TSTP Solution File: GRP642+2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : GRP642+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 : Tue May 7 07:44:56 EDT 2024
% Result : Theorem 40.95s 12.57s
% Output : Refutation 43.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2104
% Syntax : Number of formulae : 3911 ( 261 unt; 299 typ; 0 def)
% Number of atoms : 23188 (3312 equ; 0 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 79183 (2856 ~; 165 |;10637 &;56751 @)
% ( 345 <=>;8429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 640 ( 640 >; 0 *; 0 +; 0 <<)
% Number of symbols : 301 ( 299 usr; 15 con; 0-9 aty)
% Number of variables : 10515 ( 0 ^10058 !; 457 ?;10515 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v3_group_1_type,type,
v3_group_1: $i > $o ).
thf(v4_group_1_type,type,
v4_group_1: $i > $o ).
thf(l1_group_1_type,type,
l1_group_1: $i > $o ).
thf(v1_group_1_type,type,
v1_group_1: $i > $o ).
thf(m1_group_2_type,type,
m1_group_2: $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k1_latsubgr_type,type,
k1_latsubgr: $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_funct_4_type,type,
k1_funct_4: $i > $i > $i ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(r6_binop_1_type,type,
r6_binop_1: $i > $i > $i > $o ).
thf(r4_binop_1_type,type,
r4_binop_1: $i > $i > $i > $o ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k4_finseq_1_type,type,
k4_finseq_1: $i > $i ).
thf(k11_finseq_1_type,type,
k11_finseq_1: $i > $i > $i > $i ).
thf(k2_finseq_1_type,type,
k2_finseq_1: $i > $i ).
thf(np__3_type,type,
np__3: $i ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(r1_binop_1_type,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k10_finseq_1_type,type,
k10_finseq_1: $i > $i > $i ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(v4_ordinal2_type,type,
v4_ordinal2: $i > $o ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k1_numbers_type,type,
k1_numbers: $i ).
thf(k5_numbers_type,type,
k5_numbers: $i ).
thf(r1_xreal_0_type,type,
r1_xreal_0: $i > $i > $o ).
thf(k14_finseq_1_type,type,
k14_finseq_1: $i > $i ).
thf(k8_finseq_1_type,type,
k8_finseq_1: $i > $i > $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(m2_finseq_1_type,type,
m2_finseq_1: $i > $i > $o ).
thf(k3_finseq_1_type,type,
k3_finseq_1: $i > $i ).
thf(k16_finseq_1_type,type,
k16_finseq_1: $i > $i > $i > $i ).
thf(k1_card_1_type,type,
k1_card_1: $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(m1_finseq_1_type,type,
m1_finseq_1: $i > $i > $o ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(m3_realset1_type,type,
m3_realset1: $i > $i > $i > $o ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(np__2_type,type,
np__2: $i ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(l1_rlvect_1_type,type,
l1_rlvect_1: $i > $o ).
thf(l2_struct_0_type,type,
l2_struct_0: $i > $o ).
thf(r3_binop_1_type,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k4_relset_1_type,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k4_card_1_type,type,
k4_card_1: $i > $i ).
thf(k4_funct_4_type,type,
k4_funct_4: $i > $i > $i > $i > $i ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k3_realset1_type,type,
k3_realset1: $i > $i > $i > $i ).
thf(k1_group_4_type,type,
k1_group_4: $i > $i > $i > $i ).
thf(r2_wellord2_type,type,
r2_wellord2: $i > $i > $o ).
thf(np__1_type,type,
np__1: $i ).
thf(k12_finseq_1_type,type,
k12_finseq_1: $i > $i > $i ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k2_xcmplx_0_type,type,
k2_xcmplx_0: $i > $i > $i ).
thf(np__0_type,type,
np__0: $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v7_group_1_type,type,
v7_group_1: $i > $o ).
thf(k3_group_4_type,type,
k3_group_4: $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(r1_setfam_1_type,type,
r1_setfam_1: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(k1_real_1_type,type,
k1_real_1: $i > $i ).
thf(k7_group_2_type,type,
k7_group_2: $i > $i > $i ).
thf(r1_rlvect_1_type,type,
r1_rlvect_1: $i > $i > $o ).
thf(l1_vectsp_1_type,type,
l1_vectsp_1: $i > $o ).
thf(v2_group_1_type,type,
v2_group_1: $i > $o ).
thf(v6_vectsp_1_type,type,
v6_vectsp_1: $i > $o ).
thf(v8_vectsp_1_type,type,
v8_vectsp_1: $i > $o ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(k8_relset_1_type,type,
k8_relset_1: $i > $i > $i > $i > $i ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k9_relset_1_type,type,
k9_relset_1: $i > $i > $i > $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v4_finsub_1_type,type,
v4_finsub_1: $i > $o ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k4_group_4_type,type,
k4_group_4: $i > $i > $i > $i ).
thf(k1_finsop_1_type,type,
k1_finsop_1: $i > $i > $i > $i ).
thf(k4_numbers_type,type,
k4_numbers: $i ).
thf(k2_group_4_type,type,
k2_group_4: $i > $i ).
thf(k5_group_1_type,type,
k5_group_1: $i > $i ).
thf(k2_group_1_type,type,
k2_group_1: $i > $i ).
thf(k1_nat_1_type,type,
k1_nat_1: $i > $i > $i ).
thf(k1_group_1_type,type,
k1_group_1: $i > $i > $i > $i ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(k4_finseq_4_type,type,
k4_finseq_4: $i > $i > $i > $i > $i ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(v1_group_6_type,type,
v1_group_6: $i > $i > $i > $o ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(k9_group_6_type,type,
k9_group_6: $i > $i > $i > $i ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(v6_ordinal1_type,type,
v6_ordinal1: $i > $o ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(g4_vectsp_1_type,type,
g4_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(m1_orders_1_type,type,
m1_orders_1: $i > $i > $o ).
thf(k7_domain_1_type,type,
k7_domain_1: $i > $i > $i > $i ).
thf(k3_xcmplx_0_type,type,
k3_xcmplx_0: $i > $i > $i ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(k6_finseq_1_type,type,
k6_finseq_1: $i > $i ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k3_binop_1_type,type,
k3_binop_1: $i > $i > $i ).
thf(k5_group_4_type,type,
k5_group_4: $i > $i > $i ).
thf(k6_group_1_type,type,
k6_group_1: $i > $i > $i > $i ).
thf(k1_int_2_type,type,
k1_int_2: $i > $i ).
thf(k3_group_1_type,type,
k3_group_1: $i > $i > $i ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(v2_group_6_type,type,
v2_group_6: $i > $i > $i > $o ).
thf(k6_xcmplx_0_type,type,
k6_xcmplx_0: $i > $i > $i ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(k2_card_1_type,type,
k2_card_1: $i > $i ).
thf(v4_group_6_type,type,
v4_group_6: $i > $i > $i > $o ).
thf(k13_group_6_type,type,
k13_group_6: $i > $i > $i > $i ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k7_rlvect_1_type,type,
k7_rlvect_1: $i > $i > $i > $i ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k8_group_4_type,type,
k8_group_4: $i > $i > $i > $i ).
thf(k2_realset1_type,type,
k2_realset1: $i > $i > $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(v1_card_1_type,type,
v1_card_1: $i > $o ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k8_rlvect_1_type,type,
k8_rlvect_1: $i > $i > $i > $i > $i ).
thf(k2_vectsp_1_type,type,
k2_vectsp_1: $i > $i ).
thf(u1_vectsp_1_type,type,
u1_vectsp_1: $i > $i ).
thf(k2_finsop_1_type,type,
k2_finsop_1: $i > $i > $i > $i ).
thf(u1_group_1_type,type,
u1_group_1: $i > $i ).
thf(k8_group_6_type,type,
k8_group_6: $i > $i > $i > $i > $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k6_domain_1_type,type,
k6_domain_1: $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(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(k10_group_1_type,type,
k10_group_1: $i > $i > $i > $i ).
thf(k2_group_2_type,type,
k2_group_2: $i > $i > $i > $i ).
thf(k3_group_3_type,type,
k3_group_3: $i > $i > $i > $i ).
thf(k4_group_3_type,type,
k4_group_3: $i > $i > $i > $i ).
thf(k3_group_2_type,type,
k3_group_2: $i > $i > $i > $i ).
thf(k13_group_2_type,type,
k13_group_2: $i > $i > $i > $i ).
thf(r4_group_3_type,type,
r4_group_3: $i > $i > $i > $o ).
thf(r3_group_3_type,type,
r3_group_3: $i > $i > $i > $o ).
thf(k8_group_1_type,type,
k8_group_1: $i > $i ).
thf(k12_group_2_type,type,
k12_group_2: $i > $i > $i > $i ).
thf(r1_group_3_type,type,
r1_group_3: $i > $i > $i > $o ).
thf(k2_group_3_type,type,
k2_group_3: $i > $i > $i > $i ).
thf(k10_group_2_type,type,
k10_group_2: $i > $i > $i > $i ).
thf(k4_group_2_type,type,
k4_group_2: $i > $i > $i > $i ).
thf(k11_group_2_type,type,
k11_group_2: $i > $i > $i > $i ).
thf(k7_group_3_type,type,
k7_group_3: $i > $i > $i ).
thf(a_2_0_group_3_type,type,
a_2_0_group_3: $i > $i > $i ).
thf(r2_group_3_type,type,
r2_group_3: $i > $i > $i > $o ).
thf(k1_group_2_type,type,
k1_group_2: $i > $i > $i ).
thf(k14_group_2_type,type,
k14_group_2: $i > $i > $i ).
thf(k6_group_2_type,type,
k6_group_2: $i > $i ).
thf(k15_group_2_type,type,
k15_group_2: $i > $i > $i ).
thf(k7_group_1_type,type,
k7_group_1: $i > $i > $i ).
thf(k8_group_3_type,type,
k8_group_3: $i > $i > $i ).
thf(k5_group_3_type,type,
k5_group_3: $i > $i > $i > $i ).
thf(m1_group_6_type,type,
m1_group_6: $i > $i > $i > $o ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(v1_group_3_type,type,
v1_group_3: $i > $i > $o ).
thf(k4_group_6_type,type,
k4_group_6: $i > $i > $i ).
thf(k9_group_1_type,type,
k9_group_1: $i > $i ).
thf(k7_group_4_type,type,
k7_group_4: $i > $i > $i > $i ).
thf(k5_group_6_type,type,
k5_group_6: $i > $i > $i ).
thf(k18_group_2_type,type,
k18_group_2: $i > $i > $i ).
thf(k6_group_3_type,type,
k6_group_3: $i > $i > $i > $i ).
thf(a_3_0_group_2_type,type,
a_3_0_group_2: $i > $i > $i > $i ).
thf(v3_group_6_type,type,
v3_group_6: $i > $i > $i > $o ).
thf(k17_group_2_type,type,
k17_group_2: $i > $i > $i ).
thf(k7_binop_2_type,type,
k7_binop_2: $i > $i ).
thf(k3_finsub_1_type,type,
k3_finsub_1: $i > $i > $i > $i ).
thf(v1_setwiseo_type,type,
v1_setwiseo: $i > $i > $o ).
thf(k9_group_4_type,type,
k9_group_4: $i > $i ).
thf(k1_group_3_type,type,
k1_group_3: $i > $i ).
thf(k5_funct_4_type,type,
k5_funct_4: $i > $i > $i > $i > $i > $i ).
thf(k6_group_6_type,type,
k6_group_6: $i > $i > $i ).
thf(k12_group_6_type,type,
k12_group_6: $i > $i > $i > $i ).
thf(k11_group_6_type,type,
k11_group_6: $i > $i > $i ).
thf(r1_nat_1_type,type,
r1_nat_1: $i > $i > $o ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k9_group_2_type,type,
k9_group_2: $i > $i > $i > $i ).
thf(r1_group_2_type,type,
r1_group_2: $i > $i > $i > $o ).
thf(k10_group_4_type,type,
k10_group_4: $i > $i ).
thf(k1_group_6_type,type,
k1_group_6: $i > $i > $i > $i ).
thf(k7_group_6_type,type,
k7_group_6: $i > $i > $i > $i ).
thf(v2_group_4_type,type,
v2_group_4: $i > $i > $o ).
thf(a_2_2_group_3_type,type,
a_2_2_group_3: $i > $i > $i ).
thf(k10_group_3_type,type,
k10_group_3: $i > $i > $i ).
thf(k6_group_4_type,type,
k6_group_4: $i > $i ).
thf(a_1_0_group_4_type,type,
a_1_0_group_4: $i > $i ).
thf(k33_binop_2_type,type,
k33_binop_2: $i ).
thf(k8_group_2_type,type,
k8_group_2: $i > $i > $i > $i ).
thf(a_2_1_group_3_type,type,
a_2_1_group_3: $i > $i > $i ).
thf(a_1_0_finseq_1_type,type,
a_1_0_finseq_1: $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
thf(v1_group_4_type,type,
v1_group_4: $i > $i > $o ).
thf(k9_group_3_type,type,
k9_group_3: $i > $i > $i ).
thf(k11_group_3_type,type,
k11_group_3: $i > $i > $i ).
thf(p1_s2_card_1_type,type,
p1_s2_card_1: $i > $o ).
thf(k2_nat_1_type,type,
k2_nat_1: $i > $i > $i ).
thf(k16_group_2_type,type,
k16_group_2: $i > $i > $i ).
thf(k5_group_2_type,type,
k5_group_2: $i > $i ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $i > $i ).
thf(k9_domain_1_type,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(r5_group_3_type,type,
r5_group_3: $i > $i > $i > $o ).
thf(k2_finseq_4_type,type,
k2_finseq_4: $i > $i > $i > $i ).
thf(v5_group_1_type,type,
v5_group_1: $i > $i > $o ).
thf(k4_group_1_type,type,
k4_group_1: $i > $i ).
thf(a_2_0_group_2_type,type,
a_2_0_group_2: $i > $i > $i ).
thf(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(k3_finseq_4_type,type,
k3_finseq_4: $i > $i > $i > $i > $i ).
thf(a_2_0_group_4_type,type,
a_2_0_group_4: $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k10_group_6_type,type,
k10_group_6: $i > $i > $i ).
thf(a_1_0_group_2_type,type,
a_1_0_group_2: $i > $i ).
thf(p1_s1_int_1_type,type,
p1_s1_int_1: $i > $o ).
thf(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(a_1_0_group_6_type,type,
a_1_0_group_6: $i > $i ).
thf(k2_group_5_type,type,
k2_group_5: $i > $i > $i > $i ).
thf(k11_group_4_type,type,
k11_group_4: $i > $i ).
thf(a_3_0_group_6_type,type,
a_3_0_group_6: $i > $i > $i > $i ).
thf(a_3_0_group_3_type,type,
a_3_0_group_3: $i > $i > $i > $i ).
thf(a_1_1_domain_1_type,type,
a_1_1_domain_1: $i > $i ).
thf(m1_ordinal1_type,type,
m1_ordinal1: $i > $i > $o ).
thf(k3_group_5_type,type,
k3_group_5: $i > $i > $i > $i > $i ).
thf(r1_group_6_type,type,
r1_group_6: $i > $i > $o ).
thf(u2_struct_0_type,type,
u2_struct_0: $i > $i ).
thf(r2_group_6_type,type,
r2_group_6: $i > $i > $o ).
thf(k3_latsubgr_type,type,
k3_latsubgr: $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $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(k13_domain_1_type,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(a_2_3_group_3_type,type,
a_2_3_group_3: $i > $i > $i ).
thf(k4_xcmplx_0_type,type,
k4_xcmplx_0: $i > $i ).
thf(r1_ordinal1_type,type,
r1_ordinal1: $i > $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
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(f1_s2_group_4_type,type,
f1_s2_group_4: $i ).
thf(p1_s2_group_4_type,type,
p1_s2_group_4: $i > $o ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(k9_group_5_type,type,
k9_group_5: $i > $i ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(k2_group_6_type,type,
k2_group_6: $i > $i > $i > $i ).
thf(k6_finseqop_type,type,
k6_finseqop: $i > $i > $i ).
thf(k2_latsubgr_type,type,
k2_latsubgr: $i > $i > $i ).
thf(r1_finseqop_type,type,
r1_finseqop: $i > $i > $i > $o ).
thf(r6_group_3_type,type,
r6_group_3: $i > $i > $i > $o ).
thf(a_1_1_group_4_type,type,
a_1_1_group_4: $i > $i ).
thf(k3_group_6_type,type,
k3_group_6: $i > $i > $i > $i ).
