TSTP Solution File: SEU430+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU430+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:59:04 EDT 2023
% Result : Theorem 95.14s 22.02s
% Output : Refutation 97.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2144
% Syntax : Number of formulae : 3972 ( 443 unt; 361 typ; 0 def)
% Number of atoms : 17193 (3687 equ; 0 cnn)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 62125 (2310 ~; 264 |;6385 &;46233 @)
% ( 324 <=>;6609 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 720 ( 720 >; 0 *; 0 +; 0 <<)
% Number of symbols : 364 ( 361 usr; 88 con; 0-9 aty)
% Number of variables : 11725 ( 0 ^;11087 !; 638 ?;11725 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(m2_finseq_1_type,type,
m2_finseq_1: $i > $i > $o ).
thf(m2_pua2mss1_type,type,
m2_pua2mss1: $i > $i > $o ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k3_funct_5_type,type,
k3_funct_5: $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_type,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k13_finseq_1_type,type,
k13_finseq_1: $i > $i ).
thf(k4_relset_1_type,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k4_relat_1_type,type,
k4_relat_1: $i > $i ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k5_funcop_1_type,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(v1_finseq_1_type,type,
v1_finseq_1: $i > $o ).
thf(k3_finseq_1_type,type,
k3_finseq_1: $i > $i ).
thf(k3_funcop_1_type,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(v2_relat_1_type,type,
v2_relat_1: $i > $o ).
thf(k1_sysrel_type,type,
k1_sysrel: $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(k6_finseq_1_type,type,
k6_finseq_1: $i > $i ).
thf(k7_relat_1_type,type,
k7_relat_1: $i > $i > $i ).
thf(k8_relat_1_type,type,
k8_relat_1: $i > $i > $i ).
thf(k5_funct_5_type,type,
k5_funct_5: $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k2_funct_4_type,type,
k2_funct_4: $i > $i ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k4_card_3_type,type,
k4_card_3: $i > $i ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(k6_funcop_1_type,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(k4_funcop_1_type,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(k7_relset_1_type,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(m1_pboole_type,type,
m1_pboole: $i > $i > $o ).
thf(k8_pboole_type,type,
k8_pboole: $i > $i > $i > $i > $i ).
thf(a_2_1_pua2mss1_type,type,
a_2_1_pua2mss1: $i > $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_card_1_type,type,
k1_card_1: $i > $i ).
thf(k4_funct_2_type,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(k9_relset_1_type,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(r1_setfam_1_type,type,
r1_setfam_1: $i > $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(v3_ordinal1_type,type,
v3_ordinal1: $i > $o ).
thf(r1_ordinal1_type,type,
r1_ordinal1: $i > $i > $o ).
thf(v1_realset1_type,type,
v1_realset1: $i > $o ).
thf(m4_realset1_type,type,
m4_realset1: $i > $i > $o ).
thf(k3_pboole_type,type,
k3_pboole: $i > $i > $i > $i ).
thf(k2_funcop_1_type,type,
k2_funcop_1: $i > $i > $i ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(r2_pboole_type,type,
r2_pboole: $i > $i > $i > $o ).
thf(k5_relset_1_type,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(r2_wellord2_type,type,
r2_wellord2: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(k3_setfam_1_type,type,
k3_setfam_1: $i > $i > $i ).
thf(k5_xboole_0_type,type,
k5_xboole_0: $i > $i > $i ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(r5_pboole_type,type,
r5_pboole: $i > $i > $i > $o ).
thf(k3_zfmisc_1_type,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(k5_mcart_1_type,type,
k5_mcart_1: $i > $i > $i > $i > $i ).
thf(k6_mcart_1_type,type,
k6_mcart_1: $i > $i > $i > $i > $i ).
thf(k7_mcart_1_type,type,
k7_mcart_1: $i > $i > $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m3_realset1_type,type,
m3_realset1: $i > $i > $i > $o ).
thf(k4_realset1_type,type,
k4_realset1: $i > $i > $i > $i ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(k4_zfmisc_1_type,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k8_mcart_1_type,type,
k8_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k9_mcart_1_type,type,
k9_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k10_mcart_1_type,type,
k10_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k11_mcart_1_type,type,
k11_mcart_1: $i > $i > $i > $i > $i > $i ).
thf(k5_pboole_type,type,
k5_pboole: $i > $i > $i > $i ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(v3_relat_1_type,type,
v3_relat_1: $i > $o ).
thf(k10_relset_1_type,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k1_pboole_type,type,
k1_pboole: $i > $i ).
thf(v1_card_1_type,type,
v1_card_1: $i > $o ).
thf(v6_ordinal1_type,type,
v6_ordinal1: $i > $o ).
thf(k10_pboole_type,type,
k10_pboole: $i > $i > $i ).
thf(r4_pboole_type,type,
r4_pboole: $i > $i > $i > $o ).
thf(k11_pboole_type,type,
k11_pboole: $i > $i > $i > $i ).
thf(k3_mcart_1_type,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(k4_mcart_1_type,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(r2_setfam_1_type,type,
r2_setfam_1: $i > $i > $o ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k9_relset_2_type,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(m3_pboole_type,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(a_2_0_domain_1_type,type,
a_2_0_domain_1: $i > $i > $i ).
thf(r7_relat_2_type,type,
r7_relat_2: $i > $i > $o ).
thf(m2_pboole_type,type,
m2_pboole: $i > $i > $i > $o ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(k2_realset1_type,type,
k2_realset1: $i > $i > $i > $i ).
thf(v1_setfam_1_type,type,
v1_setfam_1: $i > $o ).
thf(k7_pboole_type,type,
k7_pboole: $i > $i > $i > $i > $i ).
thf(a_1_0_pua2mss1_type,type,
a_1_0_pua2mss1: $i > $i ).
thf(a_4_0_domain_1_type,type,
a_4_0_domain_1: $i > $i > $i > $i > $i ).
thf(k9_funcop_1_type,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(k10_funcop_1_type,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(a_3_0_domain_1_type,type,
a_3_0_domain_1: $i > $i > $i > $i ).
thf(m1_ordinal1_type,type,
m1_ordinal1: $i > $i > $o ).
thf(m1_orders_1_type,type,
m1_orders_1: $i > $i > $o ).
thf(a_4_0_relset_2_type,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k2_card_1_type,type,
k2_card_1: $i > $i ).
thf(r5_relat_2_type,type,
r5_relat_2: $i > $i > $o ).
thf(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(g2_vectsp_1_type,type,
g2_vectsp_1: $i > $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_type,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_3_domain_1_type,type,
a_2_3_domain_1: $i > $i > $i ).
thf(k6_enumset1_type,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(k3_relset_2_type,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k4_domain_1_type,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_subset_1_type,type,
k7_subset_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(k3_realset1_type,type,
k3_realset1: $i > $i > $i > $i ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(v1_fraenkel_type,type,
v1_fraenkel: $i > $o ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(k5_domain_1_type,type,
k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(k3_enumset1_type,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(r2_relat_2_type,type,
r2_relat_2: $i > $i > $o ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(k2_enumset1_type,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(a_3_1_pua2mss1_type,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(p1_s6_domain_1_type,type,
p1_s6_domain_1: $i > $o ).
thf(p2_s6_domain_1_type,type,
p2_s6_domain_1: $i > $o ).
thf(a_1_5_domain_1_type,type,
a_1_5_domain_1: $i > $i ).
thf(a_1_6_domain_1_type,type,
a_1_6_domain_1: $i > $i ).
thf(k2_domain_1_type,type,
k2_domain_1: $i > $i > $i > $i ).
thf(k16_domain_1_type,type,
k16_domain_1: $i > $i > $i > $i > $i ).
thf(k7_domain_1_type,type,
k7_domain_1: $i > $i > $i > $i ).
thf(f1_s8_funct_2_type,type,
f1_s8_funct_2: $i ).
thf(f2_s8_funct_2_type,type,
f2_s8_funct_2: $i ).
thf(f3_s8_funct_2_type,type,
f3_s8_funct_2: $i ).
thf(f4_s8_funct_2_type,type,
f4_s8_funct_2: $i > $i > $i ).
thf(a_0_3_domain_1_type,type,
a_0_3_domain_1: $i ).
thf(a_0_4_domain_1_type,type,
a_0_4_domain_1: $i ).
thf(a_0_5_domain_1_type,type,
a_0_5_domain_1: $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(k9_funct_2_type,type,
k9_funct_2: $i > $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(v2_card_1_type,type,
v2_card_1: $i > $o ).
thf(r2_realset1_type,type,
r2_realset1: $i > $i > $i > $o ).
thf(k4_numbers_type,type,
k4_numbers: $i ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(f1_s5_funct_2_type,type,
f1_s5_funct_2: $i ).
thf(f2_s5_funct_2_type,type,
f2_s5_funct_2: $i ).
thf(f3_s5_funct_2_type,type,
f3_s5_funct_2: $i ).
thf(p1_s5_funct_2_type,type,
p1_s5_funct_2: $i > $i > $i > $o ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k13_domain_1_type,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(g1_vectsp_1_type,type,
g1_vectsp_1: $i > $i > $i > $i ).
thf(k2_relset_2_type,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k1_enumset1_type,type,
k1_enumset1: $i > $i > $i > $i ).
thf(g1_rlvect_1_type,type,
g1_rlvect_1: $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k15_domain_1_type,type,
k15_domain_1: $i > $i > $i > $i > $i ).
thf(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(g3_vectsp_1_type,type,
g3_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_type,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k14_domain_1_type,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(r3_relat_2_type,type,
r3_relat_2: $i > $i > $o ).
thf(f1_s4_funct_2_type,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_type,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_type,type,
f3_s4_funct_2: $i > $i ).
thf(k3_domain_1_type,type,
k3_domain_1: $i > $i > $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k7_relset_2_type,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(k1_relset_2_type,type,
k1_relset_2: $i > $i > $i > $i ).
thf(f1_s7_funct_2_type,type,
f1_s7_funct_2: $i ).
thf(f2_s7_funct_2_type,type,
f2_s7_funct_2: $i ).
thf(f3_s7_funct_2_type,type,
f3_s7_funct_2: $i ).
thf(p1_s7_funct_2_type,type,
p1_s7_funct_2: $i > $i > $i > $o ).
thf(f1_s14_funct_2_type,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_type,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_type,type,
p1_s14_funct_2: $i > $i > $o ).
thf(a_1_1_domain_1_type,type,
a_1_1_domain_1: $i > $i ).
thf(k17_domain_1_type,type,
k17_domain_1: $i > $i > $i > $i > $i ).
thf(p1_s1_funct_1_type,type,
p1_s1_funct_1: $i > $i > $o ).
thf(f1_s1_funct_1_type,type,
f1_s1_funct_1: $i ).
thf(f1_s12_funct_2_type,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_type,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_type,type,
f2_s12_funct_2: $i ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s13_funct_2_type,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_type,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_type,type,
f2_s13_funct_2: $i ).
thf(a_3_8_domain_1_type,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(f1_s2_funct_2_type,type,
f1_s2_funct_2: $i ).
thf(f3_s2_funct_2_type,type,
f3_s2_funct_2: $i > $i ).
thf(f2_s2_funct_2_type,type,
f2_s2_funct_2: $i ).
thf(k9_domain_1_type,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(a_3_3_domain_1_type,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(f1_s3_funct_2_type,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_type,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_type,type,
p1_s3_funct_2: $i > $i > $o ).
thf(f1_s6_funct_2_type,type,
f1_s6_funct_2: $i ).
thf(f2_s6_funct_2_type,type,
f2_s6_funct_2: $i ).
thf(f4_s6_funct_2_type,type,
f4_s6_funct_2: $i > $i > $i ).
thf(f3_s6_funct_2_type,type,
f3_s6_funct_2: $i ).
thf(f1_s1_funct_2_type,type,
f1_s1_funct_2: $i ).
thf(f2_s1_funct_2_type,type,
f2_s1_funct_2: $i ).
thf(p1_s1_funct_2_type,type,
p1_s1_funct_2: $i > $i > $o ).
thf(a_2_0_relset_2_type,type,
a_2_0_relset_2: $i > $i > $i ).
thf(p1_s5_domain_1_type,type,
p1_s5_domain_1: $i > $o ).
thf(p2_s5_domain_1_type,type,
p2_s5_domain_1: $i > $o ).
thf(a_1_3_domain_1_type,type,
a_1_3_domain_1: $i > $i ).
thf(a_1_4_domain_1_type,type,
a_1_4_domain_1: $i > $i ).
thf(a_4_2_domain_1_type,type,
a_4_2_domain_1: $i > $i > $i > $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k5_enumset1_type,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $i > $i ).
thf(p1_s1_domain_1_type,type,
p1_s1_domain_1: $i > $o ).
thf(a_3_0_relset_2_type,type,
a_3_0_relset_2: $i > $i > $i > $i ).
thf(k13_mcart_1_type,type,
k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_6_0_domain_1_type,type,
a_6_0_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(p1_s2_domain_1_type,type,
p1_s2_domain_1: $i > $i > $o ).
thf(f1_s2_orders_1_type,type,
f1_s2_orders_1: $i ).
thf(p1_s2_orders_1_type,type,
p1_s2_orders_1: $i > $i > $o ).
thf(a_0_2_domain_1_type,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_type,type,
f3_s9_domain_1: $i ).
thf(k14_mcart_1_type,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_0_0_domain_1_type,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_type,type,
f1_s7_domain_1: $i ).
thf(f3_s11_funct_2_type,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_type,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_type,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_type,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_type,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_type,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_type,type,
f7_s11_funct_2: $i > $i ).
thf(p1_s7_domain_1_type,type,
p1_s7_domain_1: $i > $o ).
thf(f1_s3_subset_1_type,type,
f1_s3_subset_1: $i ).
thf(p1_s3_subset_1_type,type,
p1_s3_subset_1: $i > $o ).
thf(a_4_1_relset_2_type,type,
a_4_1_relset_2: $i > $i > $i > $i > $i ).
thf(f1_s10_domain_1_type,type,
f1_s10_domain_1: $i ).
thf(p1_s10_domain_1_type,type,
p1_s10_domain_1: $i > $o ).
thf(p2_s10_domain_1_type,type,
p2_s10_domain_1: $i > $o ).
thf(f1_s1_xboole_0_type,type,
f1_s1_xboole_0: $i ).
thf(p1_s1_xboole_0_type,type,
p1_s1_xboole_0: $i > $o ).
thf(k8_subset_1_type,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_type,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_type,type,
f2_s8_domain_1: $i ).
thf(g2_struct_0_type,type,
g2_struct_0: $i > $i > $i ).
thf(f1_s1_relset_1_type,type,
f1_s1_relset_1: $i ).
thf(f2_s1_relset_1_type,type,
f2_s1_relset_1: $i ).
thf(p1_s1_relset_1_type,type,
p1_s1_relset_1: $i > $i > $o ).
thf(p1_s2_card_1_type,type,
p1_s2_card_1: $i > $o ).
thf(f1_s2_xboole_0_type,type,
f1_s2_xboole_0: $i ).
thf(p1_s2_xboole_0_type,type,
p1_s2_xboole_0: $i > $o ).
thf(f2_s2_xboole_0_type,type,
f2_s2_xboole_0: $i ).
thf(f1_s1_pboole_type,type,
f1_s1_pboole: $i ).
thf(f2_s1_pboole_type,type,
f2_s1_pboole: $i > $i ).
thf(a_8_0_domain_1_type,type,
a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s8_domain_1_type,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_type,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_type,type,
p1_s8_domain_1: $i > $o ).
thf(f1_s1_subset_1_type,type,
f1_s1_subset_1: $i ).
thf(p1_s1_subset_1_type,type,
p1_s1_subset_1: $i > $o ).
thf(p1_s2_ordinal1_type,type,
p1_s2_ordinal1: $i > $o ).
thf(f1_s9_domain_1_type,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_type,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_type,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_type,type,
p1_s9_domain_1: $i > $i > $o ).
thf(a_4_1_domain_1_type,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(f1_s2_pboole_type,type,
f1_s2_pboole: $i ).
thf(f2_s2_pboole_type,type,
f2_s2_pboole: $i ).
thf(p1_s2_pboole_type,type,
p1_s2_pboole: $i > $i > $o ).
thf(p1_s1_card_1_type,type,
p1_s1_card_1: $i > $o ).
thf(p1_s1_int_1_type,type,
p1_s1_int_1: $i > $o ).
thf(p1_s4_domain_1_type,type,
p1_s4_domain_1: $i > $i > $i > $i > $o ).
thf(f1_s2_subset_1_type,type,
f1_s2_subset_1: $i ).
thf(p1_s2_subset_1_type,type,
p1_s2_subset_1: $i > $o ).
thf(f1_s4_subset_1_type,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_type,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_type,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_type,type,
f3_s4_subset_1: $i ).
thf(f1_s2_relset_1_type,type,
f1_s2_relset_1: $i ).
thf(f2_s2_relset_1_type,type,
f2_s2_relset_1: $i ).
thf(p1_s2_relset_1_type,type,
p1_s2_relset_1: $i > $i > $o ).
thf(p1_s1_tarski_type,type,
p1_s1_tarski: $i > $i > $o ).
thf(f1_s1_tarski_type,type,
f1_s1_tarski: $i ).
thf(p1_s3_domain_1_type,type,
p1_s3_domain_1: $i > $i > $i > $o ).
thf(p1_s3_xboole_0_type,type,
p1_s3_xboole_0: $i > $o ).
thf(f1_s1_orders_1_type,type,
f1_s1_orders_1: $i ).
thf(p1_s1_orders_1_type,type,
p1_s1_orders_1: $i > $i > $o ).
thf(f1_s1_relat_1_type,type,
f1_s1_relat_1: $i ).
thf(f2_s1_relat_1_type,type,
f2_s1_relat_1: $i ).
thf(p1_s1_relat_1_type,type,
p1_s1_relat_1: $i > $i > $o ).
thf(f1_s2_pua2mss1_type,type,
f1_s2_pua2mss1: $i ).
thf(f2_s2_pua2mss1_type,type,
f2_s2_pua2mss1: $i ).
thf(p1_s2_pua2mss1_type,type,
p1_s2_pua2mss1: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk27_type,type,
sk27: $i ).
thf(sk44_type,type,
sk44: $i ).
thf(sk70_type,type,
sk70: $i ).
thf(sk81_type,type,
sk81: $i ).
thf(sk95_type,type,
sk95: $i ).
thf(sk376_type,type,
sk376: $i ).
thf(sk431_type,type,
sk431: $i ).
thf(sk456_type,type,
sk456: $i ).
thf(sk471_type,type,
sk471: $i ).
thf(sk559_type,type,
sk559: $i ).
thf(sk592_type,type,
sk592: $i ).
thf(1478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_mcart_1) ).
thf(8536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_partfun1) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_funct_1) ).
thf(4729,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(6855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_5) ).
thf(5205,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_relat_1) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(4904,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(5686,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(996,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(6085,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( ( k3_zfmisc_1 @ A @ B @ C )
= k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_mcart_1) ).
thf(6387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( ( k3_zfmisc_1 @ A @ B @ C )
= k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(5561,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4094,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1016,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_domain_1) ).
thf(6167,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_rlvect_1 @ A @ B @ C )
= ( g1_rlvect_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_rlvect_1) ).
thf(7272,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_rlvect_1 @ A @ B @ C )
= ( g1_rlvect_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= B )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_card_1) ).
thf(2889,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= B )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= B )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1642,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(9273,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(1777,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(10166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
=> ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(133,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ A )
= ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(2295,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ A )
= ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_partfun1) ).
thf(2306,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r1_tarski @ ( k4_card_3 @ C ) @ ( k4_card_3 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pua2mss1) ).
thf(2341,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r1_tarski @ ( k4_card_3 @ C ) @ ( k4_card_3 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(5857,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
thf(4464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1344,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(7854,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k9_relat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_relat_1) ).
thf(4909,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k9_relat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1400,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).
thf(8154,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A
= ( k1_tarski @ C ) ) )
=> ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(1367,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_relset_2) ).
thf(7973,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) )
<=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_mcart_1) ).
thf(6231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) )
=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 ) )
& ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
!= k1_xboole_0 )
=> ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1310,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r3_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_2) ).
thf(7691,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r3_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r3_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(821,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ? [B: $i] :
( ( m4_realset1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_realset1) ).
thf(5260,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ? [B: $i] :
( ( m4_realset1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1175,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_orders_1) ).
thf(6976,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(3399,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).
thf(1995,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_5) ).
thf(2263,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(6651,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(354,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(3167,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1580,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(8976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(2876,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1040,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_realset1) ).
thf(6285,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(2463,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1536,axiom,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(8784,plain,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_card_1) ).
thf(2787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1371,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(7990,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(1549,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
thf(8843,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).
thf(8266,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(1733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(9907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).
thf(6042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1745,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_tarski @ A @ B )
& ( p1_s1_tarski @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ? [C: $i] :
( ( r2_hidden @ C @ f1_s1_tarski )
& ( p1_s1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski) ).
thf(9965,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_tarski @ A @ B )
& ( p1_s1_tarski @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ? [C: $i] :
( ( r2_hidden @ C @ f1_s1_tarski )
& ( p1_s1_tarski @ C @ B ) ) )
& ( ? [C: $i] :
( ( r2_hidden @ C @ f1_s1_tarski )
& ( p1_s1_tarski @ C @ B ) )
=> ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(6263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1466,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_realset1) ).
thf(8475,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ! [E: $i] :
( ( m1_pboole @ E @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ D @ E )
& ( r4_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_pboole) ).
