t29_funcop_1, d2_xboole_0, dt_k8_domain_1, t15_realset1, cc1_funct_2, d17_pboole, t39_subset_1, cc3_pua2mss1, t32_xboole_1, t83_finseq_1, t52_funct_5, d4_tarski, t134_relat_1, t141_zfmisc_1, t12_zfmisc_1, t174_relat_1, existence_m3_realset1, t56_subset_1, t47_funcop_1, t93_partfun1, t129_relat_1, 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, t50_domain_1, t25_finset_1, t9_zfmisc_1, t148_funct_2, t79_xboole_1, t106_relat_1, t51_funct_2, t67_xboole_1, s1_tarski, t39_setfam_1, existence_m2_realset1, redefinition_k10_relset_1, s1_relset_1, redefinition_k14_mcart_1, redefinition_k5_setfam_1, t35_card_1, dt_k1_domain_1, t58_zfmisc_1, t4_pua2mss1, rc2_pboole, t17_funct_2, t1_xboole_0, existence_m1_ordinal1, involutiveness_k4_relat_1, t35_sysrel, d4_partfun1, 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, t7_boole, t41_domain_1, cc1_funct_1, t4_funct_2, t24_funcop_1, t36_setfam_1, s11_funct_2, d10_setfam_1, t143_relat_1, t77_relat_1, t13_finset_1, t105_relat_1, t120_funct_1, rc5_funct_1, t6_realset1, t37_sysrel, t160_funct_2, d3_relset_2, t23_ordinal1, rc3_realset1, t136_partfun1, t138_relat_1, d3_partfun1, t104_zfmisc_1, t118_relat_1, t42_mcart_1, t28_domain_1, d3_relat_2, t138_partfun1, s2_domain_1, dt_k7_mcart_1, d10_relat_1, t28_card_1, t55_zfmisc_1, d2_subset_1, t66_zfmisc_1, d3_pboole, fc1_subset_1, t33_zfmisc_1, fc5_funct_1, t29_finseq_1, t22_relat_1, redefinition_k6_partfun1, t48_xboole_1, dt_k3_pua2mss1, dt_k6_domain_1, t157_funct_1, s1_funct_2, t85_partfun1, t3_ordinal1, t9_domain_1, d5_mcart_1, t45_relset_1, dt_k16_domain_1, t8_pua2mss1, d1_card_1, t66_funcop_1, dt_k11_mcart_1, t26_zfmisc_1, t48_funct_1, t21_funct_2, d2_setfam_1, t16_subset_1, dt_k2_partfun1, t69_partfun1, t7_ordinal1, t38_relset_1, t153_relat_1, rc2_funct_1, t49_partfun1, 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, dt_k3_pboole, t158_funct_2, d16_pboole, t32_card_1, t152_funct_1, t49_relset_1, t7_relset_2, t54_setfam_1, t47_funct_1, d11_relat_1, s6_funct_2, t31_xboole_1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t88_xboole_1, t19_funct_2, t51_funct_1, t130_relat_1, fraenkel_a_3_0_domain_1, t85_xboole_1, t22_finset_1, t67_funct_1, t74_relat_1, t162_funct_2, redefinition_k1_domain_1, connectedness_r1_ordinal1, t30_relset_1, t14_zfmisc_1, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, t76_funcop_1, t51_setfam_1, t45_relat_1, t17_relset_2, t56_funct_1, existence_m1_pboole, t78_finseq_2, t110_relat_1, t113_funct_2, t71_partfun1, dt_m1_pboole, t69_xboole_1, d5_funct_2, t27_sysrel, d4_realset1, existence_m3_pboole, t4_realset1, s8_funct_2, 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, dt_m2_pboole, t134_pboole, t124_zfmisc_1, t188_relat_1, fraenkel_a_3_1_domain_1, t60_funct_2, t82_xboole_1, t107_relat_1, t21_card_1, t32_zfmisc_1, t54_xboole_1, t186_relat_1, fc3_pboole, dt_k6_setfam_1, d7_relat_1, t89_relat_1, cc2_funct_1, t120_zfmisc_1, t21_funcop_1, t46_setfam_1, t9_relset_2, t169_partfun1, t71_funct_5, t49_funct_5, t18_funct_1, t55_xboole_1, s7_funct_2, 