thf(v1_finseqop_type,type,
v1_finseqop: $i > $i > $o ).
thf(546,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(4201,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)],[546]) ).
thf(810,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k3_group_1 @ B @ C ) )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_1) ).
thf(5365,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k3_group_1 @ B @ C ) )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(6,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(1823,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)],[6]) ).
thf(109,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(2263,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)],[109]) ).
thf(424,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(3666,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1594,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_vectsp_1) ).
thf(8976,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(138,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(2427,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)],[138]) ).
thf(765,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(5205,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(479,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(3927,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)],[479]) ).
thf(1266,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_finseq_1) ).
thf(7549,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(105,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(2250,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)],[105]) ).
thf(814,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( r1_xreal_0 @ A @ B )
=> ( r2_hidden @ ( k6_xcmplx_0 @ B @ A ) @ k5_numbers ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_int_1) ).
thf(5385,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( r1_xreal_0 @ A @ B )
=> ( r2_hidden @ ( k6_xcmplx_0 @ B @ A ) @ k5_numbers ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1237,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(7375,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)],[1237]) ).
thf(95,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(2199,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)],[95]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k10_finseq_1 @ A @ B )
!= ( k11_finseq_1 @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_finseq_3) ).
thf(6085,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( k10_finseq_1 @ A @ B )
!= ( k11_finseq_1 @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(544,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(4188,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)],[544]) ).
thf(598,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(4447,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)],[598]) ).
thf(489,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(3962,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)],[489]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_group_6 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k1_group_1 @ A @ D @ E ) )
= ( k1_group_1 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_group_6) ).
thf(5422,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v1_group_6 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k1_group_1 @ A @ D @ E ) )
= ( k1_group_1 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k1_group_1 @ A @ D @ E ) )
= ( k1_group_1 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) )
=> ( v1_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(474,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(3883,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1735,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_group_3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_group_3) ).
thf(9458,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_group_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(114,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(2295,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)],[114]) ).
thf(1791,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_group_4) ).
thf(9653,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(501,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(4005,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)],[501]) ).
thf(1620,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k12_group_6 @ A @ B @ ( k10_group_6 @ A @ B ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_6) ).
thf(9077,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k12_group_6 @ A @ B @ ( k10_group_6 @ A @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(278,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(3008,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)],[278]) ).
thf(69,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(2109,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)],[69]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
& ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
& ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(49,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(2031,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)],[49]) ).
thf(785,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(5260,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)],[785]) ).
thf(1152,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k4_group_1 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k3_group_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_group_1) ).
thf(6976,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k4_group_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k3_group_1 @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k3_group_1 @ A @ C ) ) )
=> ( B
= ( k4_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1244,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k8_group_3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_group_3) ).
thf(7445,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k8_group_3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(322,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(3167,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)],[322]) ).
thf(1340,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k3_group_3 @ A @ C @ D ) @ B )
= ( k3_group_3 @ A @ C @ ( k4_group_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_3) ).
thf(7922,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k3_group_3 @ A @ C @ D ) @ B )
= ( k3_group_3 @ A @ C @ ( k4_group_2 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1469,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(8514,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)],[1469]) ).
thf(251,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(2921,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)],[251]) ).
thf(432,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(3698,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)],[432]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k4_funct_4 @ A @ B @ C @ D )
= ( k4_funct_4 @ A @ B @ E @ F ) )
=> ( ( A = B )
| ( ( C = E )
& ( D = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_4) ).
thf(5390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( k4_funct_4 @ A @ B @ C @ D )
= ( k4_funct_4 @ A @ B @ E @ F ) )
=> ( ( A = B )
| ( ( C = E )
& ( D = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1316,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ E @ A @ B )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( k2_group_5 @ A @ C @ D ) )
= ( k2_group_5 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_group_6) ).
thf(7798,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ E @ A @ B )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( k2_group_5 @ A @ C @ D ) )
= ( k2_group_5 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(416,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3581,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1185,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(7143,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)],[1185]) ).
thf(878,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(5654,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)],[878]) ).
thf(159,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(2499,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)],[159]) ).
thf(171,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(2544,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)],[171]) ).
thf(1063,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(6448,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)],[1063]) ).
thf(1720,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r2_hidden @ ( k6_group_3 @ A @ C @ B ) @ ( k9_group_3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_group_3) ).
thf(9411,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r2_hidden @ ( k6_group_3 @ A @ C @ B ) @ ( k9_group_3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(972,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(6042,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1569,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r1_finseqop @ ( u1_struct_0 @ A ) @ ( k4_group_1 @ A ) @ ( u1_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_group_1) ).
thf(8887,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r1_finseqop @ ( u1_struct_0 @ A ) @ ( k4_group_1 @ A ) @ ( u1_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(1084,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(6566,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)],[1084]) ).
thf(1531,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k16_group_2 @ A @ C )
= ( k16_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_group_3) ).
thf(8755,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k16_group_2 @ A @ C )
= ( k16_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(4,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(1818,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)],[4]) ).
thf(1077,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(6527,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)],[1077]) ).
thf(727,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_vectsp_1) ).
thf(4992,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1377,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(8077,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)],[1377]) ).
thf(1663,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r1_group_6 @ A @ B )
& ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_group_6) ).
thf(9241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r1_group_6 @ A @ B )
& ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(428,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3681,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1390,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k7_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k7_group_3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_group_3) ).
thf(8129,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k7_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k7_group_3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(185,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(2590,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)],[185]) ).
thf(279,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(3012,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)],[279]) ).
thf(71,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(2114,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)],[71]) ).
thf(1600,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_group_4) ).
thf(9003,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(1696,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k15_group_2 @ A @ B )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_group_2) ).
thf(9342,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k15_group_2 @ A @ B )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(936,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(5898,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( r1_xreal_0 @ np__1 @ ( k9_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_group_1) ).
thf(5454,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( r1_xreal_0 @ np__1 @ ( k9_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(976,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(6057,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)],[976]) ).
thf(1344,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ B @ C )
= ( a_3_0_group_3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_3) ).
thf(7935,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ B @ C )
= ( a_3_0_group_3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(68,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 )
<=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_4) ).
thf(2104,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 )
=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) )
& ( ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1169,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
<=> ~ ( r1_xreal_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_card_1) ).
thf(7083,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
=> ~ ( r1_xreal_0 @ B @ A ) )
& ( ~ ( r1_xreal_0 @ B @ A )
=> ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1521,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k6_group_2 @ A ) @ B ) @ ( k6_group_2 @ A ) )
& ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ ( k6_group_2 @ A ) ) @ ( k6_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_group_4) ).
thf(8723,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k6_group_2 @ A ) @ B ) @ ( k6_group_2 @ A ) )
& ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ ( k6_group_2 @ A ) ) @ ( k6_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(1370,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k2_group_1 @ A ) @ B )
= ( k2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_group_3) ).
thf(8044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k2_group_1 @ A ) @ B )
= ( k2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(755,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(5168,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)],[755]) ).
thf(1705,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k9_group_3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_group_3) ).
thf(9373,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k9_group_3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(470,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(3858,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ k1_xboole_0 ) @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(4311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(444,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_finseq_1) ).
thf(3762,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(459,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(3813,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)],[459]) ).
thf(1378,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= D )
<=> ( C
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_group_1) ).
thf(8082,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= D )
=> ( C
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ D ) ) )
& ( ( C
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ D ) )
=> ( ( k1_group_1 @ A @ B @ C )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1288,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ k4_numbers )
=> ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k7_group_2 @ A @ B ) )
=> ( r1_rlvect_1 @ B @ ( k3_group_4 @ A @ ( k4_group_4 @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_group_4) ).
thf(7641,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ k4_numbers )
=> ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k7_group_2 @ A @ B ) )
=> ( r1_rlvect_1 @ B @ ( k3_group_4 @ A @ ( k4_group_4 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1350,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ B ) )
=> ( ( r1_rlvect_1 @ ( k11_group_3 @ B @ C ) @ A )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r1_group_2 @ B @ ( k6_group_3 @ B @ C @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_group_3) ).
thf(7958,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ B ) )
=> ( ( ( r1_rlvect_1 @ ( k11_group_3 @ B @ C ) @ A )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r1_group_2 @ B @ ( k6_group_3 @ B @ C @ D ) @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r1_group_2 @ B @ ( k6_group_3 @ B @ C @ D ) @ C ) )
=> ( r1_rlvect_1 @ ( k11_group_3 @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(246,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_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_4) ).
thf(2908,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_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(412,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(3549,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(403,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(3509,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)],[403]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r4_group_3 @ A @ B @ C )
<=> ( r3_group_3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r4_group_3) ).
thf(5242,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r4_group_3 @ A @ B @ C )
=> ( r3_group_3 @ A @ B @ C ) )
& ( ( r3_group_3 @ A @ B @ C )
=> ( r4_group_3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_3_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_group_3) ).
thf(8402,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) )
=> ( r2_hidden @ A @ ( a_2_3_group_3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(583,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(4391,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)],[583]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( 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(3153,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)],[317]) ).
thf(260,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(2947,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)],[260]) ).
thf(104,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(2248,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)],[104]) ).
thf(30,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(1939,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)],[30]) ).
thf(488,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k4_card_1 @ A )
= ( k1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_card_1) ).
thf(3959,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k4_card_1 @ A )
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
& ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_4) ).
thf(2676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
& ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(910,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ A @ C )
= ( k2_group_1 @ B ) )
=> ( r1_nat_1 @ ( k7_group_1 @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_group_1) ).
thf(5793,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ A @ C )
= ( k2_group_1 @ B ) )
=> ( r1_nat_1 @ ( k7_group_1 @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_2) ).
thf(9337,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(306,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(3108,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)],[306]) ).
thf(66,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(2099,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)],[66]) ).
thf(772,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(5224,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)],[772]) ).
thf(1227,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(7332,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)],[1227]) ).
thf(36,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(1971,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)],[36]) ).
thf(777,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(5237,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)],[777]) ).
thf(1581,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k6_group_6 @ A @ B )
= ( g1_group_1 @ ( k4_group_6 @ A @ B ) @ ( k5_group_6 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_6) ).
thf(8928,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k6_group_6 @ A @ B )
= ( g1_group_1 @ ( k4_group_6 @ A @ B ) @ ( k5_group_6 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k18_group_2 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_group_2) ).
thf(5529,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k18_group_2 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1229,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( v1_funct_1 @ ( k10_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k10_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ ( k10_group_6 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k10_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_group_6) ).
thf(7341,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( v1_funct_1 @ ( k10_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k10_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ ( k10_group_6 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k10_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1202,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( C
= ( k17_group_2 @ A @ B ) )
<=> ? [D: $i] :
( ( v1_finset_1 @ D )
& ( D
= ( k14_group_2 @ A @ B ) )
& ( C
= ( k4_card_1 @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_group_2) ).
thf(7208,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( C
= ( k17_group_2 @ A @ B ) )
=> ? [D: $i] :
( ( v1_finset_1 @ D )
& ( D
= ( k14_group_2 @ A @ B ) )
& ( C
= ( k4_card_1 @ D ) ) ) )
& ( ? [D: $i] :
( ( v1_finset_1 @ D )
& ( D
= ( k14_group_2 @ A @ B ) )
& ( C
= ( k4_card_1 @ D ) ) )
=> ( C
= ( k17_group_2 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1639,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_group_1 @ ( k11_group_3 @ A @ B ) )
& ( m1_group_2 @ ( k11_group_3 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_group_3) ).
thf(9135,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_group_1 @ ( k11_group_3 @ A @ B ) )
& ( m1_group_2 @ ( k11_group_3 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(636,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v4_finsub_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v4_finsub_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finsub_1) ).
thf(4592,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v4_finsub_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v4_finsub_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(624,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4532,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1320,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( r2_group_6 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_group_6) ).
thf(7813,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( r2_group_6 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(809,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(5361,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)],[809]) ).
thf(1493,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(8635,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)],[1493]) ).
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 ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(3367,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)],[365]) ).
thf(482,axiom,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(3942,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(513,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(4058,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)],[513]) ).
thf(40,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(1988,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)],[40]) ).
thf(53,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(2042,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)],[53]) ).
thf(78,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(2146,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)],[78]) ).
thf(93,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(2195,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)],[93]) ).
thf(1314,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(7793,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)],[1314]) ).
thf(466,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_group_6 @ C @ A @ B )
<=> ( v2_funct_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_group_6) ).
thf(3848,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v2_group_6 @ C @ A @ B )
=> ( v2_funct_1 @ C ) )
& ( ( v2_funct_1 @ C )
=> ( v2_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1052,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_funct_1 @ ( u1_group_1 @ A ) )
& ( v1_funct_2 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_group_1) ).
thf(6391,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_funct_1 @ ( u1_group_1 @ A ) )
& ( v1_funct_2 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1383,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(8101,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)],[1383]) ).
thf(1478,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k15_group_2 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k13_group_2 @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_group_2) ).
thf(8551,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( C
= ( k15_group_2 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k13_group_2 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k13_group_2 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k13_group_2 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k13_group_2 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k15_group_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(1435,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_rlvect_1 @ ( k10_group_3 @ B @ C ) @ A )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_group_3) ).
thf(8335,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_rlvect_1 @ ( k10_group_3 @ B @ C ) @ A )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( ( k4_group_3 @ B @ C @ D )
= C ) )
=> ( r1_rlvect_1 @ ( k10_group_3 @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(1736,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ C )
=> ( ( ( v6_group_1 @ A )
& ( B = D ) )
=> ( ( k17_group_2 @ A @ B )
= ( k2_nat_1 @ ( k17_group_2 @ C @ D ) @ ( k17_group_2 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t179_group_2) ).
thf(9460,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ C )
=> ( ( ( v6_group_1 @ A )
& ( B = D ) )
=> ( ( k17_group_2 @ A @ B )
= ( k2_nat_1 @ ( k17_group_2 @ C @ D ) @ ( k17_group_2 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(441,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(3745,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)],[441]) ).
thf(593,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(4418,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)],[593]) ).
thf(1660,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r6_group_3 @ A @ B @ C )
=> ( r6_group_3 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r6_group_3) ).
thf(9233,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r6_group_3 @ A @ B @ C )
=> ( r6_group_3 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(1450,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ B @ ( k4_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_group_2) ).
thf(8430,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ B @ ( k4_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(1273,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_3) ).
thf(7573,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(939,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(5906,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)],[939]) ).
thf(364,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(3365,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)],[364]) ).
thf(1613,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k11_group_3 @ A @ B )
= ( k10_group_3 @ A @ ( k7_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_group_3) ).
thf(9052,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k11_group_3 @ A @ B )
= ( k10_group_3 @ A @ ( k7_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(214,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(2740,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)],[214]) ).
thf(1047,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(6359,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)],[1047]) ).
thf(250,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(2918,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)],[250]) ).
thf(1489,axiom,
k4_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_numbers) ).
thf(8622,plain,
k4_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(504,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(4026,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)],[504]) ).
thf(792,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_group_1) ).
thf(5288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1595,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ B @ ( k9_group_3 @ A @ C ) )
<=> ( r6_group_3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_group_3) ).
thf(8981,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r2_hidden @ B @ ( k9_group_3 @ A @ C ) )
=> ( r6_group_3 @ A @ B @ C ) )
& ( ( r6_group_3 @ A @ B @ C )
=> ( r2_hidden @ B @ ( k9_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(1578,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( k9_group_3 @ A @ B )
= ( k9_group_3 @ A @ C ) )
<=> ~ ( r1_xboole_0 @ ( k9_group_3 @ A @ B ) @ ( k9_group_3 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_group_3) ).
thf(8915,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( ( k9_group_3 @ A @ B )
= ( k9_group_3 @ A @ C ) )
=> ~ ( r1_xboole_0 @ ( k9_group_3 @ A @ B ) @ ( k9_group_3 @ A @ C ) ) )
& ( ~ ( r1_xboole_0 @ ( k9_group_3 @ A @ B ) @ ( k9_group_3 @ A @ C ) )
=> ( ( k9_group_3 @ A @ B )
= ( k9_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(1177,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_vectsp_1 @ A ) )
=> ( ( v8_vectsp_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k2_group_1 @ A ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_vectsp_1) ).
thf(7115,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_vectsp_1 @ A ) )
=> ( ( ( v8_vectsp_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k2_group_1 @ A ) @ B )
= B ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k2_group_1 @ A ) @ B )
= B ) )
=> ( v8_vectsp_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1566,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k4_group_6 @ A @ B )
= ( k14_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_6) ).