thf(5582,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ! [E: $i] :
( ( m1_pboole @ E @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ D @ E )
& ( r4_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1385,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).
thf(8077,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1456,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(8417,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_sysrel) ).
thf(2309,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_sysrel @ B ) ) ) )
& ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) ) )
& ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ( r2_hidden @ ( k4_tarski @ A @ A ) @ B ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1254,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(7358,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(3509,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1754,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(9998,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relset_1) ).
thf(3498,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1658,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(9400,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(3680,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(539,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4043,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(435,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(3534,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1296,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(7601,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(358,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_orders_1) ).
thf(3185,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_5) ).
thf(1924,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1390,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_xboole_1) ).
thf(8129,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).
thf(2940,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(90,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_finseq_2) ).
thf(2104,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(6944,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_xboole_0 @ A @ B )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_sysrel) ).
thf(2231,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_xboole_0 @ A @ B )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_subset_1) ).
thf(6162,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1650,axiom,
! [A: $i] :
( ( v1_setfam_1 @ A )
<=> ~ ( r2_hidden @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(9351,plain,
! [A: $i] :
( ( ( v1_setfam_1 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ A ) )
& ( ~ ( r2_hidden @ k1_xboole_0 @ A )
=> ( v1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_partfun1) ).
thf(2808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(3905,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).
thf(6106,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ? [C: $i] : ( m2_pboole @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pboole) ).
thf(3813,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ? [C: $i] : ( m2_pboole @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(369,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_relat_1) ).
thf(3230,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(780,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
thf(5069,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( H != k1_xboole_0 )
& ? [I: $i] :
( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ? [J: $i] :
( ( m1_subset_1 @ J @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
& ( I = J )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ I )
= ( k8_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ I )
= ( k9_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ I )
= ( k10_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ I )
= ( k11_mcart_1 @ E @ F @ G @ H @ J ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_mcart_1) ).
thf(5644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( G != k1_xboole_0 )
& ( H != k1_xboole_0 )
& ? [I: $i] :
( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ? [J: $i] :
( ( m1_subset_1 @ J @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
& ( I = J )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ I )
= ( k8_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ I )
= ( k9_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ I )
= ( k10_mcart_1 @ E @ F @ G @ H @ J ) )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ I )
= ( k11_mcart_1 @ E @ F @ G @ H @ J ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1363,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(7958,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(299,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(2905,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(2908,plain,
v1_relat_1 @ sk44,
inference(cnf,[status(esa)],[2905]) ).
thf(1144,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relat_1) ).
thf(6813,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
<=> ( ( k5_relset_1 @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( ( k5_relset_1 @ A @ B @ C )
= B ) )
& ( ( ( k5_relset_1 @ A @ B @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).
thf(3040,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1596,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(9045,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(5297,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1510,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(8682,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1464,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(8463,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(39,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_5) ).
thf(1939,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(120,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2248,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_relat_1) ).
thf(3108,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(752,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relat_1) ).
thf(4960,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(6323,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2099,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(5224,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
=> ( ( k2_card_1 @ A )
= ( k2_card_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_card_1) ).
thf(5669,plain,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
=> ( ( k2_card_1 @ A )
= ( k2_card_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(3402,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).
thf(5691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1785,plain,
~ ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) )
=> ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1786,plain,
( ( sk4 != k1_xboole_0 )
| ~ sk3 ),
inference(cnf,[status(esa)],[1785]) ).
thf(1793,plain,
( ( sk4 != k1_xboole_0 )
| ~ sk3 ),
inference(lifteq,[status(thm)],[1786]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(8988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_1) ).
thf(5383,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1614,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(9152,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ( ( k7_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(1378,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).
thf(8045,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_relat_1) ).
thf(6602,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(9818,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(5614,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).
thf(9364,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(1611,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(9135,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_2) ).
thf(6732,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1788,plain,
m1_subset_1 @ sk2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ sk1 ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(1575,axiom,
! [A: $i,B: $i] : ( r1_setfam_1 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_setfam_1) ).
thf(8963,plain,
! [A: $i] : ( r1_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_5) ).
thf(2035,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1293,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(7556,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ B @ C @ D )
= ( k2_relat_1 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_realset1) ).
thf(8490,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_setfam_1) ).
thf(5701,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1589,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).
thf(9000,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s1_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(1445,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_domain_1) ).
thf(8370,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(443,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relat_1) ).
thf(3562,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_2) ).
thf(6336,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(73,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funcop_1) ).
thf(2042,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(3895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2195,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(654,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(4543,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5425,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_mcart_1) ).
thf(5814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(583,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_sysrel) ).
thf(4234,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k1_sysrel @ A ) @ ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1621,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(9184,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(625,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k5_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(4418,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k5_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(700,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(4739,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_2) ).
thf(3135,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A )
& ( r1_partfun1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(4097,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1525,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(8747,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1441,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(8353,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(415,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(3444,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(3446,plain,
v1_funct_1 @ sk81,
inference(cnf,[status(esa)],[3444]) ).
thf(1775,axiom,
! [A: $i] :
( ( m2_relset_1 @ A @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
=> ! [B: $i] :
( ( m2_relset_1 @ B @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
=> ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( p1_s2_pua2mss1 @ C @ D ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
=> ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( p1_s2_pua2mss1 @ C @ D ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_pua2mss1) ).
thf(10138,plain,
! [A: $i] :
( ( m2_relset_1 @ A @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
=> ! [B: $i] :
( ( m2_relset_1 @ B @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
=> ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( p1_s2_pua2mss1 @ C @ D ) )
& ( ( p1_s2_pua2mss1 @ C @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
=> ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( p1_s2_pua2mss1 @ C @ D ) )
& ( ( p1_s2_pua2mss1 @ C @ D )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( r2_hidden @ I @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( r2_hidden @ ( k8_mcart_1 @ A @ B @ C @ D @ I ) @ E )
& ( r2_hidden @ ( k9_mcart_1 @ A @ B @ C @ D @ I ) @ F )
& ( r2_hidden @ ( k10_mcart_1 @ A @ B @ C @ D @ I ) @ G )
& ( r2_hidden @ ( k11_mcart_1 @ A @ B @ C @ D @ I ) @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_mcart_1) ).
thf(5316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( r2_hidden @ I @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( r2_hidden @ ( k8_mcart_1 @ A @ B @ C @ D @ I ) @ E )
& ( r2_hidden @ ( k9_mcart_1 @ A @ B @ C @ D @ I ) @ F )
& ( r2_hidden @ ( k10_mcart_1 @ A @ B @ C @ D @ I ) @ G )
& ( r2_hidden @ ( k11_mcart_1 @ A @ B @ C @ D @ I ) @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(820,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(5257,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
thf(4638,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_1) ).
thf(7345,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1432,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relset_2) ).
thf(8298,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_partfun1) ).
thf(4856,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
& ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_xboole_1) ).
thf(4440,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
& ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_finseq_2) ).
thf(1988,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1651,axiom,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(9356,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(1142,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(6804,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1500,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).
thf(8650,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(45,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(1954,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(9246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(4980,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relset_2) ).
thf(6640,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(7220,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(852,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(5412,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1716,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(9774,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(377,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(3276,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).
thf(4941,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(6138,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(341,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(3103,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
= ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1761,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(10022,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(3777,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(8705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(1481,axiom,
? [A: $i] : ( v1_int_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_int_1) ).
thf(8546,plain,
? [A: $i] : ( v1_int_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(289,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_partfun1) ).
thf(2869,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1551,axiom,
( ! [A: $i] :
~ ( ( r2_hidden @ A @ f1_s1_funct_2 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ f2_s1_funct_2 )
& ( p1_s1_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s1_funct_2 @ f2_s1_funct_2 )
& ( m2_relset_1 @ A @ f1_s1_funct_2 @ f2_s1_funct_2 )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s1_funct_2 )
=> ( p1_s1_funct_2 @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_2) ).
thf(8848,plain,
( ! [A: $i] :
~ ( ( r2_hidden @ A @ f1_s1_funct_2 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ f2_s1_funct_2 )
& ( p1_s1_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s1_funct_2 @ f2_s1_funct_2 )
& ( m2_relset_1 @ A @ f1_s1_funct_2 @ f2_s1_funct_2 )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s1_funct_2 )
=> ( p1_s1_funct_2 @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(439,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_partfun1) ).
thf(3545,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_2) ).
thf(2491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C )
& ( v2_funct_1 @ E ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ D )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = H ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k7_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_mcart_1) ).
thf(6268,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = H ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k7_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).
thf(2548,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(971,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(5935,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_2) ).
thf(2227,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1479,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(8539,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
<=> ( ( k4_relset_1 @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(4266,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( ( k4_relset_1 @ B @ A @ C )
= B ) )
& ( ( ( k4_relset_1 @ B @ A @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_xboole_1) ).
thf(5745,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) )
& ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1392,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(8133,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(6009,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1752,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_2) ).
thf(9994,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(34,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_partfun1) ).
thf(1921,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).
thf(5770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(741,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).
thf(4916,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).
thf(5903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(7364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_relat_1) ).
thf(3281,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(421,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v2_funct_1 @ k1_xboole_0 )
& ( v1_finset_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finseq_1) ).
thf(3463,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v2_funct_1 @ k1_xboole_0 )
& ( v1_finset_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(3466,plain,
v2_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(1402,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(8165,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(350,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ~ ( r4_pboole @ A @ B @ ( k1_pboole @ A ) )
& ~ ( r4_pboole @ A @ ( k1_pboole @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_pboole) ).
thf(3140,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ~ ( r4_pboole @ A @ B @ ( k1_pboole @ A ) )
& ~ ( r4_pboole @ A @ ( k1_pboole @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(536,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(4030,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1247,axiom,
~ ( v1_xboole_0 @ k4_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_numbers) ).
thf(7343,plain,
~ ( v1_xboole_0 @ k4_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_relat_1) ).
thf(4607,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1375,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(8025,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_relat_1) ).
thf(4963,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_sysrel) ).
thf(1967,plain,
! [A: $i,B: $i] :
( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(273,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2819,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(558,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(4156,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_sysrel) ).
thf(5269,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_2) ).
thf(4665,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(4322,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_finseq_2) ).
thf(1904,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ~ ( ~ ( r4_pboole @ A @ B @ C )
& ( r4_pboole @ A @ ( k3_pboole @ A @ D @ B ) @ ( k3_pboole @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_pboole) ).
thf(4610,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ~ ( ~ ( r4_pboole @ A @ B @ C )
& ( r4_pboole @ A @ ( k3_pboole @ A @ D @ B ) @ ( k3_pboole @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1215,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finseq_1) ).
thf(7178,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_relat_1) ).
thf(4467,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(940,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_domain_1) ).
thf(5797,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(841,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_sysrel) ).
thf(5342,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(23,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_sysrel) ).
thf(1887,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1491,axiom,
! [A: $i,B: $i] :
( ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ B ) ) )
<=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_card_1) ).
thf(8603,plain,
! [A: $i,B: $i] :
( ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ B ) ) )
=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) )
& ( ? [C: $i] :
( A
= ( k1_tarski @ C ) )
=> ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(312,axiom,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(2957,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(6707,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(218,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_partfun1) ).
thf(2603,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1632,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(9216,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1669,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(9464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1442,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
thf(8357,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(1499,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(8647,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r2_hidden @ A @ B )
& ~ ( r2_hidden @ C @ B )
& ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(1250,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pua2mss1) ).
thf(7349,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k3_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k3_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(2501,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k3_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k3_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r2_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_pboole) ).
thf(4778,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r2_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(2682,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t163_relat_1) ).
thf(1832,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1739,axiom,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(9938,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(7011,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(1261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relset_2) ).
thf(7386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1743,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(9960,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).
thf(3820,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_relat_1) ).
thf(5553,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(373,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_partfun1) ).
thf(3248,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1765,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( C
= ( k7_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ C )
<=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(10042,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( C
= ( k7_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1492,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).
thf(8610,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(652,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4539,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_1) ).
thf(3442,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(519,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(3938,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1237,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(7279,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1354,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_2) ).
thf(7914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_funct_1) ).
thf(5306,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1791,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
= k1_xboole_0 )
| ~ sk3 ),
inference(cnf,[status(esa)],[1785]) ).
thf(1792,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
= k1_xboole_0 )
| ~ sk3 ),
inference(lifteq,[status(thm)],[1791]) ).
thf(662,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4563,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(55,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k4_card_3 @ A )
= ( k4_card_3 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_pua2mss1) ).
thf(1985,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k4_card_3 @ A )
= ( k4_card_3 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_5) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1599,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(9067,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(1659,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s5_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_4_domain_1) ).
thf(9410,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s5_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s5_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(1557,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(8875,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t179_relat_1) ).
thf(4151,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1416,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_funct_1) ).
thf(8225,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(680,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_sysrel) ).
thf(4654,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
& ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(18,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_partfun1) ).
thf(1860,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(605,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_relat_1) ).
thf(4334,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1573,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(8951,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_2) ).
thf(3148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ D @ A )
& ( m2_relset_1 @ E @ D @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ D @ A )
& ( m2_relset_1 @ F @ D @ A ) )
=> ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
= ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
=> ( E = F ) ) ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1548,axiom,
( ! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ f1_s6_funct_2 )
& ( r2_hidden @ B @ f2_s6_funct_2 ) )
=> ( r2_hidden @ ( f4_s6_funct_2 @ A @ B ) @ f3_s6_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s6_funct_2 @ f2_s6_funct_2 ) @ f3_s6_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s6_funct_2 @ f2_s6_funct_2 ) @ f3_s6_funct_2 )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ f1_s6_funct_2 )
& ( r2_hidden @ C @ f2_s6_funct_2 ) )
=> ( ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) )
= ( f4_s6_funct_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_funct_2) ).
thf(8834,plain,
( ! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ f1_s6_funct_2 )
& ( r2_hidden @ B @ f2_s6_funct_2 ) )
=> ( r2_hidden @ ( f4_s6_funct_2 @ A @ B ) @ f3_s6_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s6_funct_2 @ f2_s6_funct_2 ) @ f3_s6_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s6_funct_2 @ f2_s6_funct_2 ) @ f3_s6_funct_2 )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ f1_s6_funct_2 )
& ( r2_hidden @ C @ f2_s6_funct_2 ) )
=> ( ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) )
= ( f4_s6_funct_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2274,plain,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(6506,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1537,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(8787,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k5_pboole @ A @ B @ C )
= ( k5_pboole @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_pboole) ).
thf(3542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k5_pboole @ A @ B @ C )
= ( k5_pboole @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(592,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_partfun1) ).
thf(4275,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
thf(4349,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
=> ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1398,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pboole) ).
thf(8146,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r2_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) )
=> ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_pboole) ).
thf(2488,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r2_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) )
=> ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( ( r1_tarski @ A @ B )
& ( A != k1_xboole_0 )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( v3_ordinal1 @ D )
=> ( ( r2_hidden @ D @ A )
=> ( r1_ordinal1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(5712,plain,
! [A: $i,B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( ( r1_tarski @ A @ B )
& ( A != k1_xboole_0 )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( v3_ordinal1 @ D )
=> ( ( r2_hidden @ D @ A )
=> ( r1_ordinal1 @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_2) ).
thf(1992,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(7000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).
thf(5289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k3_relset_2 @ A @ B @ C @ D )
= ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relset_2) ).
thf(5836,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k3_relset_2 @ A @ B @ C @ D )
= ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(6643,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_2) ).
thf(8753,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(148,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(2356,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1563,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_domain_1) ).
thf(8907,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(526,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(3998,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = I ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k10_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_mcart_1) ).
thf(6396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = I ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k10_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1522,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(8717,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(153,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2373,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1195,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(7075,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(3470,plain,
v3_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(135,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(2301,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(5076,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1469,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
& ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_pboole) ).
thf(8483,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
& ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(6734,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1555,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_1) ).
thf(8870,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(1696,axiom,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_card_1) ).
thf(9629,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(1346,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
thf(7862,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_5) ).
thf(1892,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(285,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
= ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_relat_1) ).
thf(2857,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
= ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(727,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(4862,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
= ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(4353,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1118,axiom,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s8_funct_2 @ f2_s8_funct_2 ) @ f3_s8_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s8_funct_2 @ f2_s8_funct_2 ) @ f3_s8_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_funct_2 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s8_funct_2 )
=> ( ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) )
= ( f4_s8_funct_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_funct_2) ).
thf(6681,plain,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s8_funct_2 @ f2_s8_funct_2 ) @ f3_s8_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s8_funct_2 @ f2_s8_funct_2 ) @ f3_s8_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_funct_2 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s8_funct_2 )
=> ( ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) )
= ( f4_s8_funct_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C ) )
=> ( ( B = k1_xboole_0 )
| ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
= ( k6_partfun1 @ A ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
= ( k6_partfun1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_2) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C ) )
=> ( ( B = k1_xboole_0 )
| ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
= ( k6_partfun1 @ A ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
= ( k6_partfun1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(6455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1220,axiom,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(7209,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(1615,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_0_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(9155,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_0_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(1104,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(6626,plain,
! [A: $i] :
~ ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1740,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_subset_1) ).
thf(9941,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(6599,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(386,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3312,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(459,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3657,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).
thf(4368,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(5829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1294,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_domain_1) ).
thf(7560,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(1637,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(9240,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(97,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ A )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_sysrel) ).
thf(2158,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ A )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1517,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(8703,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( r1_ordinal1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(3835,plain,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( r1_ordinal1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1365,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
<=> ( r2_hidden @ A @ k4_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_int_1) ).
thf(7965,plain,
! [A: $i] :
( ( ( v1_int_1 @ A )
=> ( r2_hidden @ A @ k4_numbers ) )
& ( ( r2_hidden @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(712,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_sysrel) ).
thf(4793,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(644,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(4507,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1420,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).
thf(8252,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(599,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k1_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(4302,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k1_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
& ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_sysrel) ).
thf(3866,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
& ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
= ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).
thf(7032,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1401,axiom,
! [A: $i,B: $i] :
( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
= ( k4_zfmisc_1 @ B @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_mcart_1) ).
thf(8161,plain,
! [A: $i,B: $i] :
( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
= ( k4_zfmisc_1 @ B @ B @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(1283,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).
thf(7509,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(589,axiom,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(4253,plain,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(1280,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(7500,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1430,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_domain_1) ).
thf(8293,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(492,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3788,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ A )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_finseq_2) ).
thf(2007,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ A )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3322,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(432,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r1_tarski @ C @ D )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t188_relat_1) ).
thf(3524,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r1_tarski @ C @ D )
& ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) ) )
=> ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(266,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
= ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funcop_1) ).
thf(2794,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
= ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(3199,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(629,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_partfun1) ).
thf(4454,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(464,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
=> ( A
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_sysrel) ).
thf(3670,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
=> ( A
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(719,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(4820,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).
thf(7775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(6745,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1306,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(7677,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(1476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
<=> ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_mcart_1) ).
thf(8526,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) ) )
& ( ( ( r2_hidden @ A @ D )
& ( r2_hidden @ B @ E )
& ( r2_hidden @ C @ F ) )
=> ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_2) ).
thf(7317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(5805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= ( k1_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(4556,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= ( k1_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1454,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_realset1) ).
thf(8411,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).
thf(2178,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(111,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_sysrel) ).
thf(2222,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(690,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4696,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(5957,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1627,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(9204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
= k1_xboole_0 )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_sysrel) ).
thf(4205,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
= k1_xboole_0 ) )
& ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
= k1_xboole_0 )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(116,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2237,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2616,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_partfun1) ).
thf(4396,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E )
& ( v1_partfun1 @ E @ A @ B ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_funct_1) ).
thf(4329,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1448,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(8379,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_2) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
= ( k6_partfun1 @ B ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(664,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
<=> ? [B: $i] :
( ( v3_ordinal1 @ B )
& ( A = B )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ( ( r2_wellord2 @ C @ B )
=> ( r1_ordinal1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_card_1) ).
thf(4578,plain,
! [A: $i] :
( ( ( v1_card_1 @ A )
=> ? [B: $i] :
( ( v3_ordinal1 @ B )
& ( A = B )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ( ( r2_wellord2 @ C @ B )
=> ( r1_ordinal1 @ B @ C ) ) ) ) )
& ( ? [B: $i] :
( ( v3_ordinal1 @ B )
& ( A = B )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ( ( r2_wellord2 @ C @ B )
=> ( r1_ordinal1 @ B @ C ) ) ) )
=> ( v1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1672,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_subset_1) ).
thf(9490,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
thf(6670,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(86,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2090,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(3393,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( E
!= ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_mcart_1) ).
thf(5013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( E
!= ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
& ( E
!= ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1240,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
thf(7300,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(477,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3724,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).
thf(7104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(417,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(3453,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_1) ).
thf(2451,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_sysrel) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1341,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(7845,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(5558,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).
thf(5946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ? [D: $i] : ( m3_pboole @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ? [D: $i] : ( m3_pboole @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_relat_1) ).
thf(4147,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_mcart_1) ).
thf(8321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(718,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( ( ( k3_funcop_1 @ D @ ( k6_finseq_1 @ A ) @ F )
= ( k6_finseq_1 @ C ) )
& ( ( k3_funcop_1 @ D @ E @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_finseq_2) ).
thf(4815,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ A )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( ( ( k3_funcop_1 @ D @ ( k6_finseq_1 @ A ) @ F )
= ( k6_finseq_1 @ C ) )
& ( ( k3_funcop_1 @ D @ E @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_xboole_1) ).
thf(3621,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( k2_realset1 @ A @ B @ C )
= ( k1_realset1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(8659,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( k2_realset1 @ A @ B @ C )
= ( k1_realset1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_funct_1) ).