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, t22_relset_1, s1_subset_1, s1_domain_1, t31_sysrel, t78_relat_1, t8_mssubfam, t44_sysrel, s4_funct_2, t24_ordinal1, t59_sysrel, t7_pua2mss1, t76_funct_1, t124_funct_1, fraenkel_a_3_1_pua2mss1, t55_subset_1, t70_mcart_1, t46_funct_1, redefinition_k9_relset_1, t79_funct_2, t115_relat_1, t56_funcop_1, t136_funct_2, fraenkel_a_2_1_domain_1, t14_relset_2, commutativity_k7_subset_1, t82_card_1, d2_zfmisc_1, dt_k13_mcart_1, t27_card_1, fc11_relat_1, t51_funct_5, fc5_subset_1, existence_m1_subset_1, commutativity_k2_tarski, t3_relat_1, t69_funct_5, t24_relat_1, t8_relset_1, t84_funcop_1, t51_sysrel, redefinition_k5_domain_1, t17_relset_1, dt_k3_funct_5, d5_subset_1, t29_zfmisc_1, t25_domain_1, t35_xboole_1, t49_domain_1, t106_zfmisc_1, t114_pboole, t26_ordinal1, fraenkel_a_6_0_domain_1, t16_relset_2, s1_int_1, d6_xboole_0, 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, fraenkel_a_2_1_pua2mss1, t110_pboole, 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, idempotence_k3_pboole, 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, t121_funct_2, t70_funct_1, t100_zfmisc_1, t22_zfmisc_1, t26_domain_1, t15_xboole_1, redefinition_k1_relset_2, t60_funct_5, dt_k5_subset_1, rc1_pua2mss1, redefinition_k7_subset_1, t37_mcart_1, t116_funct_2, s2_ordinal1, t142_partfun1, t114_zfmisc_1, t31_zfmisc_1, t58_partfun1, redefinition_k7_pboole, t19_funcop_1, d1_zfmisc_1, t16_xboole_1, free_g2_vectsp_1, dt_k8_relat_1, d8_setfam_1, t26_xboole_1, t69_mcart_1, t63_xboole_1, redefinition_k7_funcop_1, t57_setfam_1, t43_funct_2, commutativity_k4_subset_1, t38_relat_1, t91_partfun1, t86_zfmisc_1, rc2_relat_1, existence_m2_relset_1, t98_xboole_1, t138_pboole, dt_k9_funcop_1, t49_funcop_1, t54_domain_1, t38_zfmisc_1, t145_partfun1, t65_mcart_1, t34_funcop_1, t72_funct_1, d2_relat_2, fraenkel_a_3_6_domain_1, t157_relat_1, t23_relset_2, t87_finseq_2, t36_ordinal1, t73_partfun1, t61_domain_1, dt_k7_funcop_1, involutiveness_k10_funcop_1, fc4_funcop_1, t29_card_1, t6_funct_2, t40_sysrel, t69_funcop_1, fraenkel_a_1_0_pua2mss1, t41_subset_1, s4_domain_1, t168_partfun1, t37_ordinal1, s14_funct_2, redefinition_k4_domain_1, rc2_int_1, t142_funct_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, t84_zfmisc_1, cc2_pboole, t3_pua2mss1, t8_setfam_1, t36_zfmisc_1, commutativity_k5_pboole, redefinition_k6_funcop_1, t94_partfun1, dt_k12_mcart_1, dt_k3_partfun1, t8_xboole_1, t37_relat_1, d3_tarski, t151_pboole, cc6_funct_2, 