thf(8879,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k4_group_6 @ A @ B )
= ( k14_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(1172,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(7096,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)],[1172]) ).
thf(385,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(3446,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)],[385]) ).
thf(1502,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(8667,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)],[1502]) ).
thf(983,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_3 @ A @ B @ C )
= ( k3_group_3 @ A @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_group_3) ).
thf(6089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_3 @ A @ B @ C )
= ( k3_group_3 @ A @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(256,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(2933,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)],[256]) ).
thf(784,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(5257,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)],[784]) ).
thf(645,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(4638,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)],[645]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_finseq_1 @ ( k11_finseq_1 @ A @ B @ C ) )
= ( k2_finseq_1 @ np__3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finseq_3) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_finseq_1 @ ( k11_finseq_1 @ A @ B @ C ) )
= ( k2_finseq_1 @ np__3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1100,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(6634,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)],[1100]) ).
thf(1599,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k7_group_1 @ A @ ( k2_group_1 @ A ) )
= np__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_group_1) ).
thf(9000,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k7_group_1 @ A @ ( k2_group_1 @ A ) )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(980,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(6078,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)],[980]) ).
thf(1018,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k1_latsubgr @ A ) )
& ( v1_funct_2 @ ( k1_latsubgr @ A ) @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ ( k1_latsubgr @ A ) @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
thf(6241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k1_latsubgr @ A ) )
& ( v1_funct_2 @ ( k1_latsubgr @ A ) @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ ( k1_latsubgr @ A ) @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(753,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(5161,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)],[753]) ).
thf(560,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(4294,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)],[560]) ).
thf(396,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(3481,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)],[396]) ).
thf(1108,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_group_1) ).
thf(6680,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(415,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(3562,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)],[415]) ).
thf(1156,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(6996,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)],[1156]) ).
thf(182,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(2580,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)],[182]) ).
thf(1247,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C != k1_xboole_0 )
=> ( ( k3_group_3 @ A @ B @ C )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_group_3) ).
thf(7452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C != k1_xboole_0 )
=> ( ( k3_group_3 @ A @ B @ C )
= B ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C != k1_xboole_0 )
=> ( ( k3_group_3 @ A @ B @ C )
= B ) ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k5_funct_4 @ A @ B @ C @ D @ E )
= ( k4_funct_4 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funct_4) ).
thf(5782,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k5_funct_4 @ A @ B @ C @ D @ E )
= ( k4_funct_4 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(437,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(3717,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)],[437]) ).
thf(123,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(2360,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)],[123]) ).
thf(1742,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k14_group_2 @ A @ B ) )
= ( u1_struct_0 @ A ) )
& ( ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k15_group_2 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_group_2) ).
thf(9481,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k14_group_2 @ A @ B ) )
= ( u1_struct_0 @ A ) )
& ( ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ ( k15_group_2 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(974,axiom,
? [A: $i] : ( l1_vectsp_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(6046,plain,
? [A: $i] : ( l1_vectsp_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1239,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ D )
<=> ( r1_rlvect_1 @ C @ D ) ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_group_2) ).
thf(7400,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ B @ D )
=> ( r1_rlvect_1 @ C @ D ) )
& ( ( r1_rlvect_1 @ C @ D )
=> ( r1_rlvect_1 @ B @ D ) ) ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1798,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( D
= ( k8_group_2 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( r1_group_2 @ A @ D @ ( k8_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_group_2) ).
thf(9672,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( D
= ( k8_group_2 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( u1_struct_0 @ D )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( r1_group_2 @ A @ D @ ( k8_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(181,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(2575,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)],[181]) ).
thf(1016,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( r1_xreal_0 @ np__0 @ A )
=> ( r2_hidden @ A @ k5_numbers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_int_1) ).
thf(6236,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( r1_xreal_0 @ np__0 @ A )
=> ( r2_hidden @ A @ k5_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(101,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(2216,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)],[101]) ).
thf(773,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5227,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(139,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(2432,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)],[139]) ).
thf(614,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(4496,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)],[614]) ).
thf(1131,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(6872,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)],[1131]) ).
thf(1135,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k3_group_1 @ A @ B ) )
<=> ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
& ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_group_1) ).
thf(6887,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k3_group_1 @ A @ B ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
& ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) ) )
& ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
& ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) )
=> ( C
= ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1305,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_3) ).
thf(7734,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(450,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( ( k2_finseq_1 @ A )
= k1_xboole_0 )
<=> ~ ( r2_hidden @ A @ ( k2_finseq_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_finseq_3) ).
thf(3777,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( ( ( k2_finseq_1 @ A )
= k1_xboole_0 )
=> ~ ( r2_hidden @ A @ ( k2_finseq_1 @ A ) ) )
& ( ~ ( r2_hidden @ A @ ( k2_finseq_1 @ A ) )
=> ( ( k2_finseq_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( 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(7364,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)],[1234]) ).
thf(545,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(4198,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)],[545]) ).
thf(988,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(6102,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)],[988]) ).
thf(137,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(2405,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)],[137]) ).
thf(430,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).
thf(3688,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(804,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(5342,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)],[804]) ).
thf(1633,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ( ( r1_group_6 @ A @ B )
& ( r1_group_6 @ B @ C ) )
=> ( r1_group_6 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_group_6) ).
thf(9116,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ( ( r1_group_6 @ A @ B )
& ( r1_group_6 @ B @ C ) )
=> ( r1_group_6 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(366,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(3370,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)],[366]) ).
thf(1783,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( m1_group_2 @ B @ D )
=> ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ ( k8_group_4 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_4) ).
thf(9625,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( m1_group_2 @ B @ D )
=> ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ ( k8_group_4 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(1730,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( r1_rlvect_1 @ C @ A )
=> ( r1_rlvect_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_group_2) ).
thf(9443,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( r1_rlvect_1 @ C @ A )
=> ( r1_rlvect_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(999,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( ( v1_finset_1 @ ( k7_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k7_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_group_3) ).
thf(6138,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( ( v1_finset_1 @ ( k7_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k7_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(509,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4047,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1573,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_group_4) ).
thf(8898,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k7_group_4 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(1023,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(6268,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)],[1023]) ).
thf(1626,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k13_group_6 @ A @ ( k6_group_6 @ A @ B ) @ ( k11_group_6 @ A @ B ) )
= ( k6_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_6) ).
thf(9096,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k13_group_6 @ A @ ( k6_group_6 @ A @ B ) @ ( k11_group_6 @ A @ B ) )
= ( k6_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(965,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k7_group_4 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) )
& ( ( k7_group_4 @ A @ B @ C )
= ( k11_group_2 @ A @ B @ ( k7_group_2 @ A @ C ) ) )
& ( ( k7_group_4 @ A @ B @ C )
= ( k10_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_4) ).
thf(6009,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k7_group_4 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) )
& ( ( k7_group_4 @ A @ B @ C )
= ( k11_group_2 @ A @ B @ ( k7_group_2 @ A @ C ) ) )
& ( ( k7_group_4 @ A @ B @ C )
= ( k10_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1646,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_group_1) ).
thf(9159,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(1417,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k12_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) )
= ( k3_group_2 @ A @ B @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_group_2) ).
thf(8239,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k12_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) )
= ( k3_group_2 @ A @ B @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(484,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(3947,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)],[484]) ).
thf(1656,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_2 @ A ) )
& ( v1_group_1 @ ( k6_group_2 @ A ) )
& ( v2_group_1 @ ( k6_group_2 @ A ) )
& ( v3_group_1 @ ( k6_group_2 @ A ) )
& ( v4_group_1 @ ( k6_group_2 @ A ) )
& ( v1_group_3 @ ( k6_group_2 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_group_6) ).
thf(9195,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_2 @ A ) )
& ( v1_group_1 @ ( k6_group_2 @ A ) )
& ( v2_group_1 @ ( k6_group_2 @ A ) )
& ( v3_group_1 @ ( k6_group_2 @ A ) )
& ( v4_group_1 @ ( k6_group_2 @ A ) )
& ( v1_group_3 @ ( k6_group_2 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(1207,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7240,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1139,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(6904,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)],[1139]) ).
thf(919,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(5825,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)],[919]) ).
thf(945,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(5938,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)],[945]) ).
thf(905,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_rlvect_1 @ C @ B )
<=> ( ( k13_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_group_2) ).
thf(5770,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( r1_rlvect_1 @ C @ B )
=> ( ( k13_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) ) )
& ( ( ( k13_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) )
=> ( r1_rlvect_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1564,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ B @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_group_1) ).
thf(8866,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ B @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(243,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(2886,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)],[243]) ).
thf(1388,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_group_3 @ A @ B )
= ( k7_group_3 @ A @ C ) )
<=> ~ ( r1_xboole_0 @ ( k7_group_3 @ A @ B ) @ ( k7_group_3 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_group_3) ).
thf(8122,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k7_group_3 @ A @ B )
= ( k7_group_3 @ A @ C ) )
=> ~ ( r1_xboole_0 @ ( k7_group_3 @ A @ B ) @ ( k7_group_3 @ A @ C ) ) )
& ( ~ ( r1_xboole_0 @ ( k7_group_3 @ A @ B ) @ ( k7_group_3 @ A @ C ) )
=> ( ( k7_group_3 @ A @ B )
= ( k7_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1714,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r1_group_6 @ A @ B )
=> ( r1_group_6 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_group_6) ).
thf(9396,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r1_group_6 @ A @ B )
=> ( r1_group_6 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(530,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(4137,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)],[530]) ).
thf(87,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(2173,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)],[87]) ).
thf(1506,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(8678,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)],[1506]) ).
thf(1433,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k8_group_1 @ ( k13_group_6 @ B @ A @ C ) ) @ ( k8_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_group_6) ).
thf(8330,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k8_group_1 @ ( k13_group_6 @ B @ A @ C ) ) @ ( k8_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k8_relset_1 @ A @ B @ D @ C ) )
& ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ D @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_partfun1) ).
thf(6306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k8_relset_1 @ A @ B @ D @ C ) )
& ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ D @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1365,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(8025,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)],[1365]) ).
thf(136,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(2400,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)],[136]) ).
thf(672,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(4760,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)],[672]) ).
thf(718,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(4963,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)],[718]) ).
thf(60,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(2067,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)],[60]) ).
thf(1792,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_group_2) ).
thf(9657,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(473,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_group_6 @ C @ B @ A )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ ( k2_funct_1 @ C ) @ ( k13_group_6 @ B @ A @ C ) @ B )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_group_6) ).
thf(3878,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_group_6 @ C @ B @ A )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ ( k2_funct_1 @ C ) @ ( k13_group_6 @ B @ A @ C ) @ B )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(24,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(1904,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)],[24]) ).
thf(1682,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k5_group_2 @ A ) )
& ( m1_group_2 @ ( k5_group_2 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_2) ).
thf(9300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k5_group_2 @ A ) )
& ( m1_group_2 @ ( k5_group_2 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(825,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k3_group_2 @ A @ ( k1_group_1 @ A @ C @ D ) @ B )
= ( k3_group_2 @ A @ C @ ( k3_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_group_2) ).
thf(5429,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k3_group_2 @ A @ ( k1_group_1 @ A @ C @ D ) @ B )
= ( k3_group_2 @ A @ C @ ( k3_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_finseq_1 @ B @ A )
& ( v4_ordinal2 @ C ) )
=> ( m2_finseq_1 @ ( k16_finseq_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_finseq_1) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_finseq_1 @ B @ A )
& ( v4_ordinal2 @ C ) )
=> ( m2_finseq_1 @ ( k16_finseq_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(201,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_finseq_1 @ A ) )
=> ( ( k4_finseq_1 @ ( k14_finseq_1 @ B ) )
= ( k2_finseq_1 @ ( k4_card_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_finseq_3) ).
thf(2698,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_finseq_1 @ A ) )
=> ( ( k4_finseq_1 @ ( k14_finseq_1 @ B ) )
= ( k2_finseq_1 @ ( k4_card_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(120,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(2339,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)],[120]) ).
thf(316,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(3148,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)],[316]) ).
thf(1471,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(8522,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)],[1471]) ).
thf(1410,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_vectsp_1 @ A ) )
=> ( ( v6_vectsp_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_vectsp_1) ).
thf(8208,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_vectsp_1 @ A ) )
=> ( ( ( v6_vectsp_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ ( k2_group_1 @ A ) )
= B ) )
=> ( v6_vectsp_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(964,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(6006,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)],[964]) ).
thf(1530,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ B @ ( k8_group_4 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_group_4) ).
thf(8753,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ B @ ( k8_group_4 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(626,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(4539,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)],[626]) ).
thf(1732,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k2_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_group_6) ).
thf(9447,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k2_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(1466,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ D ) )
& ( r2_hidden @ D @ ( k7_group_3 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_group_3) ).
thf(8500,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ D ) )
& ( r2_hidden @ D @ ( k7_group_3 @ B @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ D ) )
& ( r2_hidden @ D @ ( k7_group_3 @ B @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_2_group_3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1678,axiom,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( k11_finseq_1 @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_3) ).
thf(9287,plain,
! [A: $i,B: $i,C: $i] :
( k1_xboole_0
!= ( k11_finseq_1 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(1339,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(7914,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)],[1339]) ).
thf(1627,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( u1_struct_0 @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsubgr) ).
thf(9099,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( u1_struct_0 @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(423,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(3644,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)],[423]) ).
thf(1215,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ ( k13_group_6 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_6) ).
thf(7262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ ( k13_group_6 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(629,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(4563,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)],[629]) ).
thf(52,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(2039,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)],[52]) ).
thf(1464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_finsub_1) ).
thf(8494,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(1379,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(8089,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)],[1379]) ).
thf(1414,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_group_2) ).
thf(8225,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(1765,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v1_group_4 @ ( k2_group_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_group_4) ).
thf(9561,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v1_group_4 @ ( k2_group_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1737,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_4) ).
thf(9464,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(985,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( v2_group_4 @ B @ A )
=> ( ( r1_rlvect_1 @ B @ C )
| ( ( k5_group_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_group_4) ).
thf(6095,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( v2_group_4 @ B @ A )
=> ( ( r1_rlvect_1 @ B @ C )
| ( ( k5_group_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1636,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r2_wellord2 @ ( k14_group_2 @ A @ B ) @ ( k15_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_group_2) ).
thf(9128,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r2_wellord2 @ ( k14_group_2 @ A @ B ) @ ( k15_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(760,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(5188,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)],[760]) ).
thf(25,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(1907,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)],[25]) ).
thf(160,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(2501,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)],[160]) ).
thf(651,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(4654,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)],[651]) ).
thf(144,axiom,
! [A: $i] :
( ( l1_rlvect_1 @ A )
=> ( l2_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
thf(2444,plain,
! [A: $i] :
( ( l1_rlvect_1 @ A )
=> ( l2_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1312,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(7771,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)],[1312]) ).
thf(1044,axiom,
k5_numbers != k4_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_numbers) ).
thf(6350,plain,
k5_numbers != k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1347,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(7945,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)],[1347]) ).
thf(112,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(2274,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)],[112]) ).
thf(398,axiom,
( ( k4_card_1 @ k1_xboole_0 )
= np__0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_card_1) ).
thf(3485,plain,
( ( k4_card_1 @ k1_xboole_0 )
= np__0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(678,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(4778,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)],[678]) ).
thf(1411,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8214,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(528,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(4130,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)],[528]) ).
thf(577,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(4349,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)],[577]) ).
thf(503,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(4023,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)],[503]) ).
thf(157,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(2488,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)],[157]) ).
thf(177,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(2562,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)],[177]) ).
thf(1396,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r1_group_6 @ A @ B )
<=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v4_group_6 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_group_6) ).
thf(8146,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r1_group_6 @ A @ B )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v4_group_6 @ C @ A @ B ) ) )
& ( ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v4_group_6 @ C @ A @ B ) )
=> ( r1_group_6 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(890,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(5712,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1659,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k8_group_1 @ A )
= ( k1_card_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_group_1) ).
thf(9230,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k8_group_1 @ A )
= ( k1_card_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(888,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__2 @ B )
= ( k1_group_1 @ A @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_group_1) ).
thf(5706,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__2 @ B )
= ( k1_group_1 @ A @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(456,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_xreal_0 @ np__0 @ B )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ ( k1_int_2 @ B ) ) ) )
& ( ~ ( r1_xreal_0 @ np__0 @ B )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k3_group_1 @ A @ ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ ( k1_int_2 @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_group_1) ).