thf(2925,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(3973,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_partfun1) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(4798,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ? [E: $i,F: $i,G: $i] :
( ( D
= ( k3_mcart_1 @ E @ F @ G ) )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= E )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= F )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_mcart_1) ).
thf(3093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ? [E: $i,F: $i,G: $i] :
( ( D
= ( k3_mcart_1 @ E @ F @ G ) )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= E )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= F )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_pua2mss1) ).
thf(2335,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ A )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ B )
& ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1529,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(8759,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(6157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2777,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(709,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(4783,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(7473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(3712,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_relat_1) ).
thf(5169,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(3226,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5665,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).
thf(7460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(1457,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(8421,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ! [D: $i] :
( ( m3_pboole @ D @ A @ B @ C )
=> ( m1_pboole @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(3389,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ! [D: $i] :
( ( m3_pboole @ D @ A @ B @ C )
=> ( m1_pboole @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2508,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(9875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(1380,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k5_funcop_1 @ E @ D @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_finseq_2) ).
thf(8050,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k5_funcop_1 @ E @ D @ ( k6_finseq_1 @ B ) )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(1461,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_orders_1) ).
thf(8438,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1426,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).
thf(8274,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_zfmisc_1) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_mcart_1) ).
thf(6648,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(5448,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(748,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(4935,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(221,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(2618,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v2_relat_1 @ B )
=> ~ ( v3_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_pboole) ).
thf(2833,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v2_relat_1 @ B )
=> ~ ( v3_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1655,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(9369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(105,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(2190,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_setfam_1) ).
thf(7381,plain,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_relat_1) ).
thf(2483,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_mcart_1) ).
thf(6491,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
& ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1710,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(9743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(1452,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(8406,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_2) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( B != k1_xboole_0 )
& ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) ) )
& ~ ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
& ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_funct_2) ).
thf(3036,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
& ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(816,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ D @ C )
= ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_2) ).
thf(5246,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ D @ C )
= ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(838,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v2_relat_1 @ A )
<=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_1) ).
thf(5321,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v2_relat_1 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) )
& ( ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) )
=> ( v2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(92,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(2137,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
& ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(9700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(1513,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(8691,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3361,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(6700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(651,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funcop_1) ).
thf(4536,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(118,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(2242,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1654,axiom,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1) ).
thf(9368,plain,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(1483,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k13_finseq_1 @ A ) @ A ) )
=> ( ~ ( ~ ( v1_xboole_0 @ B )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
& ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_unialg_1) ).
thf(8554,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k13_finseq_1 @ A ) @ A ) )
=> ( ~ ( ~ ( v1_xboole_0 @ B )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
& ( v1_xboole_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_relat_1 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_orders_1) ).
thf(3588,plain,
! [A: $i,B: $i] :
( ( ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_relat_1 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_2) ).
thf(4379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( ( k2_relat_1 @ D )
= B ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( v2_funct_1 @ D )
& ( v2_funct_1 @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_1) ).
thf(4892,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(3559,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(6787,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
<=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_pua2mss1) ).
thf(4628,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) )
=> ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(7354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(6210,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ D )
=> ( ( F
= ( k11_mcart_1 @ A @ B @ C @ D @ E ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = J ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_mcart_1) ).
thf(6860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ D )
=> ( ( ( F
= ( k11_mcart_1 @ A @ B @ C @ D @ E ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = J ) ) )
& ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = J ) )
=> ( F
= ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( B
= ( k8_relat_1 @ A @ C ) )
<=> ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
thf(2982,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( B
= ( k8_relat_1 @ A @ C ) )
=> ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
=> ( B
= ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(294,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(2884,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(638,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(4483,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(7305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(724,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(4853,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(668,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( ( k3_zfmisc_1 @ A @ B @ C )
= ( a_3_0_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_domain_1) ).
thf(4604,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ( ( k3_zfmisc_1 @ A @ B @ C )
= ( a_3_0_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(850,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(5406,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
=> ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_finseq_2) ).
thf(3852,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).
thf(7217,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(3995,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(6307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(2641,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ B @ A )
= ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( r2_pboole @ A @ ( k1_pboole @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_pboole) ).
thf(4925,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( r2_pboole @ A @ ( k1_pboole @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1023,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ A @ B )
<=> ( ( r1_tarski @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_card_1) ).
thf(6200,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( ( r2_hidden @ A @ B )
=> ( ( r1_tarski @ A @ B )
& ( A != B ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( A != B ) )
=> ( r2_hidden @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1594,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(9026,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ~ ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ~ ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_1) ).
thf(1863,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1671,axiom,
( ( ! [A: $i] :
( ( r2_hidden @ A @ f1_s2_xboole_0 )
<=> ( p1_s2_xboole_0 @ A ) )
& ! [A: $i] :
( ( r2_hidden @ A @ f2_s2_xboole_0 )
<=> ( p1_s2_xboole_0 @ A ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_xboole_0) ).
thf(9472,plain,
( ( ! [A: $i] :
( ( ( r2_hidden @ A @ f1_s2_xboole_0 )
=> ( p1_s2_xboole_0 @ A ) )
& ( ( p1_s2_xboole_0 @ A )
=> ( r2_hidden @ A @ f1_s2_xboole_0 ) ) )
& ! [A: $i] :
( ( ( r2_hidden @ A @ f2_s2_xboole_0 )
=> ( p1_s2_xboole_0 @ A ) )
& ( ( p1_s2_xboole_0 @ A )
=> ( r2_hidden @ A @ f2_s2_xboole_0 ) ) ) )
=> ( f1_s2_xboole_0 = f2_s2_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(1767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).
thf(10062,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
& ( p1_s3_domain_1 @ E @ F @ G ) )
=> ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(5961,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_partfun1) ).
thf(2011,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(450,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_funct_1) ).
thf(3591,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) )
=> ( v2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1322,axiom,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(7782,plain,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4407,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_pboole @ D @ B ) )
=> ( m1_pboole @ ( k7_pboole @ A @ B @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_pboole) ).
thf(5751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_pboole @ D @ B ) )
=> ( m1_pboole @ ( k7_pboole @ A @ B @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(4888,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r2_hidden @ A @ B )
=> ( v3_ordinal1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(5839,plain,
! [A: $i,B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r2_hidden @ A @ B )
=> ( v3_ordinal1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1315,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(7745,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1633,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s5_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_3_domain_1) ).
thf(9221,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s5_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s5_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(1664,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(9440,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(4480,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1290,axiom,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(7550,plain,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(6047,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(228,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(2646,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(150,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(2364,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1345,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(7859,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(1094,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r7_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_2) ).
thf(6588,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r7_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r7_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1782,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(10197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) )
& ( ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) )
=> ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(1719,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).
thf(9797,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) ) )
& ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
& ( p1_s4_domain_1 @ F @ G @ H @ I ) )
=> ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(1629,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_2) ).
thf(9209,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1493,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( v3_ordinal1 @ B )
& ( r1_tarski @ B @ A ) ) )
=> ( v3_ordinal1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(8613,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( v3_ordinal1 @ B )
& ( r1_tarski @ B @ A ) ) )
=> ( v3_ordinal1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( k1_funct_1 @ ( k5_pboole @ A @ B @ C ) @ D )
= ( k5_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pboole) ).
thf(7269,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( ( k1_funct_1 @ ( k5_pboole @ A @ B @ C ) @ D )
= ( k5_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(87,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ A )
= ( k1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_finseq_1) ).
thf(2093,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ A )
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1616,axiom,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(9164,plain,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(612,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(4370,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).
thf(6741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_relat_1) ).
thf(5540,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_5) ).
thf(2083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ D @ A @ B )
=> ( ( k9_relset_1 @ A @ B @ C @ D )
= ( k8_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_relset_1) ).
thf(4100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ D @ A @ B )
=> ( ( k9_relset_1 @ A @ B @ C @ D )
= ( k8_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( B
= ( k7_relat_1 @ C @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(2382,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( B
= ( k7_relat_1 @ C @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
=> ( B
= ( k7_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(78,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pua2mss1) ).
thf(2061,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(561,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k3_pua2mss1 @ A )
= ( a_1_0_pua2mss1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_pua2mss1) ).
thf(4172,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k3_pua2mss1 @ A )
= ( a_1_0_pua2mss1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(60,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_relat_1) ).
thf(2000,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_partfun1) ).
thf(1900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C )
& ( r2_wellord2 @ A @ C ) )
=> ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_card_1) ).
thf(5611,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C )
& ( r2_wellord2 @ A @ C ) )
=> ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(201,axiom,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_relat_1) ).
thf(2541,plain,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(884,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(5579,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1338,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7834,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(3742,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
<=> ( ( k2_relat_1 @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).
thf(3239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
=> ( ( k2_relat_1 @ C )
= B ) )
& ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(4499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ C @ ( k2_tarski @ A @ B ) ) @ ( k1_zfmisc_1 @ C ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ C @ ( k2_tarski @ A @ B ) ) )
= ( k1_card_1 @ ( k1_zfmisc_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_5) ).
thf(3514,plain,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ C @ ( k2_tarski @ A @ B ) ) @ ( k1_zfmisc_1 @ C ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ C @ ( k2_tarski @ A @ B ) ) )
= ( k1_card_1 @ ( k1_zfmisc_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1258,axiom,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(7378,plain,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(8513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D ) )
=> ( r2_pboole @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pboole) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D ) )
=> ( r2_pboole @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1772,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ( p1_s1_orders_1 @ A @ A ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ( ( ( p1_s1_orders_1 @ A @ B )
& ( p1_s1_orders_1 @ B @ A ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
=> ( ( ( p1_s1_orders_1 @ A @ B )
& ( p1_s1_orders_1 @ B @ C ) )
=> ( p1_s1_orders_1 @ A @ C ) ) ) ) )
& ! [A: $i] :
~ ( ( r1_tarski @ A @ f1_s1_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
=> ~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( p1_s1_orders_1 @ B @ C )
& ~ ( p1_s1_orders_1 @ C @ B ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
& ( r2_hidden @ C @ A )
& ~ ( p1_s1_orders_1 @ C @ B ) ) ) ) )
=> ? [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ~ ( ( A != B )
& ( p1_s1_orders_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_orders_1) ).
thf(10099,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ( p1_s1_orders_1 @ A @ A ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ( ( ( p1_s1_orders_1 @ A @ B )
& ( p1_s1_orders_1 @ B @ A ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
=> ( ( ( p1_s1_orders_1 @ A @ B )
& ( p1_s1_orders_1 @ B @ C ) )
=> ( p1_s1_orders_1 @ A @ C ) ) ) ) )
& ! [A: $i] :
~ ( ( r1_tarski @ A @ f1_s1_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
=> ~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( p1_s1_orders_1 @ B @ C )
& ~ ( p1_s1_orders_1 @ C @ B ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f1_s1_orders_1 )
& ( r2_hidden @ C @ A )
& ~ ( p1_s1_orders_1 @ C @ B ) ) ) ) )
=> ? [A: $i] :
( ( m1_subset_1 @ A @ f1_s1_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s1_orders_1 )
=> ~ ( ( A != B )
& ( p1_s1_orders_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(1708,axiom,
( ( ( p1_s1_card_1 @ k1_xboole_0 )
& ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( p1_s1_card_1 @ A )
=> ( p1_s1_card_1 @ ( k2_card_1 @ A ) ) ) )
& ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( ( v2_card_1 @ A )
& ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s1_card_1 @ B ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( p1_s1_card_1 @ A ) ) ) ) )
=> ! [A: $i] :
( ( v1_card_1 @ A )
=> ( p1_s1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_card_1) ).
thf(9722,plain,
( ( ( p1_s1_card_1 @ k1_xboole_0 )
& ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( p1_s1_card_1 @ A )
=> ( p1_s1_card_1 @ ( k2_card_1 @ A ) ) ) )
& ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( ( v2_card_1 @ A )
& ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s1_card_1 @ B ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( p1_s1_card_1 @ A ) ) ) ) )
=> ! [A: $i] :
( ( v1_card_1 @ A )
=> ( p1_s1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(499,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(3827,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1534,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(8778,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(2428,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1678,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).
thf(9522,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(4016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(2805,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k5_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_mcart_1) ).
thf(6550,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k5_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1147,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(6820,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1033,axiom,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).
thf(6247,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
= ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).
thf(5794,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
= ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_mcart_1) ).
thf(8756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D ) )
=> ( r4_pboole @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_pboole) ).
thf(4989,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D ) )
=> ( r4_pboole @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(5044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(94,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(2147,plain,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( ( r1_ordinal1 @ A @ B )
<=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(5266,plain,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( ( ( r1_ordinal1 @ A @ B )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( r1_ordinal1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1313,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_zfmisc_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(7710,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(921,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(5719,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(370,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_relat_1 @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_funct_1) ).
thf(3233,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v3_relat_1 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(7084,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1748,axiom,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_setfam_1) ).
thf(9981,plain,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(509,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
thf(3884,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1607,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(9126,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_relat_1) ).
thf(4284,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1711,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(9745,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(869,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5507,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1561,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( p1_s5_domain_1 @ B )
=> ( p2_s5_domain_1 @ B ) ) )
=> ( r1_tarski @ ( a_1_3_domain_1 @ A ) @ ( a_1_4_domain_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_domain_1) ).
thf(8899,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( p1_s5_domain_1 @ B )
=> ( p2_s5_domain_1 @ B ) ) )
=> ( r1_tarski @ ( a_1_3_domain_1 @ A ) @ ( a_1_4_domain_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(6178,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_partfun1) ).
thf(3250,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( r1_partfun1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(5594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(422,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3471,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( m3_pboole @ D @ A @ B @ C )
<=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
& ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
& ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_pboole) ).
thf(5924,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( m3_pboole @ D @ A @ B @ C )
=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
& ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
& ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) )
& ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
& ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
& ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) )
=> ( m3_pboole @ D @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(6620,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1668,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_4_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_4_domain_1) ).
thf(9455,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_4_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_4_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(1572,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
thf(8948,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(1683,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(9539,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(1326,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_xboole_1) ).
thf(7794,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(4187,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(5201,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1360,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_mcart_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_mcart_1) ).
thf(7934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_mcart_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(546,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(4080,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( A
= ( k11_mcart_1 @ B @ C @ D @ E @ F ) )
<=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = J ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_domain_1) ).
thf(6090,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( ( A
= ( k11_mcart_1 @ B @ C @ D @ E @ F ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = J ) ) ) ) ) ) )
& ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = J ) ) ) ) ) )
=> ( A
= ( k11_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).
thf(7237,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1042,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(6303,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1543,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).
thf(8810,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(5826,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1686,axiom,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(9554,plain,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_sysrel) ).
thf(1837,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(5937,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) )
=> ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1506,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
<=> ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(8672,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
=> ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) )
=> ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(1379,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_domain_1) ).
thf(8048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_sysrel) ).
thf(4192,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(493,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(3810,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
= ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(5465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1622,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(9190,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(1516,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(8700,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(1386,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(8085,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2477,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1701,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_relset_2) ).
thf(9658,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) )
& ( ( ( k3_pua2mss1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k3_pboole @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_pboole) ).
thf(4725,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k3_pboole @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_relat_1) ).
thf(3090,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = H ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k9_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_mcart_1) ).
thf(8386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = H ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k9_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).
thf(8942,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(1068,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( v3_ordinal1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
thf(6427,plain,
! [A: $i] :
~ ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
& ( ( v3_ordinal1 @ B )
=> ( r2_hidden @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(706,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k7_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(4757,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k7_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
& ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
& ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k7_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ? [F: $i,G: $i,H: $i,I: $i] :
( ( E
= ( k4_mcart_1 @ F @ G @ H @ I ) )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= F )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= G )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= H )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_mcart_1) ).
thf(4947,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ? [F: $i,G: $i,H: $i,I: $i] :
( ( E
= ( k4_mcart_1 @ F @ G @ H @ I ) )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= F )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= G )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= H )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(396,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k1_pboole @ A ) )
& ( v3_relat_1 @ ( k1_pboole @ A ) )
& ( v1_funct_1 @ ( k1_pboole @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_pboole) ).
thf(3349,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k1_pboole @ A ) )
& ( v3_relat_1 @ ( k1_pboole @ A ) )
& ( v1_funct_1 @ ( k1_pboole @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(441,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(3556,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
= ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_relat_1) ).
thf(4994,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(382,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).
thf(3297,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(7361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(44,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k3_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relat_1) ).
thf(1951,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k3_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_2) ).
thf(3718,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1714,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(9758,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).
thf(4553,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(6972,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_partfun1) ).
thf(4327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1787,plain,
( ( r2_hidden @ sk4 @ sk2 )
| ~ sk3 ),
inference(cnf,[status(esa)],[1785]) ).
thf(1661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(9423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(1609,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(9132,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(1756,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(10006,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).
thf(5658,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(328,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3050,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(145,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funcop_1) ).
thf(2344,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
= ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(486,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3763,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(478,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(3727,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_relat_1) ).
thf(2741,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1601,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(9080,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1693,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_subset_1) ).
thf(9613,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
& ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_subset_1 )
& ( p1_s1_subset_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(1428,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).
thf(8287,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(4461,plain,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1727,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mssubfam) ).
thf(9868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(463,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(3667,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1393,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(8136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_1) ).
thf(3033,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(1910,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( k6_relset_2 @ A @ B @ C )
= ( k5_relset_2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(4680,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_mcart_1) ).
thf(8403,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(3445,plain,
v2_funct_1 @ sk81,
inference(cnf,[status(esa)],[3444]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(7095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_xboole_1) ).
thf(5066,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_funct_1) ).
thf(2359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_5) ).
thf(1970,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).
thf(3218,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(6360,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1356,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v2_relat_1 @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_pboole) ).
thf(7923,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( ( v2_relat_1 @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) )
=> ( v2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1418,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relset_2) ).
thf(8238,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).
thf(6728,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(6215,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).
thf(4808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(995,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(6075,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(119,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_sysrel) ).
thf(2245,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_sysrel) ).
thf(1936,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
=> ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1111,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).
thf(6656,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(5189,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(8694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(3467,plain,
v1_finseq_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(6748,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1673,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_setfam_1 @ A @ B )
= ( k1_setfam_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(9493,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_setfam_1 @ A @ B )
= ( k1_setfam_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_funcop_1) ).
thf(3615,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(6339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1246,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(7329,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1320,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_funct_1) ).
thf(7777,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(5053,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(5221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_finseq_2) ).
thf(1851,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_domain_1) ).
thf(8677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(2377,plain,
v1_relat_1 @ sk27,
inference(cnf,[status(esa)],[2373]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(6940,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(684,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(4668,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= B ) )
=> ( A
= ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(2801,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_relat_1) ).
thf(5238,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1790,plain,
! [A: $i] :
( sk3
| ~ ( r2_hidden @ A @ sk2 )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(1794,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| sk3
| ~ ( r2_hidden @ A @ sk2 ) ),
inference(lifteq,[status(thm)],[1790]) ).
thf(1180,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_1) ).
thf(6995,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= ( k8_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= ( k9_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= ( k10_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_domain_1) ).
thf(2685,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= ( k8_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= ( k9_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= ( k10_mcart_1 @ A @ B @ C @ D @ F ) )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_relat_1) ).
thf(5423,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(6,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_5) ).
thf(1804,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1120,axiom,
( a_0_3_domain_1
= ( k3_xboole_0 @ a_0_4_domain_1 @ a_0_5_domain_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_domain_1) ).
thf(6691,plain,
( a_0_3_domain_1
= ( k3_xboole_0 @ a_0_4_domain_1 @ a_0_5_domain_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(4248,plain,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relset_1) ).
thf(2841,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1415,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(8223,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(1427,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(8282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(3381,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(6133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1665,axiom,
( ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s2_card_1 @ B ) ) )
=> ( p1_s2_card_1 @ A ) ) )
=> ! [A: $i] :
( ( v1_card_1 @ A )
=> ( p1_s2_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_card_1) ).
thf(9444,plain,
( ! [A: $i] :
( ( v1_card_1 @ A )
=> ( ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s2_card_1 @ B ) ) )
=> ( p1_s2_card_1 @ A ) ) )
=> ! [A: $i] :
( ( v1_card_1 @ A )
=> ( p1_s2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(1460,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(8435,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).
thf(7838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1377,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relset_1) ).
thf(8041,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(1495,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(8619,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(858,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(5428,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1738,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(9936,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_xboole_1) ).
thf(3386,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(247,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2726,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1747,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(9977,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1679,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(9525,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(746,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_2) ).
thf(4930,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(966,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(5919,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
= ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_mcart_1) ).
thf(6919,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
= ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).
thf(5847,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
thf(3650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(371,axiom,
! [A: $i,B: $i] : ( r2_setfam_1 @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_setfam_1) ).
thf(3237,plain,
! [A: $i] : ( r2_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1485,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(8572,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(1503,axiom,
! [A: $i,B: $i] :
( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
=> ( ( k2_card_1 @ A )
= ( k2_card_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_card_1) ).
thf(8662,plain,
! [A: $i,B: $i] :
( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
=> ( ( k2_card_1 @ A )
= ( k2_card_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(3941,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1350,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( A
= ( k3_zfmisc_1 @ B @ C @ D ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_domain_1) ).
thf(7874,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( ( A
= ( k3_zfmisc_1 @ B @ C @ D ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) ) )
& ( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1691,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_mcart_1) ).
thf(9603,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(1274,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_relat_1) ).
thf(7468,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(5233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
= ( k3_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1565,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(8916,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(125,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_funct_5) ).
thf(2268,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(6148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1394,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(8138,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( v2_funct_1 @ B ) )
=> ( r2_wellord2 @ A @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_card_1) ).