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, t36_card_1, t58_funcop_1, t6_relset_1, t78_xboole_1, t28_xboole_1, t56_sysrel, d1_relset_1, t67_funct_5, t74_partfun1, t53_domain_1, t46_subset_1, d7_relat_2, t33_domain_1, t60_subset_1, t39_zfmisc_1, d1_realset1, t131_funct_2, t119_zfmisc_1, dt_k7_pboole, t5_xboole_0, t121_relat_1, rc1_relat_1, d6_card_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, t72_funct_5, redefinition_k1_partfun1, t20_finset_1, t1_realset1, t2_xboole_1, fc9_finseq_1, redefinition_k2_realset1, t34_funct_2, d1_funct_2, t6_zfmisc_1, t1_mssubfam, t48_relat_1, dt_k10_relset_1, d2_orders_1, d15_funct_1, s3_subset_1, t5_mcart_1, t93_relat_1, t18_funct_2, t144_funct_1, reflexivity_r1_ordinal1, dt_k4_relset_2, t121_zfmisc_1, t10_subset_1, t161_relat_1, d9_relat_1, t56_setfam_1, t27_finset_1, t96_orders_1, reflexivity_r2_setfam_1, s2_orders_1, rc1_pboole, 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, dt_k2_card_1, t32_funct_5, t51_domain_1, t1_partfun1, t150_funct_1, existence_m4_realset1, t41_xboole_1, t57_subset_1, t47_zfmisc_1, t84_partfun1, t66_funct_1, d4_xboole_0, 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, t2_setfam_1, fraenkel_a_0_4_domain_1, t46_relat_1, fc1_setfam_1, t39_mcart_1, t14_pua2mss1, t35_funct_1, s1_funct_1, t18_zfmisc_1, t29_relset_1, rc1_realset1, redefinition_k7_relset_1, t8_card_1, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, dt_k1_pboole, t45_partfun1, redefinition_k11_relset_1, existence_m1_eqrel_1, fc18_finseq_1, s2_pua2mss1, 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, t71_mcart_1, t64_xboole_1, t49_xboole_1, t136_zfmisc_1, t64_mcart_1, t16_sysrel, fc3_funct_1, reflexivity_r1_setfam_1, t111_pboole, t68_zfmisc_1, dt_m2_subset_1, t51_relset_1, t12_funct_2, t35_ordinal1, s10_domain_1, t54_subset_1, t53_funct_1, t27_finseq_1, rc1_finset_1, s3_xboole_0, dt_k7_setfam_1, t127_zfmisc_1, t123_funct_1, t21_setfam_1, t15_pboole, t70_funcop_1, t11_setfam_1, t50_relset_1, t44_subset_1, t87_relat_1, cc1_finset_1, t35_partfun1, t93_xboole_1, t21_funct_1, t50_funct_1, fc12_finset_1, t50_sysrel, t42_funct_1, t126_relat_1, t26_card_1, s5_funct_2, t73_mcart_1, fc1_relat_1, t4_mssubfam, t47_partfun1, t1_relset_2, t77_xboole_1, d6_relat_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, t35_relset_1, d1_orders_1, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t49_pboole, t23_relat_1, t16_finset_1, dt_k8_mcart_1, t149_finseq_2, t54_sysrel, t20_funcop_1, t126_zfmisc_1, fc8_relat_1, dt_k6_mcart_1, t24_sysrel, t40_relat_1, t45_sysrel, dt_m1_orders_1, t182_relat_1, t54_funcop_1, t120_funct_2, d5_card_1, redefinition_k3_funct_2, t31_mcart_1, 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, t45_domain_1, s1_card_1, t58_card_1, t42_domain_1, t75_funcop_1, fc7_relat_1, t14_funcop_1, t47_mcart_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, t3_pboole, t156_relat_1, t53_zfmisc_1, d5_funct_5, t149_pboole, t135_relat_1, d4_mcart_1, t116_pboole, 