thf(3803,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_xreal_0 @ np__0 @ B )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ ( k1_int_2 @ B ) ) ) )
& ( ~ ( r1_xreal_0 @ np__0 @ B )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k3_group_1 @ A @ ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ ( k1_int_2 @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(149,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(2466,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)],[149]) ).
thf(1418,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(8242,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)],[1418]) ).
thf(595,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(4428,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)],[595]) ).
thf(1309,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( C
= ( k10_group_6 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= ( k2_group_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_group_6) ).
thf(7743,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C
= ( k10_group_6 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= ( k2_group_1 @ B ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= ( k2_group_1 @ B ) ) )
=> ( C
= ( k10_group_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( k8_relset_1 @ B @ A @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relset_1) ).
thf(6208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( k8_relset_1 @ B @ A @ D @ C )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(286,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(3043,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)],[286]) ).
thf(1292,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ F @ A @ B )
& ( m2_relset_1 @ F @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ ( k3_group_5 @ A @ C @ D @ E ) )
= ( k3_group_5 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_group_6) ).
thf(7665,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ F @ A @ B )
& ( m2_relset_1 @ F @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ ( k3_group_5 @ A @ C @ D @ E ) )
= ( k3_group_5 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(835,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(5461,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)],[835]) ).
thf(1576,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_3 @ ( k9_group_2 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k9_group_2 @ A @ B @ C ) @ A @ B )
& ( v1_group_3 @ ( k9_group_2 @ A @ C @ B ) @ B )
& ( m1_group_6 @ ( k9_group_2 @ A @ C @ B ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_group_6) ).
thf(8907,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_3 @ ( k9_group_2 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k9_group_2 @ A @ B @ C ) @ A @ B )
& ( v1_group_3 @ ( k9_group_2 @ A @ C @ B ) @ B )
& ( m1_group_6 @ ( k9_group_2 @ A @ C @ B ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(554,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) )
=> ( B = np__0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finseq_3) ).
thf(4270,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) )
=> ( B = np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(393,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(3470,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)],[393]) ).
thf(927,axiom,
~ ( v1_xboole_0 @ k1_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).
thf(5851,plain,
~ ( v1_xboole_0 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
<=> ( m1_finseq_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_finseq_1) ).
thf(4265,plain,
! [A: $i,B: $i] :
( ( ( m2_finseq_1 @ B @ A )
=> ( m1_finseq_1 @ B @ A ) )
& ( ( m1_finseq_1 @ B @ A )
=> ( m2_finseq_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(603,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_card_1) ).
thf(4460,plain,
np__0 = k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(738,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(5076,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)],[738]) ).
thf(606,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( m1_subset_1 @ ( k2_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finseq_1) ).
thf(4471,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( m1_subset_1 @ ( k2_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(807,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k8_group_3 @ A @ C ) )
<=> ( r4_group_3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_group_3) ).
thf(5355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( k8_group_3 @ A @ C ) )
=> ( r4_group_3 @ A @ B @ C ) )
& ( ( r4_group_3 @ A @ B @ C )
=> ( r2_hidden @ B @ ( k8_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(367,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(3374,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)],[367]) ).
thf(371,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(3385,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)],[371]) ).
thf(768,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(5214,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)],[768]) ).
thf(866,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ C ) )
=> ( ( k17_group_2 @ A @ C )
= ( k17_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_group_3) ).
thf(5605,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ C ) )
=> ( ( k17_group_2 @ A @ C )
= ( k17_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(86,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(2169,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)],[86]) ).
thf(1066,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( B
= ( u1_struct_0 @ C ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_latsubgr) ).
thf(6455,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( B
= ( u1_struct_0 @ C ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1094,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k10_group_2 @ A @ C @ B ) )
= ( k2_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_4) ).
thf(6611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k10_group_2 @ A @ C @ B ) )
= ( k2_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1179,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(7124,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1000,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ? [C: $i] :
( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A )
& ( v2_group_4 @ C @ A ) )
=> ( ( B
= ( k6_group_4 @ A ) )
<=> ( ( u1_struct_0 @ B )
= ( k1_setfam_1 @ ( a_1_0_group_4 @ A ) ) ) ) )
& ( ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ~ ( v2_group_4 @ C @ A ) )
=> ( ( B
= ( k6_group_4 @ A ) )
<=> ( B
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_group_4) ).
thf(6149,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ? [C: $i] :
( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A )
& ( v2_group_4 @ C @ A ) )
=> ( ( ( B
= ( k6_group_4 @ A ) )
=> ( ( u1_struct_0 @ B )
= ( k1_setfam_1 @ ( a_1_0_group_4 @ A ) ) ) )
& ( ( ( u1_struct_0 @ B )
= ( k1_setfam_1 @ ( a_1_0_group_4 @ A ) ) )
=> ( B
= ( k6_group_4 @ A ) ) ) ) )
& ( ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ~ ( v2_group_4 @ C @ A ) )
=> ( ( ( B
= ( k6_group_4 @ A ) )
=> ( B
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) )
& ( ( B
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
=> ( B
= ( k6_group_4 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1098,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(6626,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)],[1098]) ).
thf(1518,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_group_2 @ A @ ( k6_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_2) ).
thf(8717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_group_2 @ A @ ( k6_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(1050,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_group_3 @ A @ B )
= ( a_2_1_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_group_3) ).
thf(6379,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_group_3 @ A @ B )
= ( a_2_1_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(612,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_xreal_0 @ ( k4_card_1 @ A ) @ ( k4_card_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_card_1) ).
thf(4492,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_xreal_0 @ ( k4_card_1 @ A ) @ ( k4_card_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(128,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(2373,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)],[128]) ).
thf(691,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 @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( C
= ( k3_binop_1 @ A @ B ) )
<=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).
thf(4830,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 @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( C
= ( k3_binop_1 @ A @ B ) )
=> ( r3_binop_1 @ A @ C @ B ) )
& ( ( r3_binop_1 @ A @ C @ B )
=> ( C
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(568,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(4317,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)],[568]) ).
thf(1118,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(6781,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)],[1118]) ).
thf(1438,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ k4_numbers )
=> ( ( ( k3_finseq_1 @ C )
= A )
=> ( ( k4_group_4 @ B @ C @ ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ ( k2_group_1 @ B ) ) )
= ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ ( k2_group_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_group_4) ).
thf(8367,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ k4_numbers )
=> ( ( ( k3_finseq_1 @ C )
= A )
=> ( ( k4_group_4 @ B @ C @ ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ ( k2_group_1 @ B ) ) )
= ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ ( k2_group_1 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1168,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(7075,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)],[1168]) ).
thf(1148,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( v5_group_1 @ B @ A )
=> ( ( C
= ( k7_group_1 @ A @ B ) )
<=> ( C = np__0 ) ) )
& ( ~ ( v5_group_1 @ B @ A )
=> ( ( C
= ( k7_group_1 @ A @ B ) )
<=> ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
& ( C != np__0 )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ D @ B )
= ( k2_group_1 @ A ) )
=> ( ( D = np__0 )
| ( r1_xreal_0 @ C @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_group_1) ).
thf(6936,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( v5_group_1 @ B @ A )
=> ( ( ( C
= ( k7_group_1 @ A @ B ) )
=> ( C = np__0 ) )
& ( ( C = np__0 )
=> ( C
= ( k7_group_1 @ A @ B ) ) ) ) )
& ( ~ ( v5_group_1 @ B @ A )
=> ( ( ( C
= ( k7_group_1 @ A @ B ) )
=> ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
& ( C != np__0 )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ D @ B )
= ( k2_group_1 @ A ) )
=> ( ( D = np__0 )
| ( r1_xreal_0 @ C @ D ) ) ) ) ) )
& ( ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
& ( C != np__0 )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ D @ B )
= ( k2_group_1 @ A ) )
=> ( ( D = np__0 )
| ( r1_xreal_0 @ C @ D ) ) ) ) )
=> ( C
= ( k7_group_1 @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(299,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(3084,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)],[299]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( m1_group_2 @ ( k12_group_6 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_group_6) ).
thf(5829,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( m1_group_2 @ ( k12_group_6 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1413,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= B )
| ( ( k1_group_1 @ A @ C @ B )
= B ) )
=> ( C
= ( k2_group_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_group_1) ).
thf(8220,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= B )
| ( ( k1_group_1 @ A @ C @ B )
= B ) )
=> ( C
= ( k2_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(46,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(2024,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)],[46]) ).
thf(986,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v2_binop_1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_group_1) ).
thf(6098,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v2_binop_1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1368,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(8037,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)],[1368]) ).
thf(587,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 ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).
thf(4400,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 ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(20,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(1875,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)],[20]) ).
thf(1399,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ B @ A ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ D ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_group_1) ).
thf(8161,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ B @ A ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ D ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(1258,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(7509,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)],[1258]) ).
thf(344,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(3268,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)],[344]) ).
thf(343,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ C ) )
& ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ D ) )
& ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ E @ ( k4_finseq_1 @ B ) )
=> ( ( k1_funct_1 @ B @ E )
= ( k1_group_1 @ A @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ D @ E ) ) ) ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ C ) @ ( k3_group_4 @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_group_4) ).
thf(3258,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ C ) )
& ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ D ) )
& ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ E @ ( k4_finseq_1 @ B ) )
=> ( ( k1_funct_1 @ B @ E )
= ( k1_group_1 @ A @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ D @ E ) ) ) ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ C ) @ ( k3_group_4 @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1257,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_group_6 @ B ) )
<=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_5 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_6) ).
thf(7500,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_group_6 @ B ) )
=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_5 @ B @ C @ D ) ) ) )
& ( ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_5 @ B @ C @ D ) ) )
=> ( r2_hidden @ A @ ( a_1_0_group_6 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_finseq_1 @ B ) )
<=> ? [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
& ( A = C )
& ( r1_xreal_0 @ np__1 @ C )
& ( r1_xreal_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_finseq_1) ).
thf(6382,plain,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_finseq_1 @ B ) )
=> ? [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
& ( A = C )
& ( r1_xreal_0 @ np__1 @ C )
& ( r1_xreal_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
& ( A = C )
& ( r1_xreal_0 @ np__1 @ C )
& ( r1_xreal_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_0_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(13,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 )
=> ( ( ( k1_funct_4 @ A @ B )
= B )
& ( ( k1_funct_4 @ B @ A )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_4) ).
thf(1847,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 )
=> ( ( ( k1_funct_4 @ A @ B )
= B )
& ( ( k1_funct_4 @ B @ A )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1277,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( ( k17_group_2 @ A @ ( k5_group_2 @ A ) )
= ( k9_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t183_group_2) ).
thf(7588,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( ( k17_group_2 @ A @ ( k5_group_2 @ A ) )
= ( k9_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(1565,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ~ ( ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) )
& ( ? [D: $i] :
( ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_group_2) ).
thf(8870,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ~ ( ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) )
& ( ? [D: $i] :
( ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(454,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_rlvect_1 @ ( k5_group_4 @ A @ C ) @ B )
<=> ? [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m2_finseq_1 @ E @ k4_numbers )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ E ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
& ( ( k3_group_4 @ A @ ( k4_group_4 @ A @ E @ D ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_group_4) ).
thf(3788,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_rlvect_1 @ ( k5_group_4 @ A @ C ) @ B )
=> ? [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m2_finseq_1 @ E @ k4_numbers )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ E ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
& ( ( k3_group_4 @ A @ ( k4_group_4 @ A @ E @ D ) )
= B ) ) ) )
& ( ? [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m2_finseq_1 @ E @ k4_numbers )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ E ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
& ( ( k3_group_4 @ A @ ( k4_group_4 @ A @ E @ D ) )
= B ) ) )
=> ( r1_rlvect_1 @ ( k5_group_4 @ A @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1726,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( C
= ( k10_group_3 @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= ( a_2_3_group_3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_3) ).
thf(9425,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( C
= ( k10_group_3 @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= ( a_2_3_group_3 @ A @ B ) ) )
& ( ( ( u1_struct_0 @ C )
= ( a_2_3_group_3 @ A @ B ) )
=> ( C
= ( k10_group_3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(637,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(4595,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(957,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_rlvect_1 @ C @ B )
<=> ( ( k12_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_group_2) ).
thf(5974,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( r1_rlvect_1 @ C @ B )
=> ( ( k12_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) ) )
& ( ( ( k12_group_2 @ A @ C @ B )
= ( k7_group_2 @ A @ C ) )
=> ( r1_rlvect_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(88,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 )
<=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_4) ).
thf(2178,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 )
=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) )
& ( ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1588,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k5_group_4 @ A @ B ) )
& ( m1_group_2 @ ( k5_group_4 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_4) ).
thf(8956,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k5_group_4 @ A @ B ) )
& ( m1_group_2 @ ( k5_group_4 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(146,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(2451,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)],[146]) ).
thf(1419,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r1_xreal_0 @ np__0 @ A )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_group_1) ).
thf(8246,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r1_xreal_0 @ np__0 @ A )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(902,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_setwiseo @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_group_1) ).
thf(5761,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_setwiseo @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(147,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(2456,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)],[147]) ).
thf(1716,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( r2_hidden @ A @ ( k7_group_2 @ B @ C ) )
<=> ( r1_rlvect_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_group_2) ).
thf(9401,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( ( r2_hidden @ A @ ( k7_group_2 @ B @ C ) )
=> ( r1_rlvect_1 @ C @ A ) )
& ( ( r1_rlvect_1 @ C @ A )
=> ( r2_hidden @ A @ ( k7_group_2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(952,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(5957,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)],[952]) ).
thf(726,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(4988,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)],[726]) ).
thf(1218,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_rlvect_1 @ ( k6_group_6 @ A @ C ) @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k12_group_2 @ A @ C @ D ) )
& ( B
= ( k13_group_2 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_group_6) ).
thf(7273,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r1_rlvect_1 @ ( k6_group_6 @ A @ C ) @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k12_group_2 @ A @ C @ D ) )
& ( B
= ( k13_group_2 @ A @ C @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k12_group_2 @ A @ C @ D ) )
& ( B
= ( k13_group_2 @ A @ C @ D ) ) )
=> ( r1_rlvect_1 @ ( k6_group_6 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(228,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(2794,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)],[228]) ).
thf(1367,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(8029,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)],[1367]) ).
thf(634,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(4583,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)],[634]) ).
thf(1334,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ E @ A @ B )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( k2_group_3 @ A @ C @ D ) )
= ( k2_group_3 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_group_6) ).
thf(7894,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ E @ A @ B )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( k2_group_3 @ A @ C @ D ) )
= ( k2_group_3 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(846,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(5526,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)],[846]) ).
thf(708,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(4903,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)],[708]) ).
thf(741,axiom,
! [A: $i] :
( ? [B: $i] :
( ( v4_ordinal2 @ B )
& ( r1_tarski @ A @ ( k2_finseq_1 @ B ) ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ k5_numbers )
=> ( ( B
= ( k14_finseq_1 @ A ) )
<=> ( ( ( k2_relat_1 @ B )
= A )
& ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ! [E: $i] :
( ( v4_ordinal2 @ E )
=> ! [F: $i] :
( ( v4_ordinal2 @ F )
=> ~ ( ( r1_xreal_0 @ np__1 @ C )
& ~ ( r1_xreal_0 @ D @ C )
& ( r1_xreal_0 @ D @ ( k3_finseq_1 @ B ) )
& ( E
= ( k1_funct_1 @ B @ C ) )
& ( F
= ( k1_funct_1 @ B @ D ) )
& ( r1_xreal_0 @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_finseq_1) ).
thf(5084,plain,
! [A: $i] :
( ? [B: $i] :
( ( v4_ordinal2 @ B )
& ( r1_tarski @ A @ ( k2_finseq_1 @ B ) ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ k5_numbers )
=> ( ( ( B
= ( k14_finseq_1 @ A ) )
=> ( ( ( k2_relat_1 @ B )
= A )
& ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ! [E: $i] :
( ( v4_ordinal2 @ E )
=> ! [F: $i] :
( ( v4_ordinal2 @ F )
=> ~ ( ( r1_xreal_0 @ np__1 @ C )
& ~ ( r1_xreal_0 @ D @ C )
& ( r1_xreal_0 @ D @ ( k3_finseq_1 @ B ) )
& ( E
= ( k1_funct_1 @ B @ C ) )
& ( F
= ( k1_funct_1 @ B @ D ) )
& ( r1_xreal_0 @ F @ E ) ) ) ) ) ) ) )
& ( ( ( ( k2_relat_1 @ B )
= A )
& ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ! [E: $i] :
( ( v4_ordinal2 @ E )
=> ! [F: $i] :
( ( v4_ordinal2 @ F )
=> ~ ( ( r1_xreal_0 @ np__1 @ C )
& ~ ( r1_xreal_0 @ D @ C )
& ( r1_xreal_0 @ D @ ( k3_finseq_1 @ B ) )
& ( E
= ( k1_funct_1 @ B @ C ) )
& ( F
= ( k1_funct_1 @ B @ D ) )
& ( r1_xreal_0 @ F @ E ) ) ) ) ) ) )
=> ( B
= ( k14_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1745,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ( r4_group_3 @ A @ B @ ( k7_group_2 @ A @ C ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_group_3) ).