thf(5475,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( v2_funct_1 @ B ) )
=> ( r2_wellord2 @ A @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(5951,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1387,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_subset_1 @ A )
= ( a_1_1_domain_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_domain_1) ).
thf(8117,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_subset_1 @ A )
= ( a_1_1_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(338,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
<=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
thf(3087,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ A ) )
& ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(735,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).
thf(4898,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1681,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(9530,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) )
=> ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1497,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8631,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(1318,axiom,
v3_ordinal1 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_ordinal1) ).
thf(7774,plain,
v3_ordinal1 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(40,axiom,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_relat_1) ).
thf(1942,plain,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1270,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_realset1) ).
thf(7453,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(319,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
thf(3010,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_relat_1) ).
thf(4513,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2460,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(267,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(2798,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(7091,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ B )
=> ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
& ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
& ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1480,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( m1_ordinal1 @ C @ A )
=> ( m1_ordinal1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
thf(8544,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( m1_ordinal1 @ C @ A )
=> ( m1_ordinal1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ? [H: $i] :
( ( m1_subset_1 @ H @ ( k3_zfmisc_1 @ D @ E @ F ) )
& ( G = H )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ G )
= ( k5_mcart_1 @ D @ E @ F @ H ) )
& ( ( k6_mcart_1 @ A @ B @ C @ G )
= ( k6_mcart_1 @ D @ E @ F @ H ) )
& ( ( k7_mcart_1 @ A @ B @ C @ G )
= ( k7_mcart_1 @ D @ E @ F @ H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_mcart_1) ).
thf(5031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ? [H: $i] :
( ( m1_subset_1 @ H @ ( k3_zfmisc_1 @ D @ E @ F ) )
& ( G = H )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ G )
= ( k5_mcart_1 @ D @ E @ F @ H ) )
& ( ( k6_mcart_1 @ A @ B @ C @ G )
= ( k6_mcart_1 @ D @ E @ F @ H ) )
& ( ( k7_mcart_1 @ A @ B @ C @ G )
= ( k7_mcart_1 @ D @ E @ F @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(3143,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_mcart_1) ).
thf(6175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(5694,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i,D: $i] :
( ( ( g1_group_1 @ A @ B )
= ( g1_group_1 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1734,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(9910,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
<=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(8017,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( A = C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_xboole_0 @ A @ B ) @ C ) @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_xboole_0 @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_5) ).
thf(3179,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_xboole_0 @ A @ B ) @ C ) @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_xboole_0 @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(4983,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1780,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(10185,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(1657,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k1_relset_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).
thf(9397,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k1_relset_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(1569,axiom,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_card_1) ).
thf(8938,plain,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(3407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relset_1) ).
thf(2561,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1203,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ A @ B )
<=> ~ ( r1_tarski @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_card_1) ).
thf(7111,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( ( r2_hidden @ A @ B )
=> ~ ( r1_tarski @ B @ A ) )
& ( ~ ( r1_tarski @ B @ A )
=> ( r2_hidden @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(789,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pboole) ).
thf(5107,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1113,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(6661,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1707,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_mcart_1) ).
thf(9714,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).
thf(8743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(1662,axiom,
? [A: $i] :
( ( m2_relset_1 @ A @ f1_s1_relset_1 @ f2_s1_relset_1 )
& ! [B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
<=> ( ( r2_hidden @ B @ f1_s1_relset_1 )
& ( r2_hidden @ C @ f2_s1_relset_1 )
& ( p1_s1_relset_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relset_1) ).
thf(9426,plain,
? [A: $i] :
( ( m2_relset_1 @ A @ f1_s1_relset_1 @ f2_s1_relset_1 )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( ( r2_hidden @ B @ f1_s1_relset_1 )
& ( r2_hidden @ C @ f2_s1_relset_1 )
& ( p1_s1_relset_1 @ B @ C ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_relset_1 )
& ( r2_hidden @ C @ f2_s1_relset_1 )
& ( p1_s1_relset_1 @ B @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(5620,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ E )
& ( m1_relset_1 @ E @ A @ B )
& ( v1_funct_1 @ F )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
= ( k5_relat_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(451,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_1) ).
thf(3596,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) )
& ( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(936,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(5786,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(5263,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1297,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(7604,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ B )
=> ( ( ( r2_hidden @ C @ B )
& ( A != C ) )
| ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_partfun1) ).
thf(2053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(117,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2240,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1381,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( D
= ( k11_pboole @ A @ B @ C ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_pboole) ).
thf(8053,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( D
= ( k11_pboole @ A @ B @ C ) )
=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) )
& ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) )
=> ( D
= ( k11_pboole @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_domain_1) ).
thf(6630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_setfam_1 @ ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_setfam_1) ).
thf(5932,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_setfam_1 @ ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(7930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(679,axiom,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(4648,plain,
! [A: $i,B: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= A )
& ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1577,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(8968,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(908,axiom,
! [A: $i] :
( ( k1_pboole @ A )
= ( k2_funcop_1 @ A @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pboole) ).
thf(5662,plain,
! [A: $i] :
( ( k1_pboole @ A )
= ( k2_funcop_1 @ A @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1176,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(6978,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1603,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(9085,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(1077,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(6501,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(91,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k2_funct_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2108,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k2_funct_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(205,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).
thf(2551,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1330,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_2) ).
thf(7806,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1776,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(10163,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(234,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_relat_1) ).
thf(2666,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_2) ).
thf(2649,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_pboole) ).
thf(4180,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1335,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
thf(7821,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
thf(5387,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1770,axiom,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k13_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_finseq_1) ).
thf(10094,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k13_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1307,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_2) ).
thf(7682,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) )
& ( ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_2) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ~ ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(1699,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_2_domain_1 )
<=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(9645,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_2_domain_1 )
=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) )
& ( ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) )
=> ( r2_hidden @ A @ a_0_2_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_partfun1) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2304,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1272,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(7463,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_sysrel) ).
thf(3059,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1282,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(7504,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(7508,plain,
~ ( v1_xboole_0 @ sk431 ),
inference(cnf,[status(esa)],[7504]) ).
thf(1194,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(7069,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_2) ).
thf(2497,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1408,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
<=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_2) ).
thf(8191,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(3703,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).
thf(2504,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(883,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_relat_1) ).
thf(5576,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_mcart_1) ).
thf(5850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_zfmisc_1 @ A @ B @ C )
= ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1463,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
thf(8458,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_orders_1) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(3486,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1373,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(8013,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(1049,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(6331,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_pboole @ D @ B ) )
=> ( ( k7_pboole @ A @ B @ C @ D )
= ( k5_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_pboole) ).
thf(4068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_pboole @ D @ B ) )
=> ( ( k7_pboole @ A @ B @ C @ D )
= ( k5_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(845,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(5380,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1762,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(10026,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1453,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).
thf(8408,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(8410,plain,
~ ( v1_xboole_0 @ sk559 ),
inference(cnf,[status(esa)],[8408]) ).
thf(52,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_sysrel) ).
thf(1974,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_sysrel @ A )
= ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( A
= ( k10_mcart_1 @ B @ C @ D @ E @ F ) )
<=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = I ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_domain_1) ).
thf(6433,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( ( A
= ( k10_mcart_1 @ B @ C @ D @ E @ F ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = I ) ) ) ) ) ) )
& ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = I ) ) ) ) ) )
=> ( A
= ( k10_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(6207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1715,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(9761,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(1709,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k4_numbers ) )
& ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( r2_hidden @ B @ A )
<=> ( p1_s1_int_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_int_1) ).
thf(9739,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k4_numbers ) )
& ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( ( r2_hidden @ B @ A )
=> ( p1_s1_int_1 @ B ) )
& ( ( p1_s1_int_1 @ B )
=> ( r2_hidden @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( A
= ( k6_mcart_1 @ B @ C @ D @ E ) )
<=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_domain_1) ).
thf(6876,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( ( A
= ( k6_mcart_1 @ B @ C @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = G ) ) ) ) ) )
& ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = G ) ) ) ) )
=> ( A
= ( k6_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1626,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(9201,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1737,axiom,
? [A: $i] :
( ( m2_relset_1 @ A @ f1_s2_relset_1 @ f2_s2_relset_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_relset_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s2_relset_1 )
=> ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
<=> ( p1_s2_relset_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_relset_1) ).
thf(9932,plain,
? [A: $i] :
( ( m2_relset_1 @ A @ f1_s2_relset_1 @ f2_s2_relset_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_relset_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s2_relset_1 )
=> ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( p1_s2_relset_1 @ B @ C ) )
& ( ( p1_s2_relset_1 @ B @ C )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(720,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(4829,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k4_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2566,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= A ) )
& ( ( ( k4_xboole_0 @ A @ B )
= A )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ( m2_finseq_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_2) ).
thf(1799,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ( m2_finseq_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(693,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r1_ordinal1 @ A @ B )
| ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
thf(4717,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r1_ordinal1 @ A @ B )
| ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t183_relat_1) ).
thf(1947,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1560,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(8896,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).
thf(5683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1311,axiom,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).
thf(7702,plain,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(1694,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_subset_1) ).
thf(9620,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(1490,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( A
= ( k9_mcart_1 @ B @ C @ D @ E @ F ) )
<=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_domain_1) ).
thf(8587,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( ( A
= ( k9_mcart_1 @ B @ C @ D @ E @ F ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = H ) ) ) ) ) ) )
& ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = H ) ) ) ) ) )
=> ( A
= ( k9_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
<=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_relset_2) ).
thf(7261,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) )
& ( ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) )
=> ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1075,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(6465,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r2_pboole @ A @ B @ C )
=> ( ( r2_pboole @ A @ ( k3_pboole @ A @ B @ D ) @ ( k3_pboole @ A @ C @ D ) )
& ( r2_pboole @ A @ ( k3_pboole @ A @ D @ B ) @ ( k3_pboole @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_pboole) ).
thf(3409,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r2_pboole @ A @ B @ C )
=> ( ( r2_pboole @ A @ ( k3_pboole @ A @ B @ D ) @ ( k3_pboole @ A @ C @ D ) )
& ( r2_pboole @ A @ ( k3_pboole @ A @ D @ B ) @ ( k3_pboole @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(469,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(3692,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(8576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(1587,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(8995,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(1458,axiom,
( ! [A: $i] :
( ( r2_hidden @ A @ f1_s2_funct_2 )
=> ( r2_hidden @ ( f3_s2_funct_2 @ A ) @ f2_s2_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s2_funct_2 @ f2_s2_funct_2 )
& ( m2_relset_1 @ A @ f1_s2_funct_2 @ f2_s2_funct_2 )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s2_funct_2 )
=> ( ( k1_funct_1 @ A @ B )
= ( f3_s2_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_2) ).
thf(8425,plain,
( ! [A: $i] :
( ( r2_hidden @ A @ f1_s2_funct_2 )
=> ( r2_hidden @ ( f3_s2_funct_2 @ A ) @ f2_s2_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s2_funct_2 @ f2_s2_funct_2 )
& ( m2_relset_1 @ A @ f1_s2_funct_2 @ f2_s2_funct_2 )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s2_funct_2 )
=> ( ( k1_funct_1 @ A @ B )
= ( f3_s2_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(391,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(3333,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(8307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(1778,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(10180,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(1397,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).
thf(8144,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(1396,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_domain_1) ).
thf(8142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_sysrel) ).
thf(5026,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
thf(4416,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1705,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(9694,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(1021,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(6186,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_5) ).
thf(2140,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).
thf(4086,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1581,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).
thf(8980,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(337,axiom,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(3083,plain,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(7174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(579,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relat_1) ).
thf(4223,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(5479,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(874,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 )
=> ( ( ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k7_relat_1 @ A @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 )
=> ( ( ( k8_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k8_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_sysrel) ).
thf(5544,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 )
=> ( ( ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k7_relat_1 @ A @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 )
=> ( ( ( k8_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
& ( ( k8_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(791,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relat_1) ).
thf(5153,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(636,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
!= ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_setfam_1) ).
thf(4476,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
!= ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(5571,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
& ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( r2_hidden @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_mcart_1) ).
thf(5737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
& ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( r2_hidden @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1631,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_subset_1) ).
thf(9213,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(1422,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(8262,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
& ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
& ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_5) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1389,axiom,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(8127,plain,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_vectsp_1 @ A @ B @ C )
= ( g1_vectsp_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_vectsp_1) ).
thf(7193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g1_vectsp_1 @ A @ B @ C )
= ( g1_vectsp_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(1578,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).
thf(8971,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(1404,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finset_1) ).
thf(8174,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).
thf(3824,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1550,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
thf(8846,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(1539,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(8796,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(1066,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( p1_s6_domain_1 @ B )
<=> ( p2_s6_domain_1 @ B ) ) )
=> ( ( a_1_5_domain_1 @ A )
= ( a_1_6_domain_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_domain_1) ).
thf(6409,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( ( p1_s6_domain_1 @ B )
=> ( p2_s6_domain_1 @ B ) )
& ( ( p2_s6_domain_1 @ B )
=> ( p1_s6_domain_1 @ B ) ) ) )
=> ( ( a_1_5_domain_1 @ A )
= ( a_1_6_domain_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_1) ).
thf(3903,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_2) ).
thf(4184,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_5) ).
thf(2203,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(6533,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(9684,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(2546,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_relat_1) ).
thf(4195,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(457,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3624,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1013,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(6160,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).
thf(3279,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(4212,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(1757,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(10011,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(1717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(9782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
=> ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(9176,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(1444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
thf(8361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) )
=> ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k4_relset_1 @ A @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_partfun1) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k4_relset_1 @ A @ B @ C )
= A ) )
& ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_1) ).
thf(3856,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1590,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_2) ).
thf(9008,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(1308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_domain_1) ).
thf(7687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(948,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
=> ( v3_ordinal1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_ordinal1) ).
thf(5833,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
=> ( v3_ordinal1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1127,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(6716,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funcop_1) ).
thf(5415,plain,
! [A: $i,B: $i,C: $i] :
( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = G ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k8_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_mcart_1) ).
thf(8559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = G ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k8_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(82,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_relat_1) ).
thf(2076,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(2748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(994,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) )
& ( v1_fraenkel @ ( k13_finseq_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_finseq_1) ).
thf(6070,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) )
& ( v1_fraenkel @ ( k13_finseq_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(6279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).
thf(2408,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(969,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).
thf(5930,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r4_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) )
=> ( ( r4_pboole @ A @ B @ C )
& ( r4_pboole @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_pboole) ).
thf(3190,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( r4_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) )
=> ( ( r4_pboole @ A @ B @ C )
& ( r4_pboole @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(7476,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_mcart_1 @ A @ B @ C )
= ( k3_mcart_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_mcart_1) ).
thf(6982,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k3_mcart_1 @ A @ B @ C )
= ( k3_mcart_1 @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k2_domain_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_domain_1) ).
thf(6610,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k2_domain_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1718,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(9793,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(959,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_domain_1) ).
thf(5887,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(25,axiom,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(1895,plain,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1618,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(9168,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).
thf(5198,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1545,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(8824,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(5909,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ? [E: $i,F: $i,G: $i] :
( ( D
= ( k3_mcart_1 @ E @ F @ G ) )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= E )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= F )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_mcart_1) ).
thf(3841,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
& ? [E: $i,F: $i,G: $i] :
( ( D
= ( k3_mcart_1 @ E @ F @ G ) )
& ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= E )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= F )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_relat_1) ).
thf(5295,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1612,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).
thf(9137,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m2_pboole @ C @ A @ B )
=> ( m1_pboole @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_pboole) ).
thf(5249,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m2_pboole @ C @ A @ B )
=> ( m1_pboole @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1153,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( v2_card_1 @ A )
<=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( A
!= ( k2_card_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_card_1) ).
thf(6869,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( ( ( v2_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( A
!= ( k2_card_1 @ B ) ) ) )
& ( ! [B: $i] :
( ( v1_card_1 @ B )
=> ( A
!= ( k2_card_1 @ B ) ) )
=> ( v2_card_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
& ! [E: $i,F: $i,G: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_mcart_1) ).
thf(6950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
& ! [E: $i,F: $i,G: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1750,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(9985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(1519,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(8708,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( r2_hidden @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(1676,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(9517,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(1334,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( k3_relat_1 @ C )
= ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relat_1) ).
thf(7817,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( k3_relat_1 @ C )
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(1269,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(7444,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k5_relset_2 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relset_2) ).
thf(2909,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( C
= ( k5_relset_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) )
=> ( C
= ( k5_relset_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( r2_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ B )
& ( r2_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pboole) ).
thf(4550,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( r2_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ B )
& ( r2_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_mcart_1) ).
thf(6524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( m2_pua2mss1 @ B @ A )
<=> ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pua2mss1) ).
thf(1906,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( m2_pua2mss1 @ B @ A )
=> ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) ) )
& ( ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
& ( v2_funct_1 @ B ) )
=> ( m2_pua2mss1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(2936,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ ( k1_funct_2 @ ( k1_tarski @ B ) @ A ) )
& ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_funct_2 @ ( k1_tarski @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_5) ).
thf(4470,plain,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ ( k1_funct_2 @ ( k1_tarski @ B ) @ A ) )
& ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_funct_2 @ ( k1_tarski @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1284,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(7512,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(827,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).
thf(5278,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(811,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(5230,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(893,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_1) ).
thf(5608,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
& ( B
= ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_1) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
& ( B
= ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1221,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(7212,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(2376,plain,
v1_funct_1 @ sk27,
inference(cnf,[status(esa)],[2373]) ).
thf(460,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3660,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1164,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( r2_realset1 @ A @ B @ C )
<=> ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_realset1) ).
thf(6922,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( r2_realset1 @ A @ B @ C )
=> ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) )
& ( ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
& ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
& ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
& ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) )
=> ( r2_realset1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(4919,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).
thf(3130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(989,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( ~ ( r2_hidden @ A @ B )
& ( A != B )
& ~ ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(6053,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( ~ ( r2_hidden @ A @ B )
& ( A != B )
& ~ ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5722,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(238,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(2677,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1562,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m3_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).
thf(8903,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m3_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( m3_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(4872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1635,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k1_tarski @ A ) )
=> ( ( k7_setfam_1 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(9231,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k1_tarski @ A ) )
=> ( ( k7_setfam_1 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3358,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_partfun1) ).
thf(2033,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pua2mss1) ).
thf(5762,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(121,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_sysrel) ).
thf(2253,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_5) ).
thf(3871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1090,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(6561,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(980,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5969,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ ( k1_tarski @ B ) )
<=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_card_1) ).
thf(5451,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ ( k1_tarski @ B ) )
=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) )
& ( ? [C: $i] :
( A
= ( k1_tarski @ C ) )
=> ( r2_wellord2 @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1225,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(7225,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1314,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(7742,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(1212,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).
thf(7155,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(335,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3079,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(622,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4412,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_sysrel) ).
thf(4256,plain,
! [A: $i,B: $i] :
( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
& ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(36,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_5) ).
thf(1927,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(523,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(3985,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 )
& ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(5048,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1468,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(8480,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( ( E
= ( k7_mcart_1 @ A @ B @ C @ D ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_mcart_1) ).
thf(7491,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( ( ( E
= ( k7_mcart_1 @ A @ B @ C @ D ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = H ) ) )
& ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = H ) )
=> ( E
= ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(381,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_relat_1 @ A )
<=> ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_pboole) ).
thf(3289,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v3_relat_1 @ A )
=> ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= ( k1_tarski @ k1_xboole_0 ) ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ C @ D ) )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ D ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ A @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_5) ).
thf(3738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ C @ D ) )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ A @ C ) @ ( k1_funct_2 @ B @ D ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ A @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1232,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(7257,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(787,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(5095,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1355,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(7920,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(6546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3274,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1323,axiom,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(7785,plain,
! [A: $i,B: $i] :
( ( k5_xboole_0 @ A @ B )
= ( k5_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(1205,axiom,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ k1_xboole_0 ) @ ( k2_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_card_1) ).
thf(7118,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ k1_xboole_0 ) @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
thf(8311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(1542,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(8807,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(1471,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).
thf(8495,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(682,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
thf(4662,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1564,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(8909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(487,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ? [B: $i] : ( m4_realset1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m4_realset1) ).
thf(3768,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ? [B: $i] : ( m4_realset1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(2791,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_mcart_1) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5844,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(4801,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
=> ~ ( r2_hidden @ A @ B ) )
& ( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(947,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_orders_1) ).
thf(5831,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(5050,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_partfun1) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1742,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(9952,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
<=> ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_card_1) ).
thf(2959,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
=> ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) ) )
& ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
=> ( r2_wellord2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(710,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(4786,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 )
& ( v3_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1298,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( m2_pboole @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( m1_subset_1 @ ( k1_funct_1 @ C @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_pboole) ).
thf(7611,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( m2_pboole @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( m1_subset_1 @ ( k1_funct_1 @ C @ D ) @ ( k1_funct_1 @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( m1_subset_1 @ ( k1_funct_1 @ C @ D ) @ ( k1_funct_1 @ B @ D ) ) )
=> ( m2_pboole @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(1660,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(9418,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(4000,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
=> ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
& ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_1) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
=> ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
& ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(6916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(307,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(2938,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1530,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_domain_1) ).
thf(8762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) )
=> ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C )
& ( m1_subset_1 @ G @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) )
=> ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_pua2mss1) ).
thf(1884,plain,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun1) ).
thf(6617,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
<=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
thf(4494,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) )
& ( ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(545,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(4077,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(104,axiom,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(2188,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1753,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(9996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(2393,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1520,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(8711,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(1267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_domain_1) ).
thf(7440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
=> ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k11_pboole @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_pboole) ).