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, dt_k5_mcart_1, t68_funct_5, t48_card_1, t100_relat_1, t78_mcart_1, t25_partfun1, t49_relat_1, t161_funct_1, t27_funct_1, t92_relat_1, t10_realset1, t82_funcop_1, t55_sysrel, dt_k10_mcart_1, t175_orders_1, t27_funct_5, t99_finseq_2, t48_subset_1, d18_pboole, t45_card_1, dt_k1_relset_2, dt_k5_relset_2, t145_relat_1, t50_subset_1, d15_relat_1, d10_xboole_0, cc1_int_1, t149_relat_1, t58_domain_1, t115_funct_2, idempotence_k2_xboole_0, t28_relat_1, d1_funct_1, t75_mcart_1, t30_setfam_1, t115_partfun1, fc2_funcop_1, t9_tarski, t11_relset_2, t46_xboole_1, t107_xboole_1, d3_pua2mss1, fc2_realset1, t120_pboole, t74_xboole_1, fc2_finset_1, redefinition_k10_domain_1, t7_xboole_1, d21_pboole, t10_relset_2, t77_funcop_1, t37_funct_1, s1_relat_1, t159_funct_1, redefinition_k5_relset_1, t57_funct_1, t3_xboole_0, t146_partfun1, cc1_realset1, t58_setfam_1, t12_relset_1, fc3_funcop_1, t5_xboole_1, t49_subset_1, rc1_card_1, fc1_funcop_1, t44_funcop_1, t7_tarski, dt_k5_pboole, t108_relat_1, t33_funct_1, t145_funct_2, t43_mcart_1, rc1_partfun1, t27_partfun1, symmetry_r1_partfun1, t126_funct_1, t91_xboole_1, t33_finseq_2, t47_card_1, t67_partfun1, t132_relat_1, t3_boole, t26_relset_2, d5_funct_1, t48_mcart_1, t6_ordinal1, t53_mcart_1, dt_k10_pboole, redefinition_k6_subset_1, t93_zfmisc_1, t21_relset_2, t59_card_1, redefinition_k4_relset_1, t44_funct_1, cc5_funct_2, t48_relset_1, 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, t80_relat_1, t26_sysrel, t143_partfun1, t184_relat_1, rc2_xboole_0, s7_domain_1, existence_m1_orders_1, t67_funct_2, t26_partfun1, t112_zfmisc_1, t40_xboole_1, redefinition_k2_partfun1, fc14_finset_1, t19_setfam_1, fc4_realset1, t40_mcart_1, cc4_pua2mss1, t36_relset_1, t103_relat_1, t30_zfmisc_1, dt_k10_domain_1, t15_sysrel, fraenkel_a_0_1_domain_1, s2_funct_2, fc13_finset_1, rc1_setfam_1, t45_mcart_1, t139_partfun1, fc7_finset_1, idempotence_k4_subset_1, symmetry_r4_pboole, t87_xboole_1, t81_relat_1, t24_card_1, t40_zfmisc_1, t72_funcop_1, t82_mcart_1, t174_partfun1, t80_partfun1, t55_funct_2, fraenkel_a_3_5_domain_1, t45_xboole_1, t66_relat_1, t38_partfun1, dt_m3_realset1, t78_partfun1, t2_xboole_0, existence_m2_finseq_1, t37_funct_5, t6_relat_1, d3_setfam_1, redefinition_k9_funcop_1, d2_relat_1, t39_xboole_1, t88_relat_1, t26_relat_1, t53_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, d3_xboole_0, fraenkel_a_0_5_domain_1, t38_xboole_1, fraenkel_a_4_1_domain_1, t13_pua2mss1, t13_card_1, t23_funcop_1, t190_relat_1, t71_relat_1, t119_relat_1, antisymmetry_r2_hidden, t23_relset_1, t15_relset_2, t53_setfam_1, fc15_finset_1, t27_ordinal1, t22_subset_1, redefinition_k6_domain_1
% 143.44/46.46 % No. of inferences in proof: 4543
% 143.44/46.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 40893 ms resp. 39609 ms w/o parsing
% 150.20/47.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 150.20/48.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------