thf(9490,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ( r4_group_3 @ A @ B @ ( k7_group_2 @ A @ C ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(502,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(4018,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)],[502]) ).
thf(63,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(2090,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)],[63]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k9_group_6 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_group_6) ).
thf(3393,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k9_group_6 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(601,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(4454,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)],[601]) ).
thf(1352,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_group_3) ).
thf(7969,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_1_group_3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(1210,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k8_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_3) ).
thf(7247,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k8_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(561,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r1_xreal_0 @ A @ B )
=> ( ( k2_finseq_1 @ A )
= ( k5_subset_1 @ k5_numbers @ ( k2_finseq_1 @ B ) @ ( k2_finseq_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_finseq_1) ).
thf(4297,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r1_xreal_0 @ A @ B )
=> ( ( k2_finseq_1 @ A )
= ( k5_subset_1 @ k5_numbers @ ( k2_finseq_1 @ B ) @ ( k2_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(150,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(2469,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)],[150]) ).
thf(1322,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).
thf(7818,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(107,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(2259,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)],[107]) ).
thf(1235,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ D @ B ) @ C ) @ ( k6_group_3 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_group_3) ).
thf(7369,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ D @ B ) @ C ) @ ( k6_group_3 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1056,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_group_3) ).
thf(6410,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1542,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k15_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_group_2) ).
thf(8791,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k15_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(998,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_group_1) ).
thf(6135,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ C ) )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ D @ ( k4_finseq_1 @ B ) )
=> ( ( k1_funct_1 @ C @ ( k2_xcmplx_0 @ ( k6_xcmplx_0 @ ( k3_finseq_1 @ B ) @ D ) @ np__1 ) )
= ( k3_group_1 @ A @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ D ) ) ) ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_1 @ A @ ( k3_group_4 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_group_4) ).
thf(4847,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ C ) )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ D @ ( k4_finseq_1 @ B ) )
=> ( ( k1_funct_1 @ C @ ( k2_xcmplx_0 @ ( k6_xcmplx_0 @ ( k3_finseq_1 @ B ) @ D ) @ np__1 ) )
= ( k3_group_1 @ A @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ D ) ) ) ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_1 @ A @ ( k3_group_4 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(383,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(3438,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)],[383]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_group_2 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_group_2) ).
thf(6187,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k1_group_2 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( k1_group_2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_partfun1 @ B @ C )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_4) ).
thf(2925,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_partfun1 @ B @ C )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1499,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( k2_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_group_1) ).
thf(8659,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( k2_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(38,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(1978,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)],[38]) ).
thf(1128,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ C )
=> ( r1_tarski @ ( k7_group_3 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_group_3) ).
thf(6841,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ C )
=> ( r1_tarski @ ( k7_group_3 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ C )
=> ( r1_tarski @ ( k7_group_3 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_group_6) ).
thf(3357,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ? [C: $i] :
( ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ~ ( v1_xboole_0 @ C )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1722,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r2_group_6 @ ( k5_group_2 @ A ) @ ( k5_group_2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_group_6) ).
thf(9415,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r2_group_6 @ ( k5_group_2 @ A ) @ ( k5_group_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(1082,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( ( u1_struct_0 @ E )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_latsubgr) ).
thf(6559,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( ( u1_struct_0 @ E )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(697,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ B @ ( k2_finseq_1 @ A ) )
=> ( r2_hidden @ ( k2_xcmplx_0 @ B @ C ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_1) ).
thf(4871,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ B @ ( k2_finseq_1 @ A ) )
=> ( r2_hidden @ ( k2_xcmplx_0 @ B @ C ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(61,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(2073,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)],[61]) ).
thf(1501,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(8664,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)],[1501]) ).
thf(1336,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(7899,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)],[1336]) ).
thf(467,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r2_hidden @ ( k6_xcmplx_0 @ A @ B ) @ ( k2_finseq_1 @ A ) )
<=> ~ ( r1_xreal_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_3) ).
thf(3851,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( r2_hidden @ ( k6_xcmplx_0 @ A @ B ) @ ( k2_finseq_1 @ A ) )
=> ~ ( r1_xreal_0 @ A @ B ) )
& ( ~ ( r1_xreal_0 @ A @ B )
=> ( r2_hidden @ ( k6_xcmplx_0 @ A @ B ) @ ( k2_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1445,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k10_group_2 @ A @ B @ ( k12_group_2 @ A @ B @ C ) )
= ( k12_group_2 @ A @ B @ C ) )
& ( ( k3_group_2 @ A @ C @ ( k7_group_4 @ A @ B @ B ) )
= ( k12_group_2 @ A @ B @ C ) )
& ( ( k4_group_2 @ A @ C @ ( k7_group_4 @ A @ B @ B ) )
= ( k13_group_2 @ A @ B @ C ) )
& ( ( k11_group_2 @ A @ B @ ( k13_group_2 @ A @ B @ C ) )
= ( k13_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_group_6) ).
thf(8411,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k10_group_2 @ A @ B @ ( k12_group_2 @ A @ B @ C ) )
= ( k12_group_2 @ A @ B @ C ) )
& ( ( k3_group_2 @ A @ C @ ( k7_group_4 @ A @ B @ B ) )
= ( k12_group_2 @ A @ B @ C ) )
& ( ( k4_group_2 @ A @ C @ ( k7_group_4 @ A @ B @ B ) )
= ( k13_group_2 @ A @ B @ C ) )
& ( ( k11_group_2 @ A @ B @ ( k13_group_2 @ A @ B @ C ) )
= ( k13_group_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1685,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v3_realset2 @ ( k6_group_6 @ A @ ( k6_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_group_6) ).
thf(9309,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v3_realset2 @ ( k6_group_6 @ A @ ( k6_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(923,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ B @ A ) @ D )
= ( k6_group_1 @ C @ A @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_group_1) ).
thf(5834,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ B @ A ) @ D )
= ( k6_group_1 @ C @ A @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(265,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(2964,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)],[265]) ).
thf(899,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_3 @ A @ B @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_3) ).
thf(5738,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_3 @ A @ B @ C )
= B ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_3 @ A @ B @ C )
= B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(876,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_1) ).
thf(5648,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(223,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 ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).
thf(2772,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 ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1755,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_3 @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_group_3) ).
thf(9533,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_3 @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(1698,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k1_group_2 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_group_2) ).
thf(9347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k1_group_2 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(1630,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v7_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_2) ).
thf(9108,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v7_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(704,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(4892,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)],[704]) ).
thf(325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_4 @ A @ ( k1_finsop_1 @ k4_numbers @ ( k3_finseq_1 @ B ) @ ( k2_group_4 @ np__1 ) ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_group_4) ).
thf(3184,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_4 @ A @ ( k1_finsop_1 @ k4_numbers @ ( k3_finseq_1 @ B ) @ ( k2_group_4 @ np__1 ) ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(221,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 ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).
thf(2762,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 ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1251,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k6_group_1 @ A @ np__2 @ B )
= ( k2_group_1 @ A ) )
<=> ( ( k3_group_1 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_group_1) ).
thf(7473,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k6_group_1 @ A @ np__2 @ B )
= ( k2_group_1 @ A ) )
=> ( ( k3_group_1 @ A @ B )
= B ) )
& ( ( ( k3_group_1 @ A @ B )
= B )
=> ( ( k6_group_1 @ A @ np__2 @ B )
= ( k2_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1091,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(6591,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)],[1091]) ).
thf(126,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(2367,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)],[126]) ).
thf(141,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(2437,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)],[141]) ).
thf(408,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(3537,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)],[408]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_subset_1 @ ( k7_group_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_group_1) ).
thf(5353,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_subset_1 @ ( k7_group_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(714,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(4935,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)],[714]) ).
thf(1343,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(7931,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)],[1343]) ).
thf(1281,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(7613,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)],[1281]) ).
thf(819,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_group_3 @ A @ B )
= ( k5_group_3 @ A @ ( k7_group_2 @ A @ ( k6_group_2 @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_group_3) ).
thf(5401,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_group_3 @ A @ B )
= ( k5_group_3 @ A @ ( k7_group_2 @ A @ ( k6_group_2 @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(327,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(3189,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)],[327]) ).
thf(439,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(3739,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)],[439]) ).
thf(1110,axiom,
( ( v4_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v3_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_group_1) ).
thf(6685,plain,
( ( v4_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v3_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_finseq_1 @ B @ A ) )
=> ( m2_finseq_1 @ ( k1_group_4 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_4) ).
thf(2861,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_finseq_1 @ B @ A ) )
=> ( m2_finseq_1 @ ( k1_group_4 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1703,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_group_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_1) ).
thf(9369,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_group_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(91,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(2190,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)],[91]) ).
thf(1319,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k4_group_6 @ A @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k12_group_2 @ A @ C @ D ) )
& ( B
= ( k13_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_group_6) ).
thf(7807,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k4_group_6 @ A @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k12_group_2 @ A @ C @ D ) )
& ( B
= ( k13_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_group_6 @ C @ B @ A )
& ( D
= ( k2_funct_1 @ C ) ) )
=> ( v4_group_6 @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_6) ).
thf(6110,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_group_6 @ C @ B @ A )
& ( D
= ( k2_funct_1 @ C ) ) )
=> ( v4_group_6 @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(435,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(3712,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)],[435]) ).
thf(1649,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r2_hidden @ B @ ( k9_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_group_3) ).
thf(9167,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r2_hidden @ B @ ( k9_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(457,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(3808,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)],[457]) ).
thf(167,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(2530,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)],[167]) ).
thf(579,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ k4_numbers )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( D
= ( k4_group_4 @ A @ B @ C ) )
<=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ C ) )
& ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ E @ ( k4_finseq_1 @ C ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k6_group_1 @ A @ ( k2_group_4 @ ( k4_finseq_4 @ k5_numbers @ k4_numbers @ B @ E ) ) @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_group_4) ).
thf(4364,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ k4_numbers )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( D
= ( k4_group_4 @ A @ B @ C ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ C ) )
& ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ E @ ( k4_finseq_1 @ C ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k6_group_1 @ A @ ( k2_group_4 @ ( k4_finseq_4 @ k5_numbers @ k4_numbers @ B @ E ) ) @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) )
& ( ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ C ) )
& ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ E @ ( k4_finseq_1 @ C ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k6_group_1 @ A @ ( k2_group_4 @ ( k4_finseq_4 @ k5_numbers @ k4_numbers @ B @ E ) ) @ ( k4_finseq_4 @ k5_numbers @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) )
=> ( D
= ( k4_group_4 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(270,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(2979,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)],[270]) ).
thf(800,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( k14_group_2 @ A @ ( k6_group_2 @ A ) )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
& ( ( k15_group_2 @ A @ ( k6_group_2 @ A ) )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_group_2) ).
thf(5321,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( k14_group_2 @ A @ ( k6_group_2 @ A ) )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
& ( ( k15_group_2 @ A @ ( k6_group_2 @ A ) )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1437,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(8347,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)],[1437]) ).
thf(1509,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_2 @ B @ C )
<=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_4) ).
thf(8686,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( m1_group_2 @ B @ C )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C ) )
& ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C )
=> ( m1_group_2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(711,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(4924,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)],[711]) ).
thf(443,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(3756,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)],[443]) ).
thf(487,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(3955,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)],[487]) ).
thf(340,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(3243,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(881,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(5665,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)],[881]) ).
thf(620,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 @ D @ A @ B )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_4) ).
thf(4519,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 @ D @ A @ B )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(744,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(5137,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)],[744]) ).
thf(1096,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(6616,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)],[1096]) ).
thf(661,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( A = np__0 )
| ( r2_hidden @ A @ ( k2_finseq_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_finseq_1) ).
thf(4707,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( A = np__0 )
| ( r2_hidden @ A @ ( k2_finseq_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(548,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(4211,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1775,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_group_3 @ A ) )
<=> ? [C: $i] :
( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_latsubgr) ).
thf(9589,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ ( k1_group_3 @ A ) )
=> ? [C: $i] :
( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A )
& ( B = C ) ) )
& ( ? [C: $i] :
( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A )
& ( B = C ) )
=> ( r2_hidden @ B @ ( k1_group_3 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(1303,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__3 @ B )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_group_1) ).
thf(7722,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__3 @ B )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(401,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(3492,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)],[401]) ).
thf(97,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_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_4) ).
thf(2205,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_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(609,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(4483,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)],[609]) ).
thf(1773,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r2_hidden @ ( k7_group_2 @ A @ B ) @ ( k14_group_2 @ A @ B ) )
& ( r2_hidden @ ( k7_group_2 @ A @ B ) @ ( k15_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_group_2) ).
thf(9584,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r2_hidden @ ( k7_group_2 @ A @ B ) @ ( k14_group_2 @ A @ B ) )
& ( r2_hidden @ ( k7_group_2 @ A @ B ) @ ( k15_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(752,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r2_hidden @ A @ ( k2_finseq_1 @ B ) )
<=> ( ( r1_xreal_0 @ np__1 @ A )
& ( r1_xreal_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_finseq_1) ).
thf(5157,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_finseq_1 @ B ) )
=> ( ( r1_xreal_0 @ np__1 @ A )
& ( r1_xreal_0 @ A @ B ) ) )
& ( ( ( r1_xreal_0 @ np__1 @ A )
& ( r1_xreal_0 @ A @ B ) )
=> ( r2_hidden @ A @ ( k2_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(732,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ B ) @ ( k3_group_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_group_4) ).
thf(5012,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ B ) @ ( k3_group_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1031,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) )
= ( k11_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_group_4) ).
thf(6296,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) )
= ( k11_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(746,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(5142,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(64,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(2093,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)],[64]) ).
thf(1664,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_rlvect_1 @ C @ ( k2_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_group_2) ).
thf(9252,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_rlvect_1 @ C @ ( k2_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(1134,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ D ) @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_group_2) ).
thf(6884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ D ) @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(850,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(5540,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)],[850]) ).
thf(539,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(4172,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)],[539]) ).
thf(658,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(4700,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)],[658]) ).
thf(1295,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(7674,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)],[1295]) ).
thf(1224,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(7321,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(1741,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_group_3 @ A @ B @ C )
!= k1_xboole_0 )
<=> ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_group_3) ).
thf(9472,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k3_group_3 @ A @ B @ C )
!= k1_xboole_0 )
=> ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) )
& ( ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
=> ( ( k3_group_3 @ A @ B @ C )
!= k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(1763,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(9556,plain,
! [A: $i] :
( ( r1_setfam_1 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_group_6 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_group_6) ).
thf(5174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_group_6 @ A @ B @ C @ D @ E )
= ( k5_relat_1 @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1467,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( v1_int_1 @ C )
=> ( ( ( k2_xcmplx_0 @ B @ A )
= C )
=> ( r1_xreal_0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_int_1) ).
thf(8508,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( v1_int_1 @ C )
=> ( ( ( k2_xcmplx_0 @ B @ A )
= C )
=> ( r1_xreal_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(1213,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k13_group_2 @ A @ ( k5_group_2 @ A ) @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
& ( ( k12_group_2 @ A @ ( k5_group_2 @ A ) @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_group_2) ).
thf(7254,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k13_group_2 @ A @ ( k5_group_2 @ A ) @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
& ( ( k12_group_2 @ A @ ( k5_group_2 @ A ) @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1263,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ B )
= ( a_2_0_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_group_2) ).
thf(7533,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ B )
= ( a_2_0_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(550,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(4216,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)],[550]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( B = np__1 )
& ( A = np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finseq_3) ).
thf(4323,plain,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( B = np__1 )
& ( A = np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k17_group_2 @ A @ ( k6_group_2 @ A ) )
= np__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_group_2) ).
thf(9571,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k17_group_2 @ A @ ( k6_group_2 @ A ) )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(347,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(3301,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1191,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k8_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k8_group_3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_group_3) ).
thf(7179,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k8_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k8_group_3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(348,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(3303,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)],[348]) ).