thf(3081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k11_pboole @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_relat_1) ).
thf(4677,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_relat_1) ).
thf(2514,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(6229,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(537,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(4032,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k5_funcop_1 @ B @ C @ A )
= ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1515,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(8697,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(1189,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
=> ( ( m1_orders_1 @ B @ A )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_orders_1) ).
thf(7041,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
=> ( ( ( m1_orders_1 @ B @ A )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) )
=> ( m1_orders_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_partfun1) ).
thf(3900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1157,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).
thf(6898,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(788,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(5097,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) )
& ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(419,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_1 @ A )
<=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_relat_1) ).
thf(3458,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_1 @ A )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) )
& ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1789,plain,
( sk3
| ( ( k5_setfam_1 @ sk1 @ sk2 )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1785]) ).
thf(1795,plain,
( ( ( k5_setfam_1 @ sk1 @ sk2 )
!= k1_xboole_0 )
| sk3 ),
inference(lifteq,[status(thm)],[1789]) ).
thf(1488,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_mcart_1 @ A @ B @ C )
= ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_mcart_1) ).
thf(8581,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_mcart_1 @ A @ B @ C )
= ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(7963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1586,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(8993,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(4612,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ~ ( v3_relat_1 @ ( k7_relat_1 @ B @ A ) )
& ( v3_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t190_relat_1) ).
thf(2817,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ~ ( v3_relat_1 @ ( k7_relat_1 @ B @ A ) )
& ( v3_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1773,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k7_setfam_1 @ A @ B )
= ( k7_setfam_1 @ A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(10127,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k7_setfam_1 @ A @ B )
= ( k7_setfam_1 @ A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(5799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1724,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ A )
<=> ( p1_s2_subset_1 @ C ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( r2_hidden @ C @ B )
<=> ( p1_s2_subset_1 @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_subset_1) ).
thf(9820,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ A )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ A ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_subset_1 )
=> ( ( ( r2_hidden @ C @ B )
=> ( p1_s2_subset_1 @ C ) )
& ( ( p1_s2_subset_1 @ C )
=> ( r2_hidden @ C @ B ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(1136,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_2) ).
thf(6774,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) )
& ( ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) )
=> ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( B
= ( k4_relset_1 @ B @ A @ C ) )
& ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_1) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( B
= ( k4_relset_1 @ B @ A @ C ) )
& ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1333,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_setfam_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_setfam_1) ).
thf(7815,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_setfam_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(1300,axiom,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( B
= ( k2_card_1 @ A ) )
<=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ B )
& ! [C: $i] :
( ( v1_card_1 @ C )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ C )
=> ( r1_tarski @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_card_1) ).
thf(7622,plain,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( ( B
= ( k2_card_1 @ A ) )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ B )
& ! [C: $i] :
( ( v1_card_1 @ C )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ C )
=> ( r1_tarski @ B @ C ) ) ) ) )
& ( ( ( r2_hidden @ ( k1_card_1 @ A ) @ B )
& ! [C: $i] :
( ( v1_card_1 @ C )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ C )
=> ( r1_tarski @ B @ C ) ) ) )
=> ( B
= ( k2_card_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(7038,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(1054,axiom,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(6357,plain,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1443,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(8359,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(434,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3532,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1383,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
& ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_ordinal1) ).
thf(8064,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
& ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ~ ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(367,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(3223,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(4251,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_tarski @ A @ B ) @ C ) @ ( k2_zfmisc_1 @ C @ C ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_tarski @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_5) ).
thf(4526,plain,
! [A: $i,B: $i,C: $i] :
( ( A != B )
=> ( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_tarski @ A @ B ) @ C ) @ ( k2_zfmisc_1 @ C @ C ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_tarski @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1437,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(8318,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(5567,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1764,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(10034,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(1606,axiom,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s9_domain_1) ).
thf(9125,plain,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(6385,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_sysrel @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_sysrel) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_sysrel @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) )
& ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(132,axiom,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(2293,plain,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1167,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).
thf(6937,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1115,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k4_funcop_1 @ E @ ( k6_finseq_1 @ A ) @ D )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_finseq_2) ).
thf(6667,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k4_funcop_1 @ E @ ( k6_finseq_1 @ A ) @ D )
= ( k6_finseq_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1779,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(10183,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(1287,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(7534,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(1496,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset1) ).
thf(8628,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(8629,plain,
~ ( v1_realset1 @ sk592 ),
inference(cnf,[status(esa)],[8628]) ).
thf(1309,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
thf(7689,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(956,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( A
= ( k7_mcart_1 @ B @ C @ D @ E ) )
<=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = H ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_domain_1) ).
thf(5859,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( ( A
= ( k7_mcart_1 @ B @ C @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = H ) ) ) ) ) )
& ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = H ) ) ) ) )
=> ( A
= ( k7_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3695,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).
thf(8862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(1704,axiom,
? [A: $i] :
( ( m1_pboole @ A @ f1_s2_pboole )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s2_pboole )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) )
<=> ( ( r2_hidden @ C @ ( k1_funct_1 @ f2_s2_pboole @ B ) )
& ( p1_s2_pboole @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_pboole) ).
thf(9687,plain,
? [A: $i] :
( ( m1_pboole @ A @ f1_s2_pboole )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s2_pboole )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k1_funct_1 @ f2_s2_pboole @ B ) )
& ( p1_s2_pboole @ B @ C ) ) )
& ( ( ( r2_hidden @ C @ ( k1_funct_1 @ f2_s2_pboole @ B ) )
& ( p1_s2_pboole @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(251,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funcop_1) ).
thf(2738,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( k7_relat_1 @ A @ D )
= ( k7_relat_1 @ B @ D ) )
=> ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
= ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(555,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relat_1) ).
thf(4149,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1558,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(8877,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(1504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(8665,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(3663,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(3340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_relat_1) ).
thf(5086,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(1997,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1774,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ! [B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
<=> ( ( r2_hidden @ B @ f1_s1_relat_1 )
& ( r2_hidden @ C @ f2_s1_relat_1 )
& ( p1_s1_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relat_1) ).
thf(10130,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( ( r2_hidden @ B @ f1_s1_relat_1 )
& ( r2_hidden @ C @ f2_s1_relat_1 )
& ( p1_s1_relat_1 @ B @ C ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_relat_1 )
& ( r2_hidden @ C @ f2_s1_relat_1 )
& ( p1_s1_relat_1 @ B @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(345,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_partfun1) ).
thf(3123,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(491,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(3783,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_1) ).
thf(7347,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( F
= ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_mcart_1) ).
thf(5703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( F
= ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = G ) ) )
& ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = G ) )
=> ( F
= ( k8_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1273,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_domain_1) ).
thf(7465,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_relat_1) ).
thf(3700,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1674,axiom,
( ! [A: $i] :
~ ( ( r2_hidden @ A @ f1_s1_pboole )
& ( ( f2_s1_pboole @ A )
= k1_xboole_0 ) )
=> ? [A: $i] :
( ( m1_pboole @ A @ f1_s1_pboole )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s1_pboole )
=> ( r2_hidden @ ( k1_funct_1 @ A @ B ) @ ( f2_s1_pboole @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_pboole) ).
thf(9496,plain,
( ! [A: $i] :
~ ( ( r2_hidden @ A @ f1_s1_pboole )
& ( ( f2_s1_pboole @ A )
= k1_xboole_0 ) )
=> ? [A: $i] :
( ( m1_pboole @ A @ f1_s1_pboole )
& ! [B: $i] :
( ( r2_hidden @ B @ f1_s1_pboole )
=> ( r2_hidden @ ( k1_funct_1 @ A @ B ) @ ( f2_s1_pboole @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).
thf(3832,plain,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(100,axiom,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_relat_1) ).
thf(2166,plain,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(455,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r1_ordinal1 @ ( k1_card_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_card_1) ).
thf(3619,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r1_ordinal1 @ ( k1_card_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( v2_relat_1 @ D )
& ( m1_pboole @ D @ B ) )
=> ( ( k8_pboole @ A @ B @ C @ D )
= ( k5_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_pboole) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( v2_relat_1 @ D )
& ( m1_pboole @ D @ B ) )
=> ( ( k8_pboole @ A @ B @ C @ D )
= ( k5_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1412,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_realset1) ).
thf(8212,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1302,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(7653,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(7658,plain,
~ ( v1_xboole_0 @ sk456 ),
inference(cnf,[status(esa)],[7653]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2557,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(5735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(165,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(2425,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( k4_funcop_1 @ B @ A @ C )
= ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).
thf(6372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) ) )
& ( ? [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
& ( A
= ( k3_xboole_0 @ E @ C ) )
& ~ ( r1_xboole_0 @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1410,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(8202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(445,axiom,
! [A: $i] : ( m1_pboole @ ( k1_pboole @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pboole) ).
thf(3568,plain,
! [A: $i] : ( m1_pboole @ ( k1_pboole @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_2) ).
thf(7394,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
& ~ ( r2_wellord2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_card_1) ).
thf(7021,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
& ~ ( r2_wellord2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1347,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(7865,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
& ( r2_hidden @ B @ C )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(210,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_relat_1) ).
thf(2573,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1646,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(9307,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(1447,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_funct_1) ).
thf(8376,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(1433,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).
thf(8301,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ( A != k1_xboole_0 )
& ( v6_ordinal1 @ A )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_tarski @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(6016,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( E
= ( k4_mcart_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_mcart_1) ).
thf(3170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( E
= ( k4_mcart_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relat_1) ).
thf(6261,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1640,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_subset_1) ).
thf(9248,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).
thf(5634,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
=> ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1039,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v3_relat_1 @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_pboole) ).
thf(6281,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( ( v3_relat_1 @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) )
=> ( v3_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1213,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(7158,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(6144,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(581,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_realset1 @ A )
<=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_realset1) ).
thf(4228,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
=> ~ ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1649,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(9349,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(1521,axiom,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(8715,plain,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(7077,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_partfun1) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1755,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(10000,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(1424,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(8269,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_2) ).
thf(6604,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1638,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(9243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(711,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_relat_1) ).
thf(4790,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1695,axiom,
( ! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s2_ordinal1 @ B ) ) )
=> ( p1_s2_ordinal1 @ A ) ) )
=> ! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( p1_s2_ordinal1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_ordinal1) ).
thf(9623,plain,
( ! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( ! [B: $i] :
( ( v3_ordinal1 @ B )
=> ( ( r2_hidden @ B @ A )
=> ( p1_s2_ordinal1 @ B ) ) )
=> ( p1_s2_ordinal1 @ A ) ) )
=> ! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( p1_s2_ordinal1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_sysrel) ).
thf(4337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(6059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1093,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_domain_1) ).
thf(6572,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
= ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
=> ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_vectsp_1) ).
thf(7519,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
= ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
=> ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1208,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).
thf(7130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3815,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_pboole) ).
thf(3038,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
& ( r2_pboole @ A @ B @ D ) )
=> ( r4_pboole @ A @ B @ ( k3_pboole @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(259,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(2774,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1028,axiom,
! [A: $i] :
( ( m1_pboole @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_pboole) ).
thf(6217,plain,
! [A: $i] :
( ( m1_pboole @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1145,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_domain_1) ).
thf(6815,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_sysrel) ).
thf(3683,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k6_relat_1 @ ( k1_relat_1 @ C ) ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(2906,plain,
v1_funct_1 @ sk44,
inference(cnf,[status(esa)],[2905]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_subset_1) ).
thf(6197,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(4699,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1388,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(8120,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(5631,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(7438,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_mcart_1) ).
thf(8688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(3468,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).
thf(5880,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_1) ).
thf(3106,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( r2_hidden @ E @ A )
<=> ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_mcart_1) ).
thf(7282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ( r2_hidden @ E @ A )
=> ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) ) )
& ( ? [F: $i,G: $i,H: $i] :
( ( r2_hidden @ F @ B )
& ( r2_hidden @ G @ C )
& ( r2_hidden @ H @ D )
& ( E
= ( k3_mcart_1 @ F @ G @ H ) ) )
=> ( r2_hidden @ E @ A ) ) )
=> ( A
= ( k3_zfmisc_1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(1436,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) )
=> ( B
= ( k1_pboole @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pboole) ).
thf(8313,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) )
=> ( B
= ( k1_pboole @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(2669,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1583,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(8986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).
thf(1801,plain,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(6289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1011,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(6154,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(3500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2378,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(613,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_relat_1) ).
thf(4374,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(981,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_domain_1) ).
thf(5972,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) ) )
& ( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( m1_subset_1 @ G @ B )
& ? [H: $i] :
( ( m1_subset_1 @ H @ C )
& ? [I: $i] :
( ( m1_subset_1 @ I @ D )
& ? [J: $i] :
( ( m1_subset_1 @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1281,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(7502,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(896,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relat_1) ).
thf(5616,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(290,axiom,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_relat_1) ).
thf(2871,plain,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1567,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(8926,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
thf(6460,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(7307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(67,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_sysrel @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_sysrel) ).
thf(2025,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_sysrel @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(653,axiom,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).
thf(4541,plain,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_relat_1) ).
thf(3073,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(986,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(6044,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(128,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(2278,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_2) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_partfun1 @ C @ D )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1455,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(8413,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(5780,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(5563,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_1) ).
thf(2824,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(4635,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1628,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(9206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_relat_1) ).
thf(4401,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(886,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(5584,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
= ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).
thf(9129,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(6165,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m3_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_realset1) ).
thf(8826,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m3_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
& ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(330,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_1) ).
thf(3055,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( D
= ( k5_partfun1 @ A @ B @ C ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ D )
<=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_partfun1) ).
thf(4103,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( D
= ( k5_partfun1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) ) )
& ( ! [E: $i] :
( ( ( r2_hidden @ E @ D )
=> ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) ) )
& ( ? [F: $i] :
( ( v1_funct_1 @ F )
& ( m2_relset_1 @ F @ A @ B )
& ( F = E )
& ( v1_partfun1 @ F @ A @ B )
& ( r1_partfun1 @ C @ F ) )
=> ( r2_hidden @ E @ D ) ) )
=> ( D
= ( k5_partfun1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_partfun1) ).
thf(5730,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_tarski @ D @ C ) )
=> ( r1_partfun1 @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(3668,plain,
v3_relat_1 @ sk95,
inference(cnf,[status(esa)],[3667]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( D
!= ( k5_mcart_1 @ A @ B @ C @ D ) )
& ( D
!= ( k6_mcart_1 @ A @ B @ C @ D ) )
& ( D
!= ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_mcart_1) ).
thf(2625,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( D
!= ( k5_mcart_1 @ A @ B @ C @ D ) )
& ( D
!= ( k6_mcart_1 @ A @ B @ C @ D ) )
& ( D
!= ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( F
= ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_mcart_1) ).
thf(5894,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( F
= ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = H ) ) )
& ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = H ) )
=> ( F
= ( k9_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1700,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_domain_1) ).
thf(9655,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_sysrel) ).
thf(5175,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ C @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) )
& ( ( ( ( k5_relat_1 @ C @ C )
= C )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ C @ ( k1_sysrel @ C ) ) @ C )
= k1_xboole_0 )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) )
=> ( ( A = B )
| ( ( r2_hidden @ B @ ( k4_xboole_0 @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_sysrel @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1698,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(9642,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(6710,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( r1_tarski @ ( k2_tarski @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1582,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
thf(8983,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(2780,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).
thf(4731,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_relat_1) ).
thf(4028,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(891,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( ( k1_relat_1 @ C )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pua2mss1) ).
thf(5599,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( ( k1_relat_1 @ C )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_relat_1) ).
thf(5286,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1526,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(8750,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(2446,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_1) ).
thf(2757,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(7928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(1369,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s7_funct_2 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f2_s7_funct_2 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f3_s7_funct_2 )
& ( p1_s7_funct_2 @ A @ B @ C ) ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s7_funct_2 @ f2_s7_funct_2 ) @ f3_s7_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s7_funct_2 @ f2_s7_funct_2 ) @ f3_s7_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_funct_2 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s7_funct_2 )
=> ( p1_s7_funct_2 @ B @ C @ ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_funct_2) ).
thf(7978,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s7_funct_2 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f2_s7_funct_2 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f3_s7_funct_2 )
& ( p1_s7_funct_2 @ A @ B @ C ) ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s7_funct_2 @ f2_s7_funct_2 ) @ f3_s7_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s7_funct_2 @ f2_s7_funct_2 ) @ f3_s7_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_funct_2 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s7_funct_2 )
=> ( p1_s7_funct_2 @ B @ C @ ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_partfun1) ).
thf(4332,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1713,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(9756,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(1579,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k13_finseq_1 @ A ) @ ( k13_finseq_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_finseq_1) ).
thf(8974,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k13_finseq_1 @ A ) @ ( k13_finseq_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(522,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
<=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_funct_1) ).
thf(3977,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
=> ( v2_funct_1 @ A ) )
& ( ( v2_funct_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(2923,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ? [F: $i,G: $i,H: $i,I: $i] :
( ( E
= ( k4_mcart_1 @ F @ G @ H @ I ) )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= F )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= G )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= H )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_mcart_1) ).
thf(5392,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ? [F: $i,G: $i,H: $i,I: $i] :
( ( E
= ( k4_mcart_1 @ F @ G @ H @ I ) )
& ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
= F )
& ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
= G )
& ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
= H )
& ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
= I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1209,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(7141,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_mcart_1) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1588,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(8998,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( B
= ( k1_card_1 @ A ) )
<=> ( r2_wellord2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_card_1) ).
thf(4296,plain,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( ( B
= ( k1_card_1 @ A ) )
=> ( r2_wellord2 @ A @ B ) )
& ( ( r2_wellord2 @ A @ B )
=> ( B
= ( k1_card_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1348,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(7869,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1305,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(7675,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(2928,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(1193,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).
thf(7066,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(3110,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(6738,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1783,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(10208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(1656,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(9371,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) )
& ( ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) )
=> ( m1_eqrel_1 @ B @ A ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( m1_eqrel_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(1591,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_domain_1) ).
thf(9011,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(944,axiom,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_realset1) ).
thf(5817,plain,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(2867,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( r2_pboole @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_pboole) ).
thf(3539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( r2_pboole @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1729,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(9873,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_partfun1) ).
thf(5057,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
& ( v2_funct_1 @ C ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_2) ).
thf(1841,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
& ( v2_funct_1 @ C ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(4232,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(147,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_partfun1) ).
thf(2350,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).
thf(8131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k3_pboole @ A @ B @ C )
= ( k3_pboole @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_pboole) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( k3_pboole @ A @ B @ C )
= ( k3_pboole @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1462,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8456,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(1119,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(6687,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(6449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_partfun1) ).
thf(5216,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
thf(3759,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(3838,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( F
= ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
<=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = I ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_mcart_1) ).
thf(7479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( D != k1_xboole_0 )
& ~ ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( ( F
= ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
=> ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = I ) ) )
& ( ! [G: $i,H: $i,I: $i,J: $i] :
( ( E
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( F = I ) )
=> ( F
= ( k10_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_relat_1) ).
thf(2835,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1533,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(8776,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relset_2) ).
thf(5377,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(6907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1666,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_subset_1) ).
thf(9450,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_card_1) ).
thf(2481,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(5218,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(6930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1064,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(6394,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1645,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(9294,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(5641,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1746,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(9975,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1769,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( p1_s3_xboole_0 @ C ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( p1_s3_xboole_0 @ C ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_xboole_0) ).
thf(10076,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( p1_s3_xboole_0 @ C ) )
& ( ( p1_s3_xboole_0 @ C )
=> ( r2_hidden @ C @ A ) ) )
& ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( p1_s3_xboole_0 @ C ) )
& ( ( p1_s3_xboole_0 @ C )
=> ( r2_hidden @ C @ B ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(3917,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1725,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(9841,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_card_1) ).
thf(6504,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(1353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).
thf(7911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(2931,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k5_pboole @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_pboole) ).
thf(5042,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k5_pboole @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1625,axiom,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( r2_hidden @ B @ A )
<=> ( p1_s3_subset_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1) ).
thf(9197,plain,
? [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_subset_1 )
=> ( ( ( r2_hidden @ B @ A )
=> ( p1_s3_subset_1 @ B ) )
& ( ( p1_s3_subset_1 @ B )
=> ( r2_hidden @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2633,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(3310,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(474,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_partfun1) ).
thf(3706,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( ( r1_partfun1 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1219,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_domain_1) ).
thf(7200,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ? [G: $i] :
( ( m1_subset_1 @ G @ D )
& ( A
= ( k3_mcart_1 @ E @ F @ G ) ) ) ) )
=> ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(6180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ D @ A @ B )
=> ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_1) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ D @ A @ B )
=> ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(9921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(1101,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(6614,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1429,axiom,
? [A: $i] : ( v1_card_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_1) ).
thf(8291,plain,
? [A: $i] : ( v1_card_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_relat_1) ).
thf(5089,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(840,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_1) ).
thf(5326,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(732,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relat_1) ).
thf(4890,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1253,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(7356,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1613,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(9150,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(1585,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(8990,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(517,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) ) ) )
& ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_sysrel) ).
thf(3908,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k2_relat_1 @ A ) ) ) )
& ( ( ( ( k5_relat_1 @ A @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( ( k1_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k1_sysrel @ A ) )
= ( k1_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).
thf(6212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D ) )
=> ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(244,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(2693,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1139,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(6785,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
<=> ~ ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(9582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_mcart_1) ).
thf(6672,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2234,plain,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v3_relat_1 @ B )
=> ~ ( v2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_pboole) ).
thf(3146,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v3_relat_1 @ B )
=> ~ ( v2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_sysrel) ).
thf(2449,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(327,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(3048,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1643,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_3_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B )
& ( p2_s10_domain_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_3_domain_1) ).
thf(9276,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_3_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B )
& ( p2_s10_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p1_s10_domain_1 @ B )
& ( p2_s10_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_3_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_xboole_1) ).
thf(4722,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(8180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(1598,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
<=> ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).
thf(9054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
=> ( ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
=> ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) ) )
& ( ? [H: $i,I: $i,J: $i] :
( ( m1_subset_1 @ H @ B )
& ( m1_subset_1 @ I @ C )
& ( m1_subset_1 @ J @ D )
& ( A
= ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
& ( r2_hidden @ H @ E )
& ( r2_hidden @ I @ F )
& ( r2_hidden @ J @ G ) )
=> ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(1151,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(6858,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1605,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ( p1_s2_orders_1 @ A @ A ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ( ( ( p1_s2_orders_1 @ A @ B )
& ( p1_s2_orders_1 @ B @ A ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
=> ( ( ( p1_s2_orders_1 @ A @ B )
& ( p1_s2_orders_1 @ B @ C ) )
=> ( p1_s2_orders_1 @ A @ C ) ) ) ) )
& ! [A: $i] :
~ ( ( r1_tarski @ A @ f1_s2_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
=> ~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( p1_s2_orders_1 @ B @ C )
& ~ ( p1_s2_orders_1 @ C @ B ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
& ( r2_hidden @ C @ A )
& ~ ( p1_s2_orders_1 @ B @ C ) ) ) ) )
=> ? [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ~ ( ( A != B )
& ( p1_s2_orders_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_orders_1) ).
thf(9097,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ( p1_s2_orders_1 @ A @ A ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ( ( ( p1_s2_orders_1 @ A @ B )
& ( p1_s2_orders_1 @ B @ A ) )
=> ( A = B ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
=> ( ( ( p1_s2_orders_1 @ A @ B )
& ( p1_s2_orders_1 @ B @ C ) )
=> ( p1_s2_orders_1 @ A @ C ) ) ) ) )
& ! [A: $i] :
~ ( ( r1_tarski @ A @ f1_s2_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
=> ~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( p1_s2_orders_1 @ B @ C )
& ~ ( p1_s2_orders_1 @ C @ B ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ f1_s2_orders_1 )
& ( r2_hidden @ C @ A )
& ~ ( p1_s2_orders_1 @ B @ C ) ) ) ) )
=> ? [A: $i] :
( ( m1_subset_1 @ A @ f1_s2_orders_1 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_orders_1 )
=> ~ ( ( A != B )
& ( p1_s2_orders_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
<=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).
thf(5688,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1574,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( E
= ( k6_mcart_1 @ A @ B @ C @ D ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_mcart_1) ).
thf(8954,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( ( E
= ( k6_mcart_1 @ A @ B @ C @ D ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = G ) ) )
& ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = G ) )
=> ( E
= ( k6_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_partfun1) ).
thf(4907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
=> ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ E )
& ( r2_hidden @ E @ B ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pua2mss1) ).
thf(6320,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ E )
& ( r2_hidden @ E @ B ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_mcart_1) ).
thf(5538,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_mcart_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).
thf(6890,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ B )
& ( m1_subset_1 @ F @ C ) )
=> ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
= ( k3_mcart_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(887,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(5587,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B
= ( k13_finseq_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( m2_finseq_1 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_finseq_1) ).
thf(1809,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k13_finseq_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( m2_finseq_1 @ C @ A ) )
& ( ( m2_finseq_1 @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( m2_finseq_1 @ C @ A ) )
& ( ( m2_finseq_1 @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k13_finseq_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1576,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).
thf(8965,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(1324,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(7788,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( r5_pboole @ A @ B @ C )
=> ( r5_pboole @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r5_pboole) ).
thf(2614,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( r5_pboole @ A @ B @ C )
=> ( r5_pboole @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(88,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_finseq_2) ).
thf(2096,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( m1_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_realset1) ).
thf(5890,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( m1_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( m1_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(361,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3193,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(4901,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(1351,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_relat_1 @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ A )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_pboole) ).
thf(7896,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k2_relat_1 @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ A )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(4458,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( D
= ( k3_mcart_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ ( k6_mcart_1 @ A @ B @ C @ D ) @ ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_mcart_1) ).
thf(4868,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( D
= ( k3_mcart_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ ( k6_mcart_1 @ A @ B @ C @ D ) @ ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( ( r1_ordinal1 @ A @ B )
| ( r1_ordinal1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(4813,plain,
! [A: $i,B: $i] :
( ( ( v3_ordinal1 @ A )
& ( v3_ordinal1 @ B ) )
=> ( ( r1_ordinal1 @ A @ B )
| ( r1_ordinal1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1368,axiom,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_boole) ).
thf(7975,plain,
! [A: $i] :
( ( k5_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k9_relset_1 @ B @ C @ A @ ( k3_partfun1 @ D @ B @ C ) )
= ( k3_partfun1 @ D @ B @ ( k3_xboole_0 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_partfun1) ).
thf(2271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k9_relset_1 @ B @ C @ A @ ( k3_partfun1 @ D @ B @ C ) )
= ( k3_partfun1 @ D @ B @ ( k3_xboole_0 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1600,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(9069,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_card_1) ).
thf(4456,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(230,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_partfun1) ).
thf(2652,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1239,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k2_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_card_1) ).
thf(7298,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1731,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(9884,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(1541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_2) ).
thf(8804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
=> ( D
= ( k9_funct_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_eqrel_1) ).
thf(6088,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1288,axiom,
! [A: $i,B: $i] :
( ( ( k3_zfmisc_1 @ A @ A @ A )
= ( k3_zfmisc_1 @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_mcart_1) ).
thf(7539,plain,
! [A: $i,B: $i] :
( ( ( k3_zfmisc_1 @ A @ A @ A )
= ( k3_zfmisc_1 @ B @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
= ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_mcart_1) ).
thf(6056,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
= ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_2) ).
thf(7992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( r1_partfun1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(1217,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(7190,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1265,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_orders_1) ).
thf(7420,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B ) )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(1207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
<=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(7122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_zfmisc_1) ).
thf(3455,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).
thf(5916,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(281,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ B ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( r1_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pua2mss1) ).
thf(2846,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ B ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( r1_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1091,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(6564,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_2) ).
thf(6806,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
& ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(3278,plain,
~ ( v1_xboole_0 @ sk70 ),
inference(cnf,[status(esa)],[3276]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(2597,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(297,axiom,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_card_1) ).
thf(2899,plain,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1114,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_realset1) ).
thf(6664,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(1759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_mcart_1) ).
thf(10016,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(6719,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(765,axiom,
! [A: $i] :
( ( r2_wellord2 @ A @ k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_card_1) ).
thf(5003,plain,
! [A: $i] :
( ( ( r2_wellord2 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( r2_wellord2 @ A @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
thf(4986,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_2) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( ( ( k2_relat_1 @ D )
= B )
& ( ( k2_relat_1 @ E )
= C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_5) ).
thf(2582,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_wellord2 @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(7087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
& ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( r2_hidden @ G @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( r2_hidden @ ( k5_mcart_1 @ A @ B @ C @ G ) @ D )
& ( r2_hidden @ ( k6_mcart_1 @ A @ B @ C @ G ) @ E )
& ( r2_hidden @ ( k7_mcart_1 @ A @ B @ C @ G ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_mcart_1) ).
thf(4490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( r2_hidden @ G @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ( r2_hidden @ ( k5_mcart_1 @ A @ B @ C @ G ) @ D )
& ( r2_hidden @ ( k6_mcart_1 @ A @ B @ C @ G ) @ E )
& ( r2_hidden @ ( k7_mcart_1 @ A @ B @ C @ G ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_relat_1) ).
thf(2661,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k7_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(2375,plain,
v2_funct_1 @ sk27,
inference(cnf,[status(esa)],[2373]) ).
thf(743,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( k1_realset1 @ A @ B )
= ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_realset1) ).
thf(4922,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( k1_realset1 @ A @ B )
= ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1292,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_card_1) ).
thf(7554,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(1190,axiom,
( ! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ f1_s5_funct_2 )
& ( r2_hidden @ B @ f2_s5_funct_2 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ f3_s5_funct_2 )
& ( p1_s5_funct_2 @ A @ B @ C ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s5_funct_2 @ f2_s5_funct_2 ) @ f3_s5_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s5_funct_2 @ f2_s5_funct_2 ) @ f3_s5_funct_2 )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ f1_s5_funct_2 )
& ( r2_hidden @ C @ f2_s5_funct_2 ) )
=> ( p1_s5_funct_2 @ B @ C @ ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_funct_2) ).
thf(7045,plain,
( ! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ f1_s5_funct_2 )
& ( r2_hidden @ B @ f2_s5_funct_2 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ f3_s5_funct_2 )
& ( p1_s5_funct_2 @ A @ B @ C ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s5_funct_2 @ f2_s5_funct_2 ) @ f3_s5_funct_2 )
& ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s5_funct_2 @ f2_s5_funct_2 ) @ f3_s5_funct_2 )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ f1_s5_funct_2 )
& ( r2_hidden @ C @ f2_s5_funct_2 ) )
=> ( p1_s5_funct_2 @ B @ C @ ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4287,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(734,axiom,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(4894,plain,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(4971,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(5079,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(983,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_realset1 @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_realset1) ).
thf(6012,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_realset1 @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( r1_realset1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k8_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(4045,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k8_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k8_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_funct_2) ).
thf(1845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(6362,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(7615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1697,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(9631,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ~ ( r2_hidden @ D @ C ) )
& ( ~ ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( B = k1_xboole_0 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ B @ A )
| ~ ( m2_relset_1 @ D @ B @ A )
| ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
!= ( k6_partfun1 @ A ) )
| ( v2_funct_1 @ C ) ),
inference(cnf,[status(esa)],[1796]) ).
thf(1798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
!= ( k6_partfun1 @ A ) )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ B @ A )
| ~ ( m2_relset_1 @ D @ B @ A )
| ( v2_funct_1 @ C ) ),
inference(lifteq,[status(thm)],[1797]) ).
thf(134,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relat_1) ).
thf(2298,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(404,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(3391,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).
thf(6120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_2) ).
thf(2863,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1531,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(8772,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(1301,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( r2_hidden @ F @ A )
<=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_mcart_1) ).
thf(7635,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( ( r2_hidden @ F @ A )
=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
& ( ? [G: $i,H: $i,I: $i,J: $i] :
( ( r2_hidden @ G @ B )
& ( r2_hidden @ H @ C )
& ( r2_hidden @ I @ D )
& ( r2_hidden @ J @ E )
& ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) ) )
=> ( r2_hidden @ F @ A ) ) )
=> ( A
= ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(4035,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(6453,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m4_realset1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_realset1) ).
thf(2397,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m4_realset1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1726,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f2_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f3_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_subset_1) ).
thf(9847,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f2_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f2_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f3_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f3_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(1192,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m4_realset1 @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( B
= ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_realset1) ).
thf(7058,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( ( m4_realset1 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( B
= ( k1_tarski @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( B
= ( k1_tarski @ C ) ) )
=> ( m4_realset1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1036,axiom,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(6266,plain,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(7801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= ( k7_relset_2 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(106,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_sysrel @ A ) @ A )
& ( r1_tarski @ ( k1_sysrel @ A ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_sysrel) ).
thf(2192,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_sysrel @ A ) @ A )
& ( r1_tarski @ ( k1_sysrel @ A ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(4673,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1414,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(8218,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(1766,axiom,
! [A: $i] :
( ( r1_setfam_1 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_setfam_1) ).
thf(10059,plain,
! [A: $i] :
( ( r1_setfam_1 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_partfun1) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(9037,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(1670,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9467,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).
thf(4641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1431,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(8295,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ~ ( ( B
!= ( k1_pboole @ A ) )
& ( r5_pboole @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_pboole) ).
thf(2850,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ~ ( ( B
!= ( k1_pboole @ A ) )
& ( r5_pboole @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1317,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ~ ( r2_hidden @ D @ A )
<=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_0) ).
thf(7756,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ~ ( r2_hidden @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
& ( ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) )
=> ~ ( r2_hidden @ D @ A ) ) )
=> ( A
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1332,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relset_1) ).
thf(7811,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(4593,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1191,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(7055,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( r2_pboole @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_tarski @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_pboole) ).
thf(5790,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_tarski @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_tarski @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) )
=> ( r2_pboole @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F ) )
=> ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_mcart_1) ).
thf(7832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F ) )
=> ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1226,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_relset_2 @ A @ B @ C @ D )
= ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_2) ).
thf(7228,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_relset_2 @ A @ B @ C @ D )
= ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(276,axiom,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
thf(2831,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_xboole_1) ).
thf(6146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(416,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v3_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pboole) ).
thf(3448,plain,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v3_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(5767,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(617,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4398,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( r5_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ ( k5_pboole @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_pboole) ).
thf(2688,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( r5_pboole @ A @ ( k3_pboole @ A @ B @ C ) @ ( k5_pboole @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(301,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(2920,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(2700,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1556,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(8873,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(7243,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(5555,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(9666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(411,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3412,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).
thf(3174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) )
& ( ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_5) ).
thf(4409,plain,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(7388,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_domain_1) ).
thf(8498,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ( ( ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) )
& ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( m1_subset_1 @ H @ D )
& ( m1_subset_1 @ I @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) )
=> ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(661,axiom,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(4561,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(5418,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(2224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(2454,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3305,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( ( v1_setfam_1 @ A )
& ( v1_setfam_1 @ B ) )
=> ( v1_setfam_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_setfam_1) ).
thf(4190,plain,
! [A: $i,B: $i] :
( ( ( v1_setfam_1 @ A )
& ( v1_setfam_1 @ B ) )
=> ( v1_setfam_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_2) ).
thf(3818,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( ( r1_partfun1 @ B @ D )
& ( r1_partfun1 @ C @ D ) )
=> ( r1_partfun1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m2_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(5912,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m2_realset1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1505,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(8669,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(3344,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( g2_vectsp_1 @ A @ B @ C @ D )
= ( g2_vectsp_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_vectsp_1) ).
thf(5753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( g2_vectsp_1 @ A @ B @ C @ D )
= ( g2_vectsp_1 @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1304,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
<=> ( v1_finset_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(7667,plain,
! [A: $i] :
( ( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
=> ( v1_finset_1 @ ( k3_tarski @ A ) ) )
& ( ( v1_finset_1 @ ( k3_tarski @ A ) )
=> ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(1784,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relset_2) ).
thf(10211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(1688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
& ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
<=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).
thf(9567,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
& ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
& ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) ) )
& ( ? [J: $i,K: $i,L: $i,M: $i] :
( ( m1_subset_1 @ J @ B )
& ( m1_subset_1 @ K @ C )
& ( m1_subset_1 @ L @ D )
& ( m1_subset_1 @ M @ E )
& ( A
= ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
& ( r2_hidden @ J @ F )
& ( r2_hidden @ K @ G )
& ( r2_hidden @ L @ H )
& ( r2_hidden @ M @ I ) )
=> ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(1413,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(8216,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(5948,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
=> ( r1_tarski @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(6513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1720,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(9809,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(1652,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(9358,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(7947,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(1289,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).
thf(7543,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1722,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_orders_1) ).
thf(9815,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(6508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1473,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k1_tarski @ C ) )
=> ( ( k8_setfam_1 @ A @ B )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(8509,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k1_tarski @ C ) )
=> ( ( k8_setfam_1 @ A @ B )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1003,axiom,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(6125,plain,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(54,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
thf(1980,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1173,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
<=> ( B
= ( k2_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).
thf(6966,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
=> ( B
= ( k2_subset_1 @ A ) ) )
& ( ( B
= ( k2_subset_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(5309,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(346,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
thf(3127,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1440,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1251,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_relat_1) ).
thf(7351,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1046,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r2_relat_2 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_2) ).
thf(6313,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r2_relat_2 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) )
=> ( r2_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( k1_funct_1 @ ( k1_pboole @ B ) @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_pboole) ).
thf(5638,plain,
! [A: $i,B: $i] :
( ( k1_funct_1 @ ( k1_pboole @ B ) @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(9963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1182,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_card_1) ).
thf(7009,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(5062,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_sysrel) ).
thf(3493,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_xboole_1) ).
thf(6333,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(7797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1763,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(10028,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
thf(2860,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1712,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_realset1) ).
thf(9747,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(4516,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ A ) )
& ( ~ ( r2_hidden @ B @ A )
=> ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(237,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_zfmisc_1) ).
thf(2675,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(8679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
thf(2056,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1559,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_2) ).
thf(8893,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
thf(5208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(2948,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1624,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).
thf(9194,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(3697,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( r1_partfun1 @ C @ D )
<=> ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_2) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( r1_partfun1 @ C @ D )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) )
& ( ! [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( r1_partfun1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(3488,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t181_relat_1) ).
thf(2838,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(5628,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(5347,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
<=> ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_relat_1) ).
thf(4624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
=> ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
& ( ( ( r2_hidden @ B @ C )
& ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(4246,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
=> ( r1_partfun1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(397,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ B )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
& ( v2_funct_1 @ D ) )
=> ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_pua2mss1) ).
thf(3356,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ B )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
& ( v2_funct_1 @ D ) )
=> ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_wellord2 @ ( k1_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_5) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_wellord2 @ ( k1_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ C ) ) )
& ( ( k1_card_1 @ ( k1_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
= ( k1_card_1 @ ( k2_zfmisc_1 @ ( k1_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1058,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_orders_1) ).
thf(6369,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(645,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).
thf(4510,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(703,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_2) ).
thf(4748,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).
thf(7391,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(762,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(4991,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_mcart_1) ).
thf(8061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(747,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t182_relat_1) ).
thf(4932,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1257,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(7374,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(1407,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(8185,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(1736,axiom,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_5) ).
thf(9930,plain,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(1749,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(9983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(572,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(4202,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_relat_1) ).
thf(2511,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(5226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_relat_1) ).
thf(2728,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(2030,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(580,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(4225,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(4342,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(864,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).
thf(5472,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1459,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(8433,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1399,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_setfam_1 @ C @ ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ~ ( r1_tarski @ D @ A )
& ~ ( r1_tarski @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_setfam_1) ).
thf(8151,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_setfam_1 @ C @ ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ~ ( r1_tarski @ D @ A )
& ~ ( r1_tarski @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun1) ).
thf(5596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1278,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(7488,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1395,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(8140,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1667,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(9453,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(1179,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(6992,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(5841,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(623,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4414,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(6420,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_2) ).
thf(6220,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_partfun1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(615,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ~ ( ( r4_pboole @ A @ B @ B )
& ( B
= ( k1_pboole @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_pboole) ).
thf(4392,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ~ ( ( r4_pboole @ A @ B @ B )
& ( B
= ( k1_pboole @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(577,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( a_4_0_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_domain_1) ).
thf(4217,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
= ( a_4_0_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(7234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1760,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C = k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_2) ).
thf(10018,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C = k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_partfun1) ).
thf(1918,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_1) ).
thf(3565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1680,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_domain_1) ).
thf(9527,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
=> ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
= ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).
thf(2696,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k7_mcart_1 @ A @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_mcart_1) ).
thf(5536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k7_mcart_1 @ A @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(146,axiom,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_sysrel) ).
thf(2347,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6980,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(3320,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(3665,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(8830,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_sysrel) ).
thf(3284,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1165,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_int_1) ).
thf(6928,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1291,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ! [D: $i] :
( ( m1_eqrel_1 @ D @ B )
=> ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pua2mss1) ).
thf(7552,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_eqrel_1 @ C @ A )
=> ! [D: $i] :
( ( m1_eqrel_1 @ D @ B )
=> ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_2) ).
thf(2013,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(656,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(4548,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1303,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_setfam_1) ).
thf(7659,plain,
! [A: $i,B: $i] :
( ( ( r1_setfam_1 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) ) )
=> ( r1_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_partfun1 @ A @ B @ C @ D )
= ( k7_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(4289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_partfun1 @ A @ B @ C @ D )
= ( k7_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_finseq_2) ).
thf(1839,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ B )
=> ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(5873,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(7146,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1623,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(9192,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( m2_relset_1 @ ( k9_relset_1 @ C @ A @ B @ D ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_1) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( m2_relset_1 @ ( k9_relset_1 @ C @ A @ B @ D ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(723,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( v3_relat_1 @ B )
& ( r2_pboole @ A @ C @ B ) )
=> ( v3_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_pboole) ).
thf(4851,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( v3_relat_1 @ B )
& ( r2_pboole @ A @ C @ B ) )
=> ( v3_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(7024,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(601,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).
thf(4325,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(74,axiom,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_5) ).
thf(2045,plain,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = J ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_mcart_1) ).
thf(8028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ C )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ D )
=> ( ( F
= ( k4_mcart_1 @ G @ H @ I @ J ) )
=> ( E = J ) ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D = k1_xboole_0 )
| ( E
= ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_partfun1) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(4165,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ! [E: $i] :
( ( m1_pboole @ E @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ D @ E ) )
=> ( r2_pboole @ A @ ( k3_pboole @ A @ B @ D ) @ ( k3_pboole @ A @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_pboole) ).
thf(5660,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ! [E: $i] :
( ( m1_pboole @ E @ A )
=> ( ( ( r2_pboole @ A @ B @ C )
& ( r2_pboole @ A @ D @ E ) )
=> ( r2_pboole @ A @ ( k3_pboole @ A @ B @ D ) @ ( k3_pboole @ A @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_relat_1) ).
thf(4944,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(11,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(1834,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_finseq_1) ).