thf(1495,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= ( k4_card_1 @ C ) ) )
& ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( k15_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= ( k4_card_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_group_2) ).
thf(8640,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= ( k4_card_1 @ C ) ) )
& ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( k15_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= ( k4_card_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(588,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(4407,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)],[588]) ).
thf(152,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(2473,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)],[152]) ).
thf(900,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(5751,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1304,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(7725,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)],[1304]) ).
thf(1729,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_group_3 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_group_3) ).
thf(9440,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_group_3 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(72,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(2118,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)],[72]) ).
thf(1090,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k11_group_2 @ A @ C @ B ) )
= ( k11_group_2 @ A @ C @ ( k10_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_group_2) ).
thf(6588,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k11_group_2 @ A @ C @ B ) )
= ( k11_group_2 @ A @ C @ ( k10_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(956,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v1_group_3 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_3 @ A @ B @ C )
= ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_group_3) ).
thf(5968,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_group_3 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_3 @ A @ B @ C )
= ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_3 @ A @ B @ C )
= ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) ) ) )
=> ( v1_group_3 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1331,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D
= ( k2_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k5_group_4 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_latsubgr) ).
thf(7885,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( D
= ( k2_xboole_0 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k5_group_4 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_3) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(1589,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_group_3 @ A @ B @ C )
=> ( r1_group_3 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_group_3) ).
thf(8959,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_group_3 @ A @ B @ C )
=> ( r1_group_3 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_group_2 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_2) ).
thf(7019,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_group_2 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_group_1 @ B @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_group_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(497,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(3995,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(55,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(2047,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)],[55]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ ( k6_group_3 @ B @ D @ C ) @ A )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_group_3) ).
thf(5562,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r1_rlvect_1 @ ( k6_group_3 @ B @ D @ C ) @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) )
=> ( r1_rlvect_1 @ ( k6_group_3 @ B @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(351,axiom,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(3318,plain,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1602,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( m1_group_2 @ A @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_group_2) ).
thf(9009,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( m1_group_2 @ A @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(1130,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k12_group_2 @ A @ B @ C ) @ ( k13_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_group_3) ).
thf(6865,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k12_group_2 @ A @ B @ C ) @ ( k13_group_2 @ A @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k12_group_2 @ A @ B @ C ) @ ( k13_group_2 @ A @ B @ C ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(213,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(2737,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)],[213]) ).
thf(1609,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( ( v1_finset_1 @ ( k15_group_2 @ A @ B ) )
& ( v1_finset_1 @ ( k14_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_group_2) ).
thf(9041,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( ( v1_finset_1 @ ( k15_group_2 @ A @ B ) )
& ( v1_finset_1 @ ( k14_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(245,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 ) )
=> ( ( k1_funct_4 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_4) ).
thf(2905,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 ) )
=> ( ( k1_funct_4 @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(17,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(1868,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)],[17]) ).
thf(378,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(3418,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)],[378]) ).
thf(984,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k7_group_6 @ A @ B @ ( k1_group_1 @ ( k6_group_6 @ A @ B ) @ C @ D ) )
= ( k2_group_2 @ A @ ( k7_group_6 @ A @ B @ C ) @ ( k7_group_6 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_group_6) ).
thf(6092,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k7_group_6 @ A @ B @ ( k1_group_1 @ ( k6_group_6 @ A @ B ) @ C @ D ) )
= ( k2_group_2 @ A @ ( k7_group_6 @ A @ B @ C ) @ ( k7_group_6 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(427,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(3679,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)],[427]) ).
thf(1758,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k5_group_2 @ A ) @ B ) @ B )
& ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ ( k5_group_2 @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_group_4) ).
thf(9544,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k5_group_2 @ A ) @ B ) @ B )
& ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ ( k5_group_2 @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(1007,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_group_1) ).
thf(6200,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k3_xcmplx_0 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1744,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( l1_group_1 @ ( k6_group_6 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_group_6) ).
thf(9488,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( l1_group_1 @ ( k6_group_6 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1760,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k4_group_6 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_group_6) ).
thf(9549,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k4_group_6 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(187,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(2596,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)],[187]) ).
thf(1231,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ ( k4_group_3 @ A @ C @ B ) @ ( k8_group_3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_group_3) ).
thf(7353,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ ( k4_group_3 @ A @ C @ B ) @ ( k8_group_3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(786,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(5266,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(495,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(3989,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(681,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_group_6) ).
thf(4785,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(599,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(4449,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(536,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(4160,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)],[536]) ).
thf(1088,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__1 @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_group_1) ).
thf(6582,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__1 @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(1629,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(9105,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(195,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ B ) )
= ( k4_card_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_finseq_3) ).
thf(2673,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r1_tarski @ B @ ( k2_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ B ) )
= ( k4_card_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(897,axiom,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(5734,plain,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_2) ).
thf(7042,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(883,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v2_group_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k2_group_1 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_1) ).
thf(5670,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v2_group_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( B
= ( k2_group_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(176,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(2560,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)],[176]) ).
thf(963,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ B ) )
=> ( ( D
= ( k13_group_6 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_group_6) ).
thf(6000,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ B ) )
=> ( ( ( D
= ( k13_group_6 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ A ) ) ) )
& ( ( ( u1_struct_0 @ D )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ A ) ) )
=> ( D
= ( k13_group_6 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1380,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(8091,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)],[1380]) ).
thf(843,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(5512,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)],[843]) ).
thf(700,axiom,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(4878,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1116,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
<=> ( ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_group_1) ).
thf(6773,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
=> ( ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k3_group_1 @ A @ B ) ) ) )
& ( ( ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k3_group_1 @ A @ B ) ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(735,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5044,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1358,axiom,
? [A: $i] : ( l2_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(7994,plain,
? [A: $i] : ( l2_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(1563,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ B @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( B
= ( k1_latsubgr @ A ) )
<=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( u1_struct_0 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
thf(8856,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m2_relset_1 @ B @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( B
= ( k1_latsubgr @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( u1_struct_0 @ C ) ) ) )
& ( ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( u1_struct_0 @ C ) ) )
=> ( B
= ( k1_latsubgr @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(892,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(5719,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)],[892]) ).
thf(440,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(3742,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)],[440]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( k1_funct_4 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
= ( k6_partfun1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_4) ).
thf(4344,plain,
! [A: $i,B: $i] :
( ( k1_funct_4 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
= ( k6_partfun1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(517,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( r1_rlvect_1 @ ( k8_group_4 @ A @ C @ D ) @ B )
<=> ? [E: $i] :
( ( m2_finseq_1 @ E @ ( u1_struct_0 @ A ) )
& ? [F: $i] :
( ( m2_finseq_1 @ F @ k4_numbers )
& ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ F ) )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ D ) ) )
& ( B
= ( k3_group_4 @ A @ ( k4_group_4 @ A @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_group_4) ).
thf(4091,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( r1_rlvect_1 @ ( k8_group_4 @ A @ C @ D ) @ B )
=> ? [E: $i] :
( ( m2_finseq_1 @ E @ ( u1_struct_0 @ A ) )
& ? [F: $i] :
( ( m2_finseq_1 @ F @ k4_numbers )
& ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ F ) )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ D ) ) )
& ( B
= ( k3_group_4 @ A @ ( k4_group_4 @ A @ F @ E ) ) ) ) ) )
& ( ? [E: $i] :
( ( m2_finseq_1 @ E @ ( u1_struct_0 @ A ) )
& ? [F: $i] :
( ( m2_finseq_1 @ F @ k4_numbers )
& ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ F ) )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ D ) ) )
& ( B
= ( k3_group_4 @ A @ ( k4_group_4 @ A @ F @ E ) ) ) ) )
=> ( r1_rlvect_1 @ ( k8_group_4 @ A @ C @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(901,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(5754,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)],[901]) ).
thf(990,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( a_2_2_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_group_3) ).
thf(6107,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( a_2_2_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(460,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(3816,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)],[460]) ).
thf(1046,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k2_group_1 @ A ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_group_3) ).
thf(6356,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k2_group_1 @ A ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(934,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(5893,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)],[934]) ).
thf(1517,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k14_group_2 @ A @ ( k5_group_2 @ A ) )
= ( a_1_0_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_group_2) ).
thf(8714,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k14_group_2 @ A @ ( k5_group_2 @ A ) )
= ( a_1_0_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(692,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(4836,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)],[692]) ).
thf(862,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_group_3 @ A @ B @ C )
=> ( r3_group_3 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_group_3) ).
thf(5594,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_group_3 @ A @ B @ C )
=> ( r3_group_3 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1209,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(7244,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)],[1209]) ).
thf(1271,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k4_group_2 @ A @ C @ B ) )
= ( k4_group_2 @ A @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_group_2) ).
thf(7565,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k4_group_2 @ A @ C @ B ) )
= ( k4_group_2 @ A @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(1246,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k3_group_4 @ B @ ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ C ) )
= ( k6_group_1 @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_group_4) ).
thf(7449,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k3_group_4 @ B @ ( k1_finsop_1 @ ( u1_struct_0 @ B ) @ A @ C ) )
= ( k6_group_1 @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1674,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_group_6 @ A @ B )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_group_6) ).
thf(9277,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_group_6 @ A @ B )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(1284,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(7625,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)],[1284]) ).
thf(1559,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k2_latsubgr @ A @ B ) )
& ( m1_group_2 @ ( k2_latsubgr @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_latsubgr) ).
thf(8847,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k2_latsubgr @ A @ B ) )
& ( m1_group_2 @ ( k2_latsubgr @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(1621,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k9_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_3) ).
thf(9080,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k9_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(944,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r3_group_3 @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_group_3) ).
thf(5936,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r3_group_3 @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(26,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(1910,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)],[26]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).
thf(3799,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1669,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k2_group_1 @ B )
= ( k2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_2) ).
thf(9264,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k2_group_1 @ B )
= ( k2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1508,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_3 @ A @ ( k5_group_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_group_3) ).
thf(8683,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_3 @ A @ ( k5_group_2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(1708,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ ( k7_group_2 @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_group_4) ).
thf(9380,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ ( k7_group_2 @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(1206,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(7237,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1103,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ~ ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( v1_finset_1 @ D )
=> ~ ( ( D = C )
& ( ( k4_card_1 @ D )
= A )
& ! [E: $i] :
( ( r2_hidden @ E @ B )
=> ( ( C = E )
| ( ( r2_wellord2 @ C @ E )
& ( r1_xboole_0 @ C @ E ) ) ) ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k3_tarski @ B ) )
& ( ( k4_card_1 @ C )
= ( k2_nat_1 @ A @ ( k4_card_1 @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_group_2) ).
thf(6646,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ~ ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( v1_finset_1 @ D )
=> ~ ( ( D = C )
& ( ( k4_card_1 @ D )
= A )
& ! [E: $i] :
( ( r2_hidden @ E @ B )
=> ( ( C = E )
| ( ( r2_wellord2 @ C @ E )
& ( r1_xboole_0 @ C @ E ) ) ) ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k3_tarski @ B ) )
& ( ( k4_card_1 @ C )
= ( k2_nat_1 @ A @ ( k4_card_1 @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1033,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(6303,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)],[1033]) ).
thf(1632,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k8_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k16_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_group_6) ).
thf(9113,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k8_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k16_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1548,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_group_3 @ A @ B @ C )
=> ( r2_group_3 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_group_3) ).
thf(8810,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_group_3 @ A @ B @ C )
=> ( r2_group_3 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(328,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(3191,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)],[328]) ).
thf(1147,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_group_3 @ A @ B @ C )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_group_3) ).
thf(6926,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_group_3 @ A @ B @ C )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_group_3 @ A @ B @ C )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1353,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( v6_group_1 @ ( k6_group_6 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_group_6) ).
thf(7977,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( v6_group_1 @ ( k6_group_6 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1587,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] :
( ( m1_group_2 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v2_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v1_group_3 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_3) ).
thf(8948,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] :
( ( m1_group_2 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v2_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v1_group_3 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(839,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(5492,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)],[839]) ).
thf(1762,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( v1_group_3 @ ( k9_group_2 @ A @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_group_3) ).
thf(9554,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( v1_group_3 @ ( k9_group_2 @ A @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(1556,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_1) ).
thf(8832,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(1504,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_group_1) ).
thf(8672,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(1579,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k4_group_2 @ A @ ( k3_group_1 @ A @ B ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_group_2) ).
thf(8920,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k4_group_2 @ A @ ( k3_group_1 @ A @ B ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(531,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k2_group_4 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_4) ).
thf(4140,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k2_group_4 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1475,axiom,
? [A: $i] :
( ( r1_tarski @ A @ ( k1_group_3 @ f1_s2_group_4 ) )
& ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ f1_s2_group_4 ) )
=> ( ( r2_hidden @ B @ A )
<=> ( p1_s2_group_4 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_group_4) ).
thf(8540,plain,
? [A: $i] :
( ( r1_tarski @ A @ ( k1_group_3 @ f1_s2_group_4 ) )
& ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ f1_s2_group_4 ) )
=> ( ( ( r2_hidden @ B @ A )
=> ( p1_s2_group_4 @ B ) )
& ( ( p1_s2_group_4 @ B )
=> ( r2_hidden @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1541,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v3_realset2 @ A )
=> ( ( k5_group_2 @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_group_6) ).
thf(8788,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v3_realset2 @ A )
=> ( ( k5_group_2 @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(1439,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(8371,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)],[1439]) ).
thf(194,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(2670,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)],[194]) ).
thf(458,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).
thf(3810,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) )
& ( ( r1_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1268,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) )
& ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_group_2) ).
thf(7555,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) )
& ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(1752,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_2 @ A @ B )
= ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_group_2) ).
thf(9512,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_2 @ A @ B )
= ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(1274,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(7576,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)],[1274]) ).
thf(1654,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_3 @ ( k8_group_4 @ A @ B @ C ) @ A )
& ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_group_4) ).
thf(9190,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_3 @ ( k8_group_4 @ A @ B @ C ) @ A )
& ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(1514,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ D )
<=> ( r1_rlvect_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_group_2) ).
thf(8700,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r1_group_2 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ B @ D )
=> ( r1_rlvect_1 @ C @ D ) )
& ( ( r1_rlvect_1 @ C @ D )
=> ( r1_rlvect_1 @ B @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ B @ D )
=> ( r1_rlvect_1 @ C @ D ) )
& ( ( r1_rlvect_1 @ C @ D )
=> ( r1_rlvect_1 @ B @ D ) ) ) )
=> ( r1_group_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_finseq_3) ).
thf(4585,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) ) )
& ( ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1424,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(8270,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)],[1424]) ).
thf(1615,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ B )
& ( ( k9_group_1 @ B )
= np__1 ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_2) ).
thf(9058,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ B )
& ( ( k9_group_1 @ B )
= np__1 ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(377,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(3403,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)],[377]) ).
thf(666,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).
thf(4725,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(301,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(3090,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)],[301]) ).
thf(1496,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k5_group_3 @ A @ C @ B ) @ ( k2_group_2 @ A @ ( k4_group_2 @ A @ B @ ( k1_group_2 @ A @ C ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_group_3) ).
thf(8651,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k5_group_3 @ A @ C @ B ) @ ( k2_group_2 @ A @ ( k4_group_2 @ A @ B @ ( k1_group_2 @ A @ C ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(178,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(2565,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)],[178]) ).
thf(1585,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k14_group_2 @ A @ B )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t173_group_2) ).
thf(8942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k14_group_2 @ A @ B )
= ( k1_tarski @ ( u1_struct_0 @ A ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(1060,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(6427,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)],[1060]) ).
thf(758,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(5177,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)],[758]) ).
thf(360,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(3349,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)],[360]) ).
thf(22,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r6_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).
thf(1888,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r6_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
=> ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1561,axiom,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
thf(8852,plain,
! [A: $i] : ( m1_ordinal1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(1364,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k10_group_4 @ A ) )
& ( v1_funct_2 @ ( k10_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ ( k10_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_group_4) ).
thf(8021,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k10_group_4 @ A ) )
& ( v1_funct_2 @ ( k10_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ ( k10_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1151,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(6972,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)],[1151]) ).
thf(960,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( F
= ( k2_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) )
=> ( ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( u1_struct_0 @ ( k8_group_4 @ A @ C @ D ) ) )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( u1_struct_0 @ ( k5_group_4 @ A @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_latsubgr) ).
thf(5988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( F
= ( k2_xboole_0 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ D ) ) )
=> ( ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( u1_struct_0 @ ( k8_group_4 @ A @ C @ D ) ) )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ ( u1_struct_0 @ ( k5_group_4 @ A @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(854,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(5551,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)],[854]) ).