thf(1913,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1421,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( v3_ordinal1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_ordinal1) ).
thf(8260,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( v3_ordinal1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
thf(5966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(3447,plain,
v1_relat_1 @ sk81,
inference(cnf,[status(esa)],[3444]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).
thf(4997,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_partfun1) ).
thf(5510,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ~ ( ( v1_partfun1 @ E @ A @ B )
& ( r1_partfun1 @ C @ E )
& ( r1_partfun1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1406,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(8183,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(1477,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
=> ( v3_ordinal1 @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_ordinal2) ).
thf(8533,plain,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v3_ordinal1 @ B ) )
=> ( v3_ordinal1 @ ( k1_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(660,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ~ ( ( r4_pboole @ A @ B @ C )
& ( r5_pboole @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_pboole) ).
thf(4559,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ~ ( ( r4_pboole @ A @ B @ C )
& ( r5_pboole @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(855,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relat_1) ).
thf(5421,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_relat_1) ).
thf(4780,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2743,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1781,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_5_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p2_s10_domain_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_5_domain_1) ).
thf(10188,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_5_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p2_s10_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s10_domain_1 )
& ( A = B )
& ( p2_s10_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_5_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(1417,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_domain_1) ).
thf(8228,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ( ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ B )
& ? [G: $i] :
( ( m1_subset_1 @ G @ C )
& ? [H: $i] :
( ( m1_subset_1 @ H @ D )
& ? [I: $i] :
( ( m1_subset_1 @ I @ E )
& ( A
= ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) )
=> ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(848,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(5389,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(20,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ A @ C )
= D )
<=> ( ( k1_funct_1 @ B @ D )
= C ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1866,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( ( k1_funct_1 @ A @ C )
= D )
=> ( ( k1_funct_1 @ B @ D )
= C ) )
& ( ( ( k1_funct_1 @ B @ D )
= C )
=> ( ( k1_funct_1 @ A @ C )
= D ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(81,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 )
& ( ( k5_relat_1 @ B @ A )
= B )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ B )
= B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_sysrel) ).
thf(2071,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( ( k5_relat_1 @ A @ B )
= A )
& ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
= k1_xboole_0 )
& ( ( k5_relat_1 @ B @ A )
= B )
& ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) )
& ( ( ( ( k5_relat_1 @ B @ A )
= A )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ B )
= B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 ) )
=> ( ( k1_sysrel @ A )
= ( k1_sysrel @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(232,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relat_1) ).
thf(2658,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1487,axiom,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(8579,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_partfun1) ).
thf(1807,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(5184,plain,
! [A: $i,B: $i] :
( ( v1_xboole_0 @ B )
=> ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(2907,plain,
v2_relat_1 @ sk44,
inference(cnf,[status(esa)],[2905]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_relat_1) ).
thf(2443,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_msualg_1) ).
thf(3729,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
& ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
=> ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1592,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(9014,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( A
= ( k8_mcart_1 @ B @ C @ D @ E @ F ) )
<=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_domain_1) ).
thf(6341,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ~ ( v1_xboole_0 @ E )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
=> ( ( ( A
= ( k8_mcart_1 @ B @ C @ D @ E @ F ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = G ) ) ) ) ) ) )
& ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ D )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ E )
=> ( ( F
= ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
=> ( A = G ) ) ) ) ) )
=> ( A
= ( k8_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(5191,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(843,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(5351,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( A
= ( k5_mcart_1 @ B @ C @ D @ E ) )
<=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_domain_1) ).
thf(6790,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
=> ( ( ( A
= ( k5_mcart_1 @ B @ C @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = F ) ) ) ) ) )
& ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ D )
=> ( ( E
= ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
=> ( A = F ) ) ) ) )
=> ( A
= ( k5_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1204,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( r5_pboole @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_pboole) ).
thf(7114,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( r5_pboole @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) )
=> ( r5_pboole @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
& ( ( k1_card_1 @ C )
= ( k1_card_1 @ D ) ) )
=> ( ( k1_card_1 @ ( k1_funct_2 @ A @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_5) ).
thf(3780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
& ( ( k1_card_1 @ C )
= ( k1_card_1 @ D ) ) )
=> ( ( k1_card_1 @ ( k1_funct_2 @ A @ C ) )
= ( k1_card_1 @ ( k1_funct_2 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(3465,plain,
v1_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(2591,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(6903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( ( k4_relset_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(923,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_realset1) ).
thf(5724,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1349,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(7872,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2283,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).
thf(6818,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(284,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2855,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_xboole_1) ).
thf(6607,plain,
! [A: $i,B: $i,C: $i] :
( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
= ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1535,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ~ ( r1_xboole_0 @ A @ D )
& ~ ( r1_xboole_0 @ B @ E )
& ~ ( r1_xboole_0 @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_mcart_1) ).
thf(8780,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
=> ( ~ ( r1_xboole_0 @ A @ D )
& ~ ( r1_xboole_0 @ B @ E )
& ~ ( r1_xboole_0 @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k6_mcart_1 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_mcart_1) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( m1_subset_1 @ ( k6_mcart_1 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(825,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(5272,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
= ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(131,axiom,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
thf(2290,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(672,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(4615,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(161,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2406,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(7344,plain,
~ ( v1_xboole_0 @ k4_numbers ),
inference(polarity_switch,[status(thm)],[7343]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_1) ).
thf(4089,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(6893,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relset_2) ).
thf(2554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_setfam_1) ).
thf(4683,plain,
! [A: $i,B: $i] :
( ( ( r2_setfam_1 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) )
=> ( r2_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_partfun1) ).
thf(3383,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1489,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_2) ).
thf(8584,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ C )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(1409,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8197,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(271,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
~ ( ( v1_finset_1 @ B )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
& ( v1_finset_1 @ C )
& ( ( k9_relat_1 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t195_orders_1) ).
thf(2811,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
~ ( ( v1_finset_1 @ B )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
& ( v1_finset_1 @ C )
& ( ( k9_relat_1 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1648,axiom,
? [A: $i] :
! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ( r2_hidden @ B @ f1_s1_xboole_0 )
& ( p1_s1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0) ).
thf(9343,plain,
? [A: $i] :
! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ f1_s1_xboole_0 )
& ( p1_s1_xboole_0 @ B ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_xboole_0 )
& ( p1_s1_xboole_0 @ B ) )
=> ( r2_hidden @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(1161,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(6913,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(315,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relat_1) ).
thf(2971,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(6910,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
<=> ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_mcart_1) ).
thf(8634,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
=> ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 ) )
& ( ( ( k3_zfmisc_1 @ A @ B @ C )
!= k1_xboole_0 )
=> ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ B @ C )
=> ( ( k9_relset_1 @ A @ B @ C @ D )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_1) ).
thf(5010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ B @ C )
=> ( ( k9_relset_1 @ A @ B @ C @ D )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(7384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1206,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(7120,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(506,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(3859,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( A
= ( k2_zfmisc_1 @ B @ C ) )
=> ( ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( ( ( k1_relat_1 @ A )
= B )
& ( ( k2_relat_1 @ A )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( k2_relat_1 @ C )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_2) ).
thf(3252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) ) )
& ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ D )
& ( m2_relset_1 @ E @ B @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ D )
& ( m2_relset_1 @ F @ B @ D ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
= ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
=> ( E = F ) ) ) ) )
=> ( ( k2_relat_1 @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ~ ( ~ ( r5_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D )
& ( r5_pboole @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_pboole) ).
thf(5505,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ~ ( ~ ( r5_pboole @ A @ B @ C )
& ( r2_pboole @ A @ C @ D )
& ( r5_pboole @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1620,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(9179,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1419,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_funct_1 @ A @ B )
& ( p1_s1_funct_1 @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ! [B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
<=> ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1) ).
thf(8240,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_funct_1 @ A @ B )
& ( p1_s1_funct_1 @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_2) ).
thf(2152,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(628,axiom,
! [A: $i] :
? [B: $i] :
( ( v3_ordinal1 @ B )
& ( r2_wellord2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_card_1) ).
thf(4451,plain,
! [A: $i] :
? [B: $i] :
( ( v3_ordinal1 @ B )
& ( r2_wellord2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(967,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_subset_1) ).
thf(5922,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_finseq_2) ).
thf(2081,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [F: $i] :
( ( m2_finseq_1 @ F @ A )
=> ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(2399,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(2680,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1286,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(7530,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
& ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
& ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(911,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r5_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_2) ).
thf(5672,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r5_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r5_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(2494,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1684,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_1_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(9542,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_1_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_1_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(4745,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).
thf(2944,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_2) ).
thf(4182,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_partfun1 @ B @ C )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1554,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( r4_pboole @ A @ B @ C )
<=> ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_pboole) ).
thf(8865,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( r4_pboole @ A @ B @ C )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) )
& ( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_xboole_0 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) )
=> ( r4_pboole @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(6516,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(8172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(667,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_xboole_1) ).
thf(4602,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(4197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(3324,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(6305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C )
& ( v1_finset_1 @ D ) )
=> ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1425,axiom,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ ( k1_card_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_card_1) ).
thf(8272,plain,
! [A: $i,B: $i] :
( ( v1_card_1 @ B )
=> ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ ( k1_card_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t173_relat_1) ).
thf(5164,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A )
=> ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(4175,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(557,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_relat_1) ).
thf(4153,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(576,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
= ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t189_relat_1) ).
thf(4214,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
= ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_funct_1) ).
thf(3585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(6118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B )
& ( v1_finset_1 @ C ) )
=> ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1663,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(9434,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_partfun1) ).
thf(7312,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k1_funct_2 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).
thf(5109,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k1_funct_2 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ D @ B )
& ( m1_eqrel_1 @ E @ C ) )
=> ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).
thf(7747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ D @ B )
& ( m1_eqrel_1 @ E @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) ) )
& ( ? [F: $i,G: $i] :
( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
& ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
& ( A
= ( k12_mcart_1 @ B @ C @ F @ G ) ) )
=> ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(768,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relat_1) ).
thf(5023,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(141,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_sysrel) ).
thf(2330,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) )
= k1_xboole_0 ) )
& ( ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
= k1_xboole_0 )
=> ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(851,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_relat_1) ).
thf(5409,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1682,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(9537,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( m1_pboole @ B @ A )
<=> ( ( k1_relat_1 @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).
thf(2576,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( m1_pboole @ B @ A )
=> ( ( k1_relat_1 @ B )
= A ) )
& ( ( ( k1_relat_1 @ B )
= A )
=> ( m1_pboole @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_5) ).
thf(2066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(6521,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(3677,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ~ ( r1_xboole_0 @ A @ E )
& ~ ( r1_xboole_0 @ B @ F )
& ~ ( r1_xboole_0 @ C @ G )
& ~ ( r1_xboole_0 @ D @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_mcart_1) ).
thf(6062,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ~ ( r1_xboole_0 @ A @ E )
& ~ ( r1_xboole_0 @ B @ F )
& ~ ( r1_xboole_0 @ C @ G )
& ~ ( r1_xboole_0 @ D @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1450,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m2_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(8399,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m2_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) )
=> ( m2_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(619,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_relat_1) ).
thf(4404,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(6536,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
& ! [G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ D )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ A ) ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= ( k5_mcart_1 @ A @ B @ C @ E ) )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= ( k6_mcart_1 @ A @ B @ C @ E ) )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= ( k7_mcart_1 @ A @ B @ C @ E ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_domain_1) ).
thf(2902,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ( ( ( k5_mcart_1 @ A @ B @ C @ D )
= ( k5_mcart_1 @ A @ B @ C @ E ) )
& ( ( k6_mcart_1 @ A @ B @ C @ D )
= ( k6_mcart_1 @ A @ B @ C @ E ) )
& ( ( k7_mcart_1 @ A @ B @ C @ D )
= ( k7_mcart_1 @ A @ B @ C @ E ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(805,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_pboole) ).
thf(5211,plain,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1630,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_mcart_1) ).
thf(9211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(1092,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(6569,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1647,axiom,
! [A: $i,B: $i] :
( ( ( A != k1_xboole_0 )
=> ( ( B
= ( k1_setfam_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( B
= ( k1_setfam_1 @ A ) )
<=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(9311,plain,
! [A: $i,B: $i] :
( ( ( A != k1_xboole_0 )
=> ( ( ( B
= ( k1_setfam_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( B
= ( k1_setfam_1 @ A ) )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(1732,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(9887,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(1329,axiom,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(7804,plain,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(485,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).
thf(3761,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1074,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(6462,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(800,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(5194,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(745,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_1) ).
thf(4927,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(7152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(4619,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(123,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2258,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1439,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).
thf(8324,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(7744,plain,
~ ( v1_xboole_0 @ sk471 ),
inference(cnf,[status(esa)],[7742]) ).
thf(3464,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_partfun1) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( v1_partfun1 @ D @ A @ B )
& ( r1_partfun1 @ C @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_relat_1) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k9_relset_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(3337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
=> ( ( k9_relset_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1768,axiom,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(10073,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).
thf(3992,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_pua2mss1) ).
thf(2003,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1124,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(6703,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(2374,plain,
v1_xboole_0 @ sk27,
inference(cnf,[status(esa)],[2373]) ).
thf(1721,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(9812,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
= ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).
thf(7081,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
= ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1685,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
= ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(9551,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
= ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(2517,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(9166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(5728,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1384,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(8070,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_sysrel) ).
thf(4014,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_partfun1) ).
thf(1957,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1172,axiom,
! [A: $i] :
( ( v1_realset1 @ A )
<=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_realset1) ).
thf(6957,plain,
! [A: $i] :
( ( ( v1_realset1 @ A )
=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) )
& ( ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) )
=> ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( v2_relat_1 @ B )
& ( r2_pboole @ A @ B @ C ) )
=> ( v2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_pboole) ).
thf(5606,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ( ( ( v2_relat_1 @ B )
& ( r2_pboole @ A @ B @ C ) )
=> ( v2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1121,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_orders_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(6693,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_orders_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
& ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1634,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(9229,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(4356,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1467,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(8478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3733,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_subset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(716,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_ordinal1 @ ( k1_relat_1 @ A ) )
=> ( m1_ordinal1 @ A @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_ordinal1) ).
thf(4811,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v3_ordinal1 @ ( k1_relat_1 @ A ) )
=> ( m1_ordinal1 @ A @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_domain_1 @ A @ B @ C @ D )
= ( k1_enumset1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).
thf(7231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_domain_1 @ A @ B @ C @ D )
= ( k1_enumset1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_partfun1) ).
thf(4596,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( r1_partfun1 @ C @ D )
& ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(3892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
= ( k4_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_mcart_1) ).
thf(5954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_mcart_1 @ A @ B @ C @ D )
= ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1233,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(7259,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1339,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7836,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(4719,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ A @ B @ C )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(6050,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_zfmisc_1 @ A @ B @ C )
= ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(311,axiom,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( A = B )
<=> ( r2_wellord2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_card_1) ).
thf(2951,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ! [B: $i] :
( ( v1_card_1 @ B )
=> ( ( ( A = B )
=> ( r2_wellord2 @ A @ B ) )
& ( ( r2_wellord2 @ A @ B )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_mcart_1) ).
thf(7029,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(4523,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_relat_1) ).
thf(5477,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(3132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_5) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1597,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(9051,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(1010,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(6150,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1741,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s6_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_6_domain_1) ).
thf(9944,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s6_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p2_s6_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ ( k1_funct_1 @ E @ C ) @ D ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k9_relset_1 @ A @ B @ D @ E ) @ C )
= ( k1_funct_1 @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_2) ).
thf(6226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ ( k1_funct_1 @ E @ C ) @ D ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k9_relset_1 @ A @ B @ D @ E ) @ C )
= ( k1_funct_1 @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_2) ).
thf(3203,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m2_relset_1 @ E @ B @ C ) )
=> ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
=> ( ( ( C = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
| ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v2_funct_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(6366,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
= ( k2_tarski @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_card_1) ).
thf(3062,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun1) ).
thf(8933,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(6782,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_mcart_1) ).
thf(7955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
= ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1540,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).
thf(8801,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(3469,plain,
v1_finset_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3463]) ).
thf(320,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ D @ C ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_orders_1) ).
thf(3015,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ D @ C ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(8653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(1610,axiom,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_domain_1) ).
thf(9134,plain,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(1475,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(8516,plain,
! [A: $i,B: $i] :
( ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(151,axiom,
! [A: $i] :
? [B: $i] :
( ( v3_ordinal1 @ B )
& ~ ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ( ~ ( r2_hidden @ C @ A )
=> ( r1_ordinal1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_ordinal1) ).
thf(2366,plain,
! [A: $i] :
? [B: $i] :
( ( v3_ordinal1 @ B )
& ~ ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( v3_ordinal1 @ C )
=> ( ~ ( r2_hidden @ C @ A )
=> ( r1_ordinal1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1359,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
thf(7932,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(1494,axiom,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_orders_1) ).
thf(8616,plain,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(224,axiom,
! [A: $i] : ( r1_setfam_1 @ ( k3_setfam_1 @ A @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_setfam_1) ).
thf(2636,plain,
! [A: $i] : ( r1_setfam_1 @ ( k3_setfam_1 @ A @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(2751,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_partfun1) ).
thf(8790,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(563,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(4178,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1343,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(7851,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_relat_1) ).
thf(3897,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_5) ).
thf(4565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_mcart_1) ).
thf(4755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
= ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_partfun1) ).
thf(5092,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
= ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1411,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_1) ).
thf(8207,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(4281,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3347,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(6114,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1523,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
<=> ( B
= ( k1_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).
thf(8737,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
=> ( B
= ( k1_subset_1 @ A ) ) )
& ( ( B
= ( k1_subset_1 @ A ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(1446,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(8373,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(4210,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_1) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_mcart_1) ).
thf(2746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
=> ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(4083,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(534,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pboole) ).
thf(4024,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_mcart_1) ).
thf(6380,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
= ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_relat_1) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3196,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
& ( A
= ( k2_xboole_0 @ C @ D ) ) )
=> ( E
= ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_sysrel) ).
thf(5251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
& ( A
= ( k2_xboole_0 @ C @ D ) ) )
=> ( E
= ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_relat_1) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( k10_pboole @ A @ B )
= ( k2_funcop_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_pboole) ).
thf(3030,plain,
! [A: $i,B: $i] :
( ( k10_pboole @ A @ B )
= ( k2_funcop_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(627,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(4442,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
& ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(7808,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(4912,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(6612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3045,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(9083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(1687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(9564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_pua2mss1) ).
thf(2021,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_5) ).
thf(2063,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1045,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(6309,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1751,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(9987,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2783,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_relat_1) ).
thf(5324,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(826,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
=> ( ( k7_relat_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t187_relat_1) ).
thf(5275,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
=> ( ( k7_relat_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F )
& ( r1_tarski @ G @ H ) )
=> ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_mcart_1) ).
thf(8675,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_tarski @ E @ F )
& ( r1_tarski @ G @ H ) )
=> ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(249,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2731,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_finseq_2) ).
thf(4242,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
& ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1593,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
thf(9023,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( k1_relset_2 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k3_pboole @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pboole) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( m1_pboole @ ( k3_pboole @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).
thf(5280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m4_realset1 @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_realset1) ).
thf(5060,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_realset1 @ A )
& ( m4_realset1 @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).
thf(5623,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4659,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1532,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_2) ).
thf(8773,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(533,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
& ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_sysrel) ).
thf(4019,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
& ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = G ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k6_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_mcart_1) ).
thf(7246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ C )
=> ( ( E
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( D = G ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( D
= ( k6_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(7214,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(722,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(4848,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1636,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(9235,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_partfun1) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_relat_1) ).
thf(1977,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relat_1) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(7987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(446,axiom,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_5) ).
thf(3570,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
thf(6697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(178,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
thf(2467,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(6383,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1675,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(9504,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).
thf(4239,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v1_funct_2 @ C @ A @ B )
<=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( v1_funct_2 @ C @ A @ B )
<=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(4831,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v1_funct_2 @ C @ A @ B )
=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) )
& ( ( A
= ( k4_relset_1 @ A @ B @ C ) )
=> ( v1_funct_2 @ C @ A @ B ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( ( v1_funct_2 @ C @ A @ B )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k3_domain_1 @ A @ B @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_domain_1) ).
thf(7708,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( m1_subset_1 @ ( k3_domain_1 @ A @ B @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(510,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v3_relat_1 @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t184_relat_1) ).
thf(3886,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v3_relat_1 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) ) )
& ( ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( B = k1_xboole_0 ) )
=> ( v3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(7780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(813,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(5236,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1325,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(7791,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).
thf(8548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(10229,plain,
! [A: $i] :
( sk3
| ~ ( r2_hidden @ A @ sk2 )
| ~ ( v1_xboole_0 @ k1_xboole_0 )
| ( A != sk431 ) ),
inference(paramod_ordered,[status(thm)],[1794,7508]) ).
thf(10230,plain,
( sk3
| ~ ( r2_hidden @ sk431 @ sk2 )
| ~ ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[10229:[bind(A,$thf( sk431 ))]]) ).
thf(10322,plain,
( sk3
| ~ ( r2_hidden @ sk431 @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[10230,3464]) ).
thf(10323,plain,
( sk3
| ~ ( r2_hidden @ sk431 @ sk2 ) ),
inference(simp,[status(thm)],[10322]) ).
thf(863,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
= ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funcop_1) ).
thf(5468,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( k7_relat_1 @ A @ C )
= ( k7_relat_1 @ B @ C ) )
=> ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
= ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2539,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relset_2) ).
thf(3076,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(4071,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ B )
= ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_partfun1) ).
thf(1902,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k2_tarski @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mssubfam) ).