thf(411,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(3546,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)],[411]) ).
thf(1126,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 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_4) ).
thf(6833,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 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1836,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1638,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r6_group_3 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r6_group_3) ).
thf(9132,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r6_group_3 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(1591,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v5_group_1 @ ( k2_group_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_1) ).
thf(8964,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ~ ( v5_group_1 @ ( k2_group_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(764,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(5201,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)],[764]) ).
thf(1278,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(7591,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)],[1278]) ).
thf(670,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(4740,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)],[670]) ).
thf(288,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ~ ( r1_xreal_0 @ np__0 @ A )
=> ( r1_xreal_0 @ A @ ( k1_real_1 @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_int_1) ).
thf(3050,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ~ ( r1_xreal_0 @ np__0 @ A )
=> ( r1_xreal_0 @ A @ ( k1_real_1 @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(172,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(2547,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)],[172]) ).
thf(119,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(2313,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)],[119]) ).
thf(1679,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k15_group_2 @ A @ ( k5_group_2 @ A ) )
= ( a_1_0_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_group_2) ).
thf(9291,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k15_group_2 @ A @ ( k5_group_2 @ A ) )
= ( a_1_0_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(1333,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_group_2 @ E @ B )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ! [G: $i] :
( ( m1_group_2 @ G @ A )
=> ( ( ( ( u1_struct_0 @ F )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ B @ E ) )
=> ( m1_group_6 @ F @ A @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_latsubgr) ).
thf(7891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_group_2 @ E @ B )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ! [G: $i] :
( ( m1_group_2 @ G @ A )
=> ( ( ( ( u1_struct_0 @ F )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k3_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ B @ E ) )
=> ( m1_group_6 @ F @ A @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(519,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(4104,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(791,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k11_group_2 @ A @ C @ ( k7_group_2 @ A @ D ) ) @ B )
= ( k11_group_2 @ A @ C @ ( k11_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_group_2) ).
thf(5285,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k11_group_2 @ A @ C @ ( k7_group_2 @ A @ D ) ) @ B )
= ( k11_group_2 @ A @ C @ ( k11_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(1375,axiom,
? [A: $i] : ( v1_int_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_int_1) ).
thf(8073,plain,
? [A: $i] : ( v1_int_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1299,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k14_group_2 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k12_group_2 @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_group_2) ).
thf(7686,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( C
= ( k14_group_2 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k12_group_2 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k12_group_2 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k12_group_2 @ A @ B @ E ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k12_group_2 @ A @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k14_group_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(222,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(2769,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)],[222]) ).
thf(770,axiom,
r1_tarski @ k5_numbers @ k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).
thf(5221,plain,
r1_tarski @ k5_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(653,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(4668,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)],[653]) ).
thf(1112,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( k2_group_3 @ A @ ( k6_group_1 @ A @ D @ B ) @ C )
= ( k6_group_1 @ A @ D @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_group_3) ).
thf(6691,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( k2_group_3 @ A @ ( k6_group_1 @ A @ D @ B ) @ C )
= ( k6_group_1 @ A @ D @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1431,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(8319,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)],[1431]) ).
thf(644,axiom,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(4636,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(162,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(2509,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)],[162]) ).
thf(191,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(2631,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)],[191]) ).
thf(693,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(4840,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)],[693]) ).
thf(740,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(5081,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1145,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(6919,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)],[1145]) ).
thf(1255,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) )
= ( k13_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_group_2) ).
thf(7486,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) )
= ( k13_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(491,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(3968,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)],[491]) ).
thf(979,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(6075,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)],[979]) ).
thf(1572,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k16_group_2 @ A @ ( k5_group_2 @ A ) )
= ( k8_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t182_group_2) ).
thf(8895,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k16_group_2 @ A @ ( k5_group_2 @ A ) )
= ( k8_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_group_2 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_2) ).
thf(7346,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_group_2 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A
= ( k6_domain_1 @ ( u1_struct_0 @ B ) @ C ) ) )
=> ( r2_hidden @ A @ ( a_1_0_group_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(29,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(1936,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)],[29]) ).
thf(1457,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(8462,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)],[1457]) ).
thf(1512,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ( ( m1_group_2 @ A @ B )
& ( m1_group_2 @ B @ C ) )
=> ( m1_group_2 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_group_2) ).
thf(8694,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ( ( m1_group_2 @ A @ B )
& ( m1_group_2 @ B @ C ) )
=> ( m1_group_2 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(116,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(2300,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)],[116]) ).
thf(452,axiom,
! [A: $i] :
? [B: $i] : ( m1_finseq_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_1) ).
thf(3784,plain,
! [A: $i] :
? [B: $i] : ( m1_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(392,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(3467,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(871,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(5626,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)],[871]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k5_group_3 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_3) ).
thf(6413,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k5_group_3 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( k5_group_3 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(451,axiom,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(3782,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(938,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k9_group_2 @ A @ C @ D ) @ B ) @ ( k9_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k6_group_3 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_group_3) ).
thf(5904,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k9_group_2 @ A @ C @ D ) @ B ) @ ( k9_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k6_group_3 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1226,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
<=> ( r1_xreal_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_card_1) ).
thf(7329,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) )
=> ( r1_xreal_0 @ A @ B ) )
& ( ( r1_xreal_0 @ A @ B )
=> ( r1_tarski @ ( k1_card_1 @ A ) @ ( k1_card_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(891,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ~ ( ~ ( r1_xreal_0 @ B @ A )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ~ ( ( C
= ( k6_xcmplx_0 @ B @ A ) )
& ( r1_xreal_0 @ np__1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_int_1) ).
thf(5714,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ~ ( ~ ( r1_xreal_0 @ B @ A )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ~ ( ( C
= ( k6_xcmplx_0 @ B @ A ) )
& ( r1_xreal_0 @ np__1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1107,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k13_group_2 @ A @ D @ B ) @ C )
= ( k11_group_2 @ A @ D @ ( k3_group_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_group_3) ).
thf(6677,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k13_group_2 @ A @ D @ B ) @ C )
= ( k11_group_2 @ A @ D @ ( k3_group_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1429,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(8314,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)],[1429]) ).
thf(83,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 @ ( k1_funct_4 @ A @ B ) ) )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_4) ).
thf(2157,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 @ ( k1_funct_4 @ A @ B ) ) )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1642,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r5_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_group_2 @ A @ C @ ( k6_group_3 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_group_3) ).
thf(9145,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r5_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_group_2 @ A @ C @ ( k6_group_3 @ A @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_group_2 @ A @ C @ ( k6_group_3 @ A @ B @ D ) ) )
=> ( r5_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(308,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(3122,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)],[308]) ).
thf(1201,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_3 @ A @ B ) @ C )
= ( k2_group_2 @ A @ C @ ( k7_group_3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_group_3) ).
thf(7205,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_3 @ A @ B ) @ C )
= ( k2_group_2 @ A @ C @ ( k7_group_3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1039,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ D @ C )
=> ( r1_rlvect_1 @ D @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_group_4) ).
thf(6335,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ D @ C )
=> ( r1_rlvect_1 @ D @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1211,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( v1_int_1 @ D )
=> ( ( k2_group_3 @ A @ ( k6_group_1 @ A @ D @ B ) @ C )
= ( k6_group_1 @ A @ D @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_group_3) ).
thf(7249,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( v1_int_1 @ D )
=> ( ( k2_group_3 @ A @ ( k6_group_1 @ A @ D @ B ) @ C )
= ( k6_group_1 @ A @ D @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(619,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(4512,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)],[619]) ).
thf(730,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(5006,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)],[730]) ).
thf(722,axiom,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(4974,plain,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1701,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ B @ D )
= C ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ D @ B )
= C ) ) ) ) ) )
=> ( ( v4_group_1 @ A )
& ( v3_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_group_1) ).
thf(9355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ B @ D )
= C ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ D @ B )
= C ) ) ) ) ) )
=> ( ( v4_group_1 @ A )
& ( v3_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(1362,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(8009,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)],[1362]) ).
thf(230,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(2841,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)],[230]) ).
thf(1005,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(6195,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1428,axiom,
! [A: $i] :
( ( A = k4_numbers )
<=> ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ~ ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( B != C )
& ( B
!= ( k1_real_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_int_1) ).
thf(8282,plain,
! [A: $i] :
( ( ( A = k4_numbers )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ~ ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( B != C )
& ( B
!= ( k1_real_1 @ C ) ) ) ) )
& ( ~ ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( B != C )
& ( B
!= ( k1_real_1 @ C ) ) ) )
=> ( r2_hidden @ B @ A ) ) ) )
& ( ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ~ ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( B != C )
& ( B
!= ( k1_real_1 @ C ) ) ) ) )
& ( ~ ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( B != C )
& ( B
!= ( k1_real_1 @ C ) ) ) )
=> ( r2_hidden @ B @ A ) ) )
=> ( A = k4_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(1283,axiom,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
thf(7623,plain,
! [A: $i] :
? [B: $i] : ( m1_ordinal1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(267,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_4) ).
thf(2973,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(610,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(4486,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)],[610]) ).
thf(1092,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_6 @ A @ B @ C ) @ ( k7_group_6 @ A @ B @ D ) )
= ( k1_group_1 @ ( k6_group_6 @ A @ B ) @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_group_6) ).
thf(6603,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k2_group_2 @ A @ ( k7_group_6 @ A @ B @ C ) @ ( k7_group_6 @ A @ B @ D ) )
= ( k1_group_1 @ ( k6_group_6 @ A @ B ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1189,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ ( k12_group_2 @ A @ C @ B ) @ ( k4_group_6 @ A @ C ) )
& ( r2_hidden @ ( k13_group_2 @ A @ C @ B ) @ ( k4_group_6 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_group_6) ).
thf(7173,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ ( k12_group_2 @ A @ C @ B ) @ ( k4_group_6 @ A @ C ) )
& ( r2_hidden @ ( k13_group_2 @ A @ C @ B ) @ ( k4_group_6 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1067,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(6459,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)],[1067]) ).
thf(997,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_int_1) ).
thf(6133,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1238,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ( v6_group_1 @ C )
& ! [D: $i] :
( ( v1_finset_1 @ D )
=> ! [E: $i] :
( ( v1_finset_1 @ E )
=> ~ ( ( D
= ( k12_group_2 @ A @ C @ B ) )
& ( E
= ( k13_group_2 @ A @ C @ B ) )
& ( ( k9_group_1 @ C )
= ( k4_card_1 @ D ) )
& ( ( k9_group_1 @ C )
= ( k4_card_1 @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_group_2) ).
thf(7389,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ( v6_group_1 @ C )
& ! [D: $i] :
( ( v1_finset_1 @ D )
=> ! [E: $i] :
( ( v1_finset_1 @ E )
=> ~ ( ( D
= ( k12_group_2 @ A @ C @ B ) )
& ( E
= ( k13_group_2 @ A @ C @ B ) )
& ( ( k9_group_1 @ C )
= ( k4_card_1 @ D ) )
& ( ( k9_group_1 @ C )
= ( k4_card_1 @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(205,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(2709,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)],[205]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_group_2 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_2) ).
thf(5577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_group_2 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_group_2 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(912,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ B @ ( k4_group_6 @ A @ C ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_group_6) ).
thf(5798,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ B @ ( k4_group_6 @ A @ C ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1582,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( m1_group_2 @ ( k5_group_2 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_group_2) ).
thf(8931,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( m1_group_2 @ ( k5_group_2 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(1369,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_group_3 @ A @ ( k7_group_2 @ A @ ( k6_group_2 @ A ) ) @ B )
= ( a_2_0_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_group_3) ).
thf(8041,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_group_3 @ A @ ( k7_group_2 @ A @ ( k6_group_2 @ A ) ) @ B )
= ( a_2_0_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1596,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k2_group_3 @ A @ D @ C ) )
=> ( B = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_group_3) ).
thf(8984,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k2_group_3 @ A @ D @ C ) )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(1363,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_group_1) ).
thf(8016,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_1 @ A @ B )
= ( k3_group_1 @ A @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_group_1) ).
thf(9576,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_1 @ A @ B )
= ( k3_group_1 @ A @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( l1_struct_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_subset_1 @ D @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g4_vectsp_1 @ A @ B @ C @ D @ E )
= ( g4_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_g4_vectsp_1) ).
thf(3518,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( l1_struct_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_subset_1 @ D @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( g4_vectsp_1 @ A @ B @ C @ D @ E )
= ( g4_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)],[405]) ).
thf(1568,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k5_group_2 @ A ) @ B ) @ ( k5_group_2 @ A ) )
& ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ ( k5_group_2 @ A ) ) @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_group_2) ).
thf(8884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k5_group_2 @ A ) @ B ) @ ( k5_group_2 @ A ) )
& ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ ( k5_group_2 @ A ) ) @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(210,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(2724,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k7_rlvect_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_group_4) ).
thf(4930,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k7_rlvect_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(932,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(5889,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)],[932]) ).
thf(1259,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(7513,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)],[1259]) ).
thf(338,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v6_group_1 @ A )
<=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_1) ).
thf(3237,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_finset_1 @ ( u1_struct_0 @ A ) )
=> ( v6_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1692,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v4_group_6 @ ( k11_group_6 @ A @ ( k5_group_2 @ A ) ) @ A @ ( k6_group_6 @ A @ ( k5_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_group_6) ).
thf(9333,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v4_group_6 @ ( k11_group_6 @ A @ ( k5_group_2 @ A ) ) @ A @ ( k6_group_6 @ A @ ( k5_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(1500,axiom,
! [A: $i,B: $i] : ( r1_setfam_1 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_setfam_1) ).
thf(8662,plain,
! [A: $i] : ( r1_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(1778,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( D
= ( k6_group_3 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( k4_group_3 @ A @ ( k7_group_2 @ A @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_group_3) ).
thf(9603,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( D
= ( k6_group_3 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k4_group_3 @ A @ ( k7_group_2 @ A @ B ) @ C ) ) )
& ( ( ( u1_struct_0 @ D )
= ( k4_group_3 @ A @ ( k7_group_2 @ A @ B ) @ C ) )
=> ( D
= ( k6_group_3 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_finseq_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_group_4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_4) ).
thf(4109,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_finseq_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_group_4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1250,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
<=> ( r2_hidden @ A @ k4_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_int_1) ).
thf(7468,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)],[1250]) ).
thf(110,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(2268,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1550,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r2_group_6 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_group_6) ).
thf(8815,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r2_group_6 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(551,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(4219,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)],[551]) ).
thf(292,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_vectsp_1) ).
thf(3060,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(300,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(3087,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)],[300]) ).
thf(1002,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(6175,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)],[1002]) ).
thf(556,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(4276,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)],[556]) ).
thf(276,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(3000,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)],[276]) ).
thf(1750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_card_1 @ ( k8_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_1) ).
thf(9508,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_card_1 @ ( k8_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(1796,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k9_group_2 @ A @ B @ C ) @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_group_4) ).
thf(9667,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k9_group_2 @ A @ B @ C ) @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(1711,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( u1_struct_0 @ ( k6_group_6 @ A @ B ) )
= ( k4_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_group_6) ).
thf(9387,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( u1_struct_0 @ ( k6_group_6 @ A @ B ) )
= ( k4_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(1360,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ B )
& ( ( u1_struct_0 @ E )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_latsubgr) ).
thf(7998,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ B )
& ( ( u1_struct_0 @ E )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(803,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) )
<=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_group_2) ).
thf(5337,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) )
=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) ) )
& ( ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) )
=> ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(173,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(2551,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)],[173]) ).
thf(602,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k5_subset_1 @ k5_numbers @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) ) )
=> ( r1_xreal_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finseq_1) ).
thf(4457,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( k2_finseq_1 @ A )
= ( k5_subset_1 @ k5_numbers @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) ) )
=> ( r1_xreal_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1788,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ? [C: $i] : ( m1_group_6 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_group_6) ).
thf(9645,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ? [C: $i] : ( m1_group_6 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(1754,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k7_group_4 @ A @ B @ C ) )
= ( k11_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_4) ).
thf(9530,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k7_group_4 @ A @ B @ C ) )
= ( k11_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(1032,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(6299,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)],[1032]) ).
thf(1767,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k11_group_4 @ A ) )
= ( k1_group_3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_group_4) ).
thf(9566,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k11_group_4 @ A ) )
= ( k1_group_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(569,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_group_4) ).
thf(4320,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k12_group_6 @ A @ B @ C ) )
& ( v1_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v2_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v3_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v4_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k12_group_6 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_group_6) ).