thf(6778,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( B
= ( k2_tarski @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v3_relat_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(4691,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v3_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v3_relat_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_subset_1) ).
thf(6548,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).
thf(4501,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( k3_zfmisc_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).
thf(9600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
= ( k3_zfmisc_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(1566,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( D
= ( k3_pboole @ A @ B @ C ) )
<=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k3_xboole_0 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pboole) ).
thf(8918,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_pboole @ C @ A )
=> ! [D: $i] :
( ( m1_pboole @ D @ A )
=> ( ( ( D
= ( k3_pboole @ A @ B @ C ) )
=> ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k3_xboole_0 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) )
& ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ D @ E )
= ( k3_xboole_0 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) )
=> ( D
= ( k3_pboole @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(1295,axiom,
! [A: $i,B: $i] :
( ( r2_tarski @ A @ B )
<=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( D = F )
<=> ( E = G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_tarski) ).
thf(7563,plain,
! [A: $i,B: $i] :
( ( ( r2_tarski @ A @ B )
=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) )
=> ( r2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1552,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
<=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_1) ).
thf(8857,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) )
& ( ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(6658,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(650,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(4533,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).
thf(5155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ B @ ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_setfam_1) ).
thf(6173,plain,
! [A: $i,B: $i] :
( ( r1_setfam_1 @ B @ ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1758,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( k3_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_realset1) ).
thf(10013,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( k3_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
= ( k7_relat_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_relat_1) ).
thf(2690,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
= ( k7_relat_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( v2_relat_1 @ D )
& ( m1_pboole @ D @ B ) )
=> ( ( v2_relat_1 @ ( k8_pboole @ A @ B @ C @ D ) )
& ( m1_pboole @ ( k8_pboole @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_pboole) ).
thf(2018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( v2_relat_1 @ D )
& ( m1_pboole @ D @ B ) )
=> ( ( v2_relat_1 @ ( k8_pboole @ A @ B @ C @ D ) )
& ( m1_pboole @ ( k8_pboole @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_setfam_1 @ A @ B )
& ( r1_setfam_1 @ B @ C ) )
=> ( r1_setfam_1 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_setfam_1) ).
thf(5788,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_setfam_1 @ A @ B )
& ( r1_setfam_1 @ B @ C ) )
=> ( r1_setfam_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(329,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3052,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1604,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(9087,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) )
=> ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(1170,axiom,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(6948,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1511,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(8685,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(1352,axiom,
! [A: $i] :
( ( v1_funct_1 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(7900,plain,
! [A: $i] :
( ( ( v1_funct_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) )
=> ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(1728,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
<=> ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(9870,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(795,axiom,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_sysrel) ).
thf(5172,plain,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(3528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(236,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( k4_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_realset1) ).
thf(2672,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( k4_realset1 @ A @ B @ C )
= ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) )
& ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_1) ).
thf(2879,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k7_relat_1 @ C @ A ) )
& ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
= ( k7_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( r4_pboole @ A @ B @ C )
=> ( r4_pboole @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_pboole) ).
thf(3461,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( ( r4_pboole @ A @ B @ C )
=> ( r4_pboole @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(5591,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(41,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_sysrel) ).
thf(1944,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ ( k1_sysrel @ A ) ) ) @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(692,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_orders_1) ).
thf(4702,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r1_tarski @ B @ A )
& ( v6_ordinal1 @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) ) ) )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B )
& ( r1_tarski @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1570,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(8940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(48,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1962,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( E
= ( k5_mcart_1 @ A @ B @ C @ D ) )
<=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_mcart_1) ).
thf(7181,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ~ ! [D: $i] :
( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( E
= ( k5_mcart_1 @ A @ B @ C @ D ) )
=> ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = F ) ) )
& ( ! [F: $i,G: $i,H: $i] :
( ( D
= ( k3_mcart_1 @ F @ G @ H ) )
=> ( E = F ) )
=> ( E
= ( k5_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1342,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).
thf(7848,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(383,axiom,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= A )
& ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_sysrel) ).
thf(3299,plain,
! [A: $i,B: $i] :
~ ( ( A != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= A )
& ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_mcart_1) ).
thf(6842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
& ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relat_1) ).
thf(5458,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(110,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k4_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(2206,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k4_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k4_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_relat_1) ).
thf(5618,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1243,axiom,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_card_1) ).
thf(7310,plain,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_pboole) ).
thf(2887,plain,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3405,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1641,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(9267,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(4752,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(4742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
= ( k5_funcop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ D )
& ( r2_wellord2 @ A @ C )
& ( r2_wellord2 @ B @ D ) )
=> ( r2_wellord2 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_card_1) ).
thf(5255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ D )
& ( r2_wellord2 @ A @ C )
& ( r2_wellord2 @ B @ D ) )
=> ( r2_wellord2 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1692,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(9611,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(4977,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_2) ).
thf(3316,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
=> ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
& ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
<=> ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_mcart_1) ).
thf(6632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
=> ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) ) )
& ( ( ( r2_hidden @ A @ E )
& ( r2_hidden @ B @ F )
& ( r2_hidden @ C @ G )
& ( r2_hidden @ D @ H ) )
=> ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1148,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(6839,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).
thf(6141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(1644,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s6_domain_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_5_domain_1) ).
thf(9286,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s6_domain_1 @ C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C )
& ( p1_s6_domain_1 @ C ) )
=> ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).
thf(5732,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(440,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( a_2_0_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_domain_1) ).
thf(3553,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( a_2_0_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(7057,plain,
~ ( v1_xboole_0 @ sk376 ),
inference(cnf,[status(esa)],[7055]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(5293,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(8818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(726,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(4858,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(2470,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ A ) )
=> ( ~ ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ B ) )
=> ( ~ ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ C @ B )
& ( r2_hidden @ C @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ B ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ A ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_sysrel) ).
thf(7823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ A ) )
=> ( ~ ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ B ) )
=> ( ~ ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ C @ B )
& ( r2_hidden @ C @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ C @ B ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ A ) ) )
& ( ( ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
& ( r2_hidden @ D @ A ) )
=> ( ~ ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ D @ B )
& ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(7970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(882,axiom,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r1_ordinal1 @ ( k3_tarski @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal2) ).
thf(5574,plain,
! [A: $i] :
( ( v3_ordinal1 @ A )
=> ( r1_ordinal1 @ ( k3_tarski @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(317,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_partfun1) ).
thf(2980,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
<=> ~ ( ( r2_hidden @ A @ B )
<=> ( r2_hidden @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(8465,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
=> ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) ) )
& ( ~ ( ( ( r2_hidden @ A @ B )
=> ( r2_hidden @ A @ C ) )
& ( ( r2_hidden @ A @ C )
=> ( r2_hidden @ A @ B ) ) )
=> ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(1771,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_subset_1) ).
thf(10096,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(2655,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).
thf(9519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k5_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_pboole) ).
thf(7442,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setfam_1) ).
thf(6067,plain,
! [A: $i,B: $i] :
( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(3669,plain,
v1_relat_1 @ sk95,
inference(cnf,[status(esa)],[3667]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_2) ).
thf(4734,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
= ( k6_partfun1 @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ D )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(22641,plain,
$false,
inference(e,[status(thm)],[8536,1879,4729,6855,5205,2544,4904,5686,6085,6387,5561,4094,6167,7272,2889,9273,10166,2295,2306,2341,5857,4464,7854,4909,8154,7973,6231,7691,5260,6976,3399,1995,2263,6651,3167,8976,2876,6285,2463,8784,2787,7990,8843,8266,9907,6042,9965,6263,8475,5582,8077,8417,2309,7358,3509,9998,3498,9400,3680,4043,3534,7601,3185,1924,8129,2940,2104,6944,2231,6162,9351,2808,3905,6106,2644,3813,3230,5069,5644,7958,2908,6813,2527,3040,9045,5297,8682,8463,1939,2248,3108,4960,6323,2099,5224,5669,3402,5691,1793,8988,5383,9152,8045,6602,9818,5614,9364,9135,6732,1788,8963,2035,7556,4220,8490,5701,9000,8370,3562,6336,2042,3895,2195,4543,5425,5814,4234,9184,3745,4418,4739,3135,4097,8747,8353,3446,10138,5316,5257,4638,7345,8298,4856,4440,1988,9356,6804,8650,1954,9246,4980,6640,7220,5412,9774,3276,4941,6138,3103,10022,3777,8705,8546,2869,8848,3545,2491,6268,2548,5935,2227,8539,4266,5745,8133,6009,9994,1921,5770,4916,5903,7364,3281,3466,8165,3140,4030,7343,4607,8025,4963,1967,2819,4156,5269,4665,4322,1904,4610,7178,4467,5797,5342,1887,8603,2957,6707,4546,2603,9216,9464,8357,8647,7349,2501,4778,2682,1832,9938,7011,7386,9960,3820,5553,3248,10042,8610,4539,3442,3938,7279,7914,5306,1792,4563,1985,2039,9067,9410,8875,4151,8225,4654,1860,4334,8951,3148,8834,2274,6506,8787,3542,4275,4349,8146,2488,5712,1992,7000,5289,5836,6643,8753,2356,8907,3998,6396,8717,2373,7075,3470,2301,5076,8483,6734,8870,9629,7862,1892,3463,2857,4862,4353,6681,2169,6455,7209,9155,6626,9941,6599,3312,3657,4368,2520,5829,7560,9240,2158,8703,3835,7965,4793,4507,8252,4302,3866,7032,8161,7509,4253,7500,8293,3788,2007,3322,3524,2794,3199,4454,3670,4820,7775,6745,7677,8526,7317,5805,4556,8411,2178,2222,4696,5957,9204,4205,2237,2616,4396,4329,8379,2027,4578,9490,6670,2090,3393,5013,7300,3724,7104,3453,2451,1858,7845,5558,5946,3438,4147,8321,4815,3621,8659,2925,3973,1960,4798,3093,2335,8759,6157,2777,4783,7473,3712,5169,3226,5665,7460,8421,3389,2508,9875,8050,8438,8274,2437,3537,6648,5448,4935,2618,2833,9369,2190,7381,2483,6491,9743,8406,1796,3036,5246,5321,2137,9700,8691,3361,6700,4536,2242,9368,8554,3588,4379,4892,3559,6787,4628,7354,6210,6860,2982,2884,4483,7305,4853,4604,5406,3852,7217,3995,6307,2641,4925,6200,9026,1863,9472,10062,5961,2011,3591,7782,4407,2473,5751,4888,5839,7745,9221,9440,4480,7550,6047,2646,2364,2164,7859,6588,10197,9797,9209,5291,8613,7269,2093,9164,4370,6741,5540,2083,4100,2905,2382,2061,4172,2000,1900,5611,2541,5579,7834,3742,3239,4499,3514,7378,8513,2441,10099,9722,3827,8778,2428,9522,4016,2805,6550,6820,6247,5794,8756,4989,5044,2147,5266,7710,5719,3233,7084,9981,3884,9126,4284,9745,5507,8899,6178,3250,5594,3471,5924,6620,9455,8948,9539,7794,4187,5201,7934,4080,6090,7237,6303,8810,5826,9554,1837,5937,8672,8048,4192,3810,5465,9190,8700,8085,2477,9658,4725,3090,8386,8942,6427,4757,4947,3349,3556,4994,3297,7361,1951,3718,9758,4553,6972,4327,1787,9423,9132,10006,5658,3050,2344,3763,3727,2741,9080,9613,8287,4461,9868,3667,8136,3033,1910,4680,8403,3445,7095,5066,2359,1970,3218,6360,7923,8238,6728,6215,4808,6075,2245,1936,6656,5189,8694,3467,6748,9493,3615,6339,7329,7777,5053,5221,1851,8677,2377,6940,4668,2801,5238,1794,6995,2685,5423,4974,1804,6691,4248,2841,8223,8282,3381,6133,9444,8435,7838,8041,8619,5428,9936,3386,2726,9977,9525,4930,5919,6919,4012,5847,3650,3237,8572,8662,3941,2638,7874,9603,7468,5233,8916,2268,3440,6148,8138,5475,5951,8117,3087,4898,9530,8631,7774,1942,7453,3010,4513,2460,2798,7091,8544,5031,3143,6175,5694,9910,8017,3179,4983,10185,9397,8938,3407,2561,7111,5107,6661,9714,8743,9426,5620,3596,5786,5263,7604,2053,2240,8053,6630,5932,7930,4648,8968,5662,6978,9085,6501,2108,2551,7806,10163,2666,2649,4180,7821,5387,10094,7682,3573,9645,2536,2304,7463,3059,7508,7069,2497,8191,3703,2504,5576,5850,8458,3611,3486,8013,6331,4068,5380,10026,3770,8410,1974,6433,6207,9761,9739,6876,9201,9932,4829,2566,1799,4717,1947,8896,5683,7702,9620,8587,7261,6465,3409,3692,8576,8995,8425,3333,8307,10180,8144,8142,5026,4416,9694,6186,2140,4086,8980,3083,7174,4223,2370,3215,5479,5544,5153,4476,5571,5737,9213,8262,2338,8127,7193,8971,8174,3824,8846,8796,6409,3903,4184,2203,6533,9684,2546,4195,3624,6160,3279,4212,10011,9782,9176,8361,4966,3856,9008,7687,5833,6716,5415,8559,2076,2748,6070,6279,2408,5930,3190,7476,6982,6610,9793,5887,1895,9168,5198,8824,5909,3841,5295,9137,5249,6869,6950,9985,8708,9517,7817,7444,2909,4550,6524,1906,2936,4470,7512,5278,5230,5608,4503,7212,2376,3660,6922,4919,3130,6053,5722,2677,8903,2176,4872,9231,3358,2033,5762,2253,3871,6561,5969,5451,7225,7742,7155,3079,4412,4256,1927,3985,5048,8480,7491,3289,3738,7257,5095,7920,6546,3274,7785,7118,8311,8807,8495,4662,8909,3768,2791,2789,5844,4801,5831,5050,1965,9952,2959,4786,7611,9418,4000,3187,6916,2938,8762,1884,6617,4494,4077,2188,9996,2393,8711,7440,3081,4677,2514,6229,4032,8697,7041,3900,6898,5097,3458,1795,8581,7963,8993,4612,2817,10127,5799,9820,6774,2827,7815,7622,7038,6357,8359,3532,8064,3223,2161,4251,4526,8318,5567,10034,9125,6385,2326,2293,6937,6667,10183,7534,8629,7689,5859,3695,8862,9687,2738,4149,8877,8665,3663,3340,5086,1997,10130,3123,3783,7347,5703,7465,3700,9496,3832,2166,3619,2457,8212,1897,7658,2557,5735,2425,6372,8202,3568,7394,7021,7865,2573,9307,8376,8301,6016,3170,6261,9248,5634,6281,7158,6144,8408,4228,9349,8715,7077,1933,10000,8269,6604,9243,2079,4790,9623,4337,6059,6572,7519,7130,3815,3038,2422,2774,6217,6815,3683,2906,6197,4699,8120,5631,7438,8688,3468,5880,3106,7282,8313,2669,8986,1801,6289,6154,3500,2378,4374,5972,7502,5616,2871,8926,6460,7307,2025,4541,3073,6044,2278,2974,8413,5780,5563,2824,4635,7504,9206,4401,5584,9129,6165,8826,4009,3055,4103,5730,3668,2625,5894,9655,5175,9642,6710,8983,2780,4731,4028,5599,5286,8750,2446,2757,7928,7978,4332,9756,8974,3977,2923,5392,7141,2874,8998,4296,7869,7675,2928,7066,3110,6738,10208,9371,9011,5817,2867,3539,9873,5057,1841,4232,2350,8131,2401,8456,6687,6449,5216,3759,3838,7479,2835,8776,5377,6907,9450,2481,5218,6930,6394,9294,5641,9975,10076,3917,9841,6504,7911,2931,5042,9197,2288,2633,3310,3706,7200,6180,3512,9921,6614,8291,5089,5326,4890,7356,9150,8990,3908,6212,2693,6785,9582,6672,2234,3146,2449,3048,9276,4722,8180,9054,6858,9097,3444,5688,8954,4907,6320,5538,6890,5587,1809,8965,7788,2614,2096,5890,3193,4901,7896,4458,4868,4813,7975,2271,9069,4456,2652,7298,9884,8804,6088,7539,6056,7992,7190,7420,7122,3455,5916,2846,6564,6806,2256,3278,2597,2899,6664,10016,6719,5003,4986,4168,2582,7087,4490,2661,2375,4922,5074,7554,7045,4287,4894,4971,5079,6012,4045,1845,6362,7615,9631,1798,2298,3391,6120,2863,8772,7635,4035,6453,2397,9847,7058,6266,7801,2192,4673,8218,10059,2588,9037,9467,4641,8295,2850,7756,7811,4593,7055,5790,7832,7228,2831,6146,3448,5767,4398,2688,2920,2700,8873,7243,5555,9666,3412,3174,4409,7388,8498,4561,5418,2224,2454,3305,4190,3818,5912,8669,3344,5753,7667,1785,10211,9567,8216,5948,6513,9809,9358,7947,7543,9815,6508,8509,6125,1980,6966,5309,3127,8327,7351,6313,5638,9963,7009,5062,3493,6333,7797,10028,2860,9747,4516,2675,8679,2056,8893,5208,2948,9194,3697,2411,3488,2838,5628,5347,4624,4246,3356,5240,6369,4510,4748,2320,7391,4991,8061,4932,7374,8185,9930,9983,4202,2511,5226,2728,2030,4225,4342,5472,8433,8151,5596,7488,8140,9453,6992,5841,4414,6420,6220,4392,4217,7234,10018,1918,3565,9527,2696,5536,2347,6980,3320,3665,8830,3284,6928,7552,2013,4548,7659,4289,1839,5873,7146,9192,2479,4851,7024,4325,2045,8028,1949,4165,5660,4944,1834,1913,8260,5966,3447,4997,5510,8183,8533,4559,5421,4780,2743,10188,8228,5389,1866,2071,2658,8579,1807,5184,2907,2443,3729,2594,9014,6341,5191,5351,6790,7114,3780,3465,2591,6903,3613,5724,7872,2283,6818,7653,2855,6607,8780,2853,5272,2290,4615,2406,7344,4089,6893,2554,4683,3383,8584,8197,2811,9343,6913,2971,6910,8634,5010,7384,7120,3859,3252,5505,9179,8240,2152,4451,5922,2081,2399,2680,7530,5672,2494,9542,4745,2944,4182,8865,6516,8172,2475,4602,4197,3324,6305,8272,5164,4293,4175,4153,4214,3585,6118,9434,7312,5109,7747,5023,2330,5409,2198,9537,2576,2066,5699,6521,3677,6062,8399,4404,6536,2902,5211,4074,9211,6569,9311,9887,7804,3761,6462,5194,4927,7152,4619,2258,8324,2155,7744,3464,3521,2736,3337,10073,3992,2003,6703,2374,9812,7081,9551,2517,9166,5728,8070,4014,1957,6957,5606,6693,9229,4356,8478,3733,4811,7231,4596,3892,5954,7259,7836,4719,6050,2951,7029,4523,5477,3132,2050,9051,6150,9944,6226,3203,6366,3062,8933,6782,7955,8801,3469,3015,8653,9134,8516,2366,7932,8616,2636,2751,8790,4178,7851,3897,4565,4755,5092,8207,4281,3347,6114,8737,8373,4210,4007,2746,4083,4024,6380,2404,3196,5251,4865,3030,4442,7808,4912,6612,3045,9083,9564,3673,2021,2063,6309,9987,2783,5324,5275,8675,2731,4242,9023,4066,5280,5060,5623,4659,8773,4019,7246,7214,4848,9235,1829,1977,2966,2430,7987,2600,3570,2485,6697,2467,6383,9504,4239,4831,7708,3886,7780,5236,7791,8548,10323,5468,2539,3076,4071,1902,6778,4691,6548,4501,9600,8918,7563,8857,6658,4533,5155,6173,10013,2690,2018,5788,3052,9087,6948,8685,7900,9870,5172,3528,2754,2672,2879,3461,5591,1944,4702,8940,1962,7181,7848,3299,6842,5458,2206,5618,7310,2887,3405,9267,4752,4742,5255,9611,4977,3316,6632,6839,6141,9286,5732,3553,7057,5293,8818,4858,2470,7823,7970,5574,8628,2980,8465,10096,2655,9519,7442,6067,3669,4734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU430+2 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:37:12 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.89/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.70/1.35 % [INFO] Parsing done (473ms).
% 2.70/1.36 % [INFO] Running in sequential loop mode.
% 3.25/1.58 % [INFO] eprover registered as external prover.
% 3.25/1.58 % [INFO] cvc4 registered as external prover.
% 3.25/1.58 % [INFO] Scanning for conjecture ...
% 4.25/1.91 % [INFO] Found a conjecture and 4501 axioms. Running axiom selection ...
% 6.23/2.84 % [INFO] Axiom selection finished. Selected 1782 axioms (removed 2719 axioms).
% 8.80/3.65 % [INFO] Problem is first-order (TPTP FOF).
% 9.06/3.69 % [INFO] Type checking passed.
% 9.06/3.69 % [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 ...
% 95.14/22.01 % External prover 'e' found a proof!
% 95.14/22.01 % [INFO] Killing All external provers ...
% 95.14/22.01 % Time passed: 21493ms (effective reasoning time: 20642ms)
% 95.14/22.01 % 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)>
% 95.14/22.02 % 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
% 95.14/22.02 % No. of inferences in proof: 3611
% 95.14/22.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21493 ms resp. 20642 ms w/o parsing
% 97.61/23.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 97.61/23.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------