thf(7101,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v3_struct_0 @ ( k12_group_6 @ A @ B @ C ) )
& ( v1_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v2_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v3_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v4_group_1 @ ( k12_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k12_group_6 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(572,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( k2_vectsp_1 @ A )
= ( u1_vectsp_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_vectsp_1) ).
thf(4333,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( k2_vectsp_1 @ A )
= ( u1_vectsp_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(946,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(5941,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)],[946]) ).
thf(449,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 ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(3775,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 ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(315,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(3141,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)],[315]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_rlvect_1 @ A @ B @ C )
= ( k10_finseq_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_rlvect_1) ).
thf(3952,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_rlvect_1 @ A @ B @ C )
= ( k10_finseq_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1171,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) )
<=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_group_2) ).
thf(7091,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) )
=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) )
& ( ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ B ) ) )
=> ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1476,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( v3_realset2 @ A )
<=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_6) ).
thf(8544,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( ( v3_realset2 @ A )
=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) )
& ( ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(240,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(2877,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)],[240]) ).
thf(1492,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( a_1_0_group_6 @ A ) )
=> ( r1_group_2 @ A @ ( k9_group_5 @ A ) @ ( k5_group_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_group_6) ).
thf(8631,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( a_1_0_group_6 @ A ) )
=> ( r1_group_2 @ A @ ( k9_group_5 @ A ) @ ( k5_group_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(1557,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ D @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_group_1) ).
thf(8835,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ D @ B )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(1195,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__0 @ B )
= ( k2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_group_1) ).
thf(7189,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ np__0 @ B )
= ( k2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ B @ ( k2_group_5 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_group_6) ).
thf(9640,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ B @ ( k2_group_5 @ A @ C @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ B @ ( k2_group_5 @ A @ C @ D ) ) ) )
=> ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(1150,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= np__2 ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_group_3) ).
thf(6967,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= np__2 ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1794,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( k6_group_3 @ A @ C @ B )
= A )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_group_3) ).
thf(9662,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( k6_group_3 @ A @ C @ B )
= A )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(877,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ ( k1_card_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_card_1) ).
thf(5651,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ ( k1_card_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(676,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(4772,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)],[676]) ).
thf(993,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k5_group_1 @ A ) )
& ( v1_funct_2 @ ( k5_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_1) ).
thf(6116,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k5_group_1 @ A ) )
& ( v1_funct_2 @ ( k5_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_group_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(302,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] :
( ( ( 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 )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3094,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] :
( ( ( 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 )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(594,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(4425,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)],[594]) ).
thf(961,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(5992,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)],[961]) ).
thf(1806,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_group_4) ).
thf(9714,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(1724,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= np__1 ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t181_group_2) ).
thf(9419,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k17_group_2 @ A @ B )
= np__1 ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(1422,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
| ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) )
=> ( ( B
= ( k3_group_1 @ A @ C ) )
& ( C
= ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_group_1) ).
thf(8258,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
| ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) )
=> ( ( B
= ( k3_group_1 @ A @ C ) )
& ( C
= ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(384,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(3441,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)],[384]) ).
thf(836,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k2_group_3 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_group_3) ).
thf(5464,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k2_group_3 @ A @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k2_group_3 @ A @ B @ D ) ) )
=> ( r1_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1779,axiom,
? [A: $i] : ( l1_group_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(9609,plain,
? [A: $i] : ( l1_group_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(57,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(2053,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)],[57]) ).
thf(1325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( r2_hidden @ B @ ( k7_group_2 @ A @ D ) )
& ( r2_hidden @ C @ ( k7_group_2 @ A @ D ) ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ B @ C ) @ ( k7_group_2 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_group_2) ).
thf(7841,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( r2_hidden @ B @ ( k7_group_2 @ A @ D ) )
& ( r2_hidden @ C @ ( k7_group_2 @ A @ D ) ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ B @ C ) @ ( k7_group_2 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(860,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( v4_group_6 @ D @ A @ B )
& ( v4_group_6 @ E @ B @ C ) )
=> ( v4_group_6 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_group_6) ).
thf(5588,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( v4_group_6 @ D @ A @ B )
& ( v4_group_6 @ E @ B @ C ) )
=> ( v4_group_6 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(696,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(4861,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)],[696]) ).
thf(511,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(4054,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(880,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(5662,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)],[880]) ).
thf(329,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(3194,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)],[329]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k3_finsub_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_finsub_1) ).
thf(7480,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k3_finsub_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1623,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k1_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k1_group_6 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k1_group_6 @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_6) ).
thf(9085,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k1_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k1_group_6 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k1_group_6 @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(1053,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k3_group_1 @ A @ B ) @ C )
= ( k3_group_1 @ A @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_group_3) ).
thf(6395,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k3_group_1 @ A @ B ) @ C )
= ( k3_group_1 @ A @ ( k2_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(597,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r2_hidden @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_finseq_1 @ A ) )
=> ( B = np__0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_3) ).
thf(4444,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r2_hidden @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_finseq_1 @ A ) )
=> ( B = np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(193,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 ) )
=> ( ( r3_binop_1 @ A @ B @ C )
<=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).
thf(2666,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 ) )
=> ( ( ( r3_binop_1 @ A @ B @ C )
=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) )
& ( ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) )
=> ( r3_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1459,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= D )
<=> ( B
= ( k1_group_1 @ A @ D @ ( k3_group_1 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_group_1) ).
thf(8467,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= D )
=> ( B
= ( k1_group_1 @ A @ D @ ( k3_group_1 @ A @ C ) ) ) )
& ( ( B
= ( k1_group_1 @ A @ D @ ( k3_group_1 @ A @ C ) ) )
=> ( ( k1_group_1 @ A @ B @ C )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1024,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(6271,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)],[1024]) ).
thf(1261,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(7523,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)],[1261]) ).
thf(1323,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(7821,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)],[1323]) ).
thf(815,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(5387,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)],[815]) ).
thf(978,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k12_group_2 @ A @ B @ C )
= ( k13_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_group_3) ).
thf(6065,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k12_group_2 @ A @ B @ C )
= ( k13_group_2 @ A @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k12_group_2 @ A @ B @ C )
= ( k13_group_2 @ A @ B @ C ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1667,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ B @ ( k2_group_1 @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_3) ).
thf(9260,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ B @ ( k2_group_1 @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(1293,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_group_6 @ C @ B @ A )
<=> ( r1_group_2 @ B @ ( k12_group_6 @ B @ A @ C ) @ ( k5_group_2 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_6) ).
thf(7668,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_group_6 @ C @ B @ A )
=> ( r1_group_2 @ B @ ( k12_group_6 @ B @ A @ C ) @ ( k5_group_2 @ B ) ) )
& ( ( r1_group_2 @ B @ ( k12_group_6 @ B @ A @ C ) @ ( k5_group_2 @ B ) )
=> ( v2_group_6 @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(799,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k10_group_2 @ A @ C @ B )
= ( k11_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_group_2) ).
thf(5317,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k10_group_2 @ A @ C @ B )
= ( k11_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1603,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_4 @ A @ B @ B )
= ( k7_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_group_4) ).
thf(9012,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_4 @ A @ B @ B )
= ( k7_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(1643,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k4_group_6 @ A @ B )
= ( k14_group_2 @ A @ B ) )
& ( ( k4_group_6 @ A @ B )
= ( k15_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_group_6) ).
thf(9149,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k4_group_6 @ A @ B )
= ( k14_group_2 @ A @ B ) )
& ( ( k4_group_6 @ A @ B )
= ( k15_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r2_hidden @ A @ ( k10_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r1_rlvect_1 @ D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_group_2) ).
thf(6433,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r2_hidden @ A @ ( k10_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r1_rlvect_1 @ D @ F ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r1_rlvect_1 @ D @ F ) ) )
=> ( r2_hidden @ A @ ( k10_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1011,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(6211,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)],[1011]) ).
thf(373,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(3390,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)],[373]) ).
thf(155,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(2482,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)],[155]) ).
thf(1776,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k8_group_4 @ A @ B @ C ) @ D ) @ ( k8_group_4 @ A @ B @ ( k8_group_4 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_group_4) ).
thf(9598,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ ( k8_group_4 @ A @ B @ C ) @ D ) @ ( k8_group_4 @ A @ B @ ( k8_group_4 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(7,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(1825,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)],[7]) ).
thf(949,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(5947,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)],[949]) ).
thf(1571,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ~ ( v2_group_4 @ C @ A ) )
=> ( r1_rlvect_1 @ ( k6_group_4 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_4) ).
thf(8891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ~ ( v2_group_4 @ C @ A ) )
=> ( r1_rlvect_1 @ ( k6_group_4 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(197,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(2681,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)],[197]) ).
thf(749,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(5149,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)],[749]) ).
thf(970,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 )
& ( ( k3_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_group_2) ).
thf(6033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 )
& ( ( k3_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1158,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k10_group_2 @ A @ D @ B ) @ C )
= ( k2_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_group_2) ).
thf(7014,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k10_group_2 @ A @ D @ B ) @ C )
= ( k2_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(188,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_4) ).
thf(2598,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1183,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( v1_int_1 @ C )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v3_group_1 @ D )
& ( v4_group_1 @ D )
& ( l1_group_1 @ D ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ D ) )
=> ( ( k4_group_4 @ D @ ( k3_finseq_4 @ k4_numbers @ ( k2_group_4 @ A ) @ ( k2_group_4 @ B ) @ ( k2_group_4 @ C ) ) @ ( k8_rlvect_1 @ D @ E @ F @ G ) )
= ( k8_rlvect_1 @ D @ ( k6_group_1 @ D @ A @ E ) @ ( k6_group_1 @ D @ B @ F ) @ ( k6_group_1 @ D @ C @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_group_4) ).
thf(7138,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( v1_int_1 @ C )
=> ! [D: $i] :
( ( ~ ( v3_struct_0 @ D )
& ( v3_group_1 @ D )
& ( v4_group_1 @ D )
& ( l1_group_1 @ D ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ D ) )
=> ( ( k4_group_4 @ D @ ( k3_finseq_4 @ k4_numbers @ ( k2_group_4 @ A ) @ ( k2_group_4 @ B ) @ ( k2_group_4 @ C ) ) @ ( k8_rlvect_1 @ D @ E @ F @ G ) )
= ( k8_rlvect_1 @ D @ ( k6_group_1 @ D @ A @ E ) @ ( k6_group_1 @ D @ B @ F ) @ ( k6_group_1 @ D @ C @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(362,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3354,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_struct_0 @ A )
=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_xboole_0 @ ( u1_struct_0 @ A ) )
=> ( v3_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1351,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_group_3) ).
thf(7966,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(81,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(2153,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)],[81]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( k4_finseq_1 @ ( k10_finseq_1 @ A @ B ) )
= ( k2_finseq_1 @ np__2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_3) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( k4_finseq_1 @ ( k10_finseq_1 @ A @ B ) )
= ( k2_finseq_1 @ np__2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1534,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ A )
& ( ( k17_group_2 @ A @ B )
= ( k9_group_1 @ A ) ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t184_group_2) ).
thf(8764,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ A )
& ( ( k17_group_2 @ A @ B )
= ( k9_group_1 @ A ) ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(873,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(5639,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)],[873]) ).
thf(1747,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( r1_xreal_0 @ ( k9_group_1 @ B ) @ ( k9_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_group_2) ).
thf(9498,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( r1_xreal_0 @ ( k9_group_1 @ B ) @ ( k9_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1203,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_group_3 @ A @ ( k2_group_2 @ A @ C @ D ) @ B ) @ ( k2_group_2 @ A @ ( k4_group_3 @ A @ C @ B ) @ ( k4_group_3 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_3) ).
thf(7221,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_group_3 @ A @ ( k2_group_2 @ A @ C @ D ) @ B ) @ ( k2_group_2 @ A @ ( k4_group_3 @ A @ C @ B ) @ ( k4_group_3 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(447,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(3770,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)],[447]) ).
thf(1307,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_group_1) ).
thf(7738,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(28,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(1932,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)],[28]) ).
thf(1392,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(8137,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_finseq_1) ).
thf(3222,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(409,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3540,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(158,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(2497,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)],[158]) ).
thf(664,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(4717,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)],[664]) ).
thf(1453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ D @ B @ C )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_group_6 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E )
= ( k2_group_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_6) ).
thf(8439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ D @ B @ C )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_group_6 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E )
= ( k2_group_1 @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E )
= ( k2_group_1 @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_0_group_6 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(904,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k9_group_4 @ A ) )
& ( v1_funct_2 @ ( k9_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ ( k9_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_4) ).
thf(5766,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k9_group_4 @ A ) )
& ( v1_funct_2 @ ( k9_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ ( k9_group_4 @ A ) @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1279,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_4 @ A @ ( k8_rlvect_1 @ A @ B @ C @ D ) )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D ) )
& ( ( k3_group_4 @ A @ ( k8_rlvect_1 @ A @ B @ C @ D ) )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_group_4) ).
thf(7597,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_4 @ A @ ( k8_rlvect_1 @ A @ B @ C @ D ) )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D ) )
& ( ( k3_group_4 @ A @ ( k8_rlvect_1 @ A @ B @ C @ D ) )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1161,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_rlvect_1) ).
thf(7027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(14,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(1852,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)],[14]) ).
thf(576,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(4347,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)],[576]) ).
thf(1170,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(7086,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)],[1170]) ).
thf(1482,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= B )
<=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_group_3) ).
thf(8587,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k2_group_3 @ A @ B @ C )
= B )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) )
& ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
=> ( ( k2_group_3 @ A @ B @ C )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1064,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(6450,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5823,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(307,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(3115,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)],[307]) ).
thf(1141,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k7_group_6 @ A @ B @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_group_6) ).
thf(6908,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ( ( k7_group_6 @ A @ B @ C )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_group_2) ).
thf(5217,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1538,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
<=> ( m1_group_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
thf(8775,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ B ) )
& ( ( m1_group_2 @ C @ B )
=> ( m1_group_6 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(293,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(3064,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)],[293]) ).
thf(1119,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_tarski @ ( k12_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_group_2) ).
thf(6784,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_tarski @ ( k12_group_2 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(865,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ B @ ( k8_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_group_3) ).
thf(5603,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r2_hidden @ B @ ( k8_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1395,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_subset_1 @ ( k2_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
thf(8144,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_subset_1 @ ( k2_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1394,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m2_subset_1 @ ( k9_group_1 @ A ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_1) ).
thf(8142,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m2_subset_1 @ ( k9_group_1 @ A ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_1) ).
thf(3074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(515,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(4069,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)],[515]) ).
thf(111,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(2272,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)],[111]) ).
thf(592,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(4416,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)],[592]) ).
thf(76,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(2140,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)],[76]) ).
thf(219,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(2756,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)],[219]) ).
thf(320,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(3162,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)],[320]) ).
thf(331,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( v1_int_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_int_1) ).
thf(3201,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( v1_int_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(127,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2370,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(780,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(5245,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)],[780]) ).
thf(1402,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_group_2 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) @ B )
= k1_xboole_0 )
& ( ( k2_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_group_2) ).
thf(8174,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_group_2 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) @ B )
= k1_xboole_0 )
& ( ( k2_group_2 @ A @ B @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(703,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(4889,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)],[703]) ).
thf(674,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_rlvect_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( r2_hidden @ C @ ( k2_finseq_1 @ D ) )
& ( ( k3_finseq_1 @ B )
= D ) )
=> ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_rlvect_1) ).
thf(4765,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_rlvect_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( r2_hidden @ C @ ( k2_finseq_1 @ D ) )
& ( ( k3_finseq_1 @ B )
= D ) )
=> ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(216,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(2748,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)],[216]) ).
thf(1442,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k3_group_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_group_1) ).
thf(8393,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k3_group_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(829,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) )
= ( k3_group_2 @ A @ B @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_group_2) ).
thf(5447,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) )
= ( k3_group_2 @ A @ B @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1650,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
thf(9169,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(822,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_tarski @ ( k13_group_2 @ A @ C @ ( k6_group_1 @ A @ np__2 @ B ) ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_group_2) ).
thf(5417,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_tarski @ ( k13_group_2 @ A @ C @ ( k6_group_1 @ A @ np__2 @ B ) ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_int_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_group_1) ).
thf(5887,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_int_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(42,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(1996,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)],[42]) ).
thf(1515,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k2_group_1 @ B )
= ( k2_group_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_group_2) ).
thf(8708,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k2_group_1 @ B )
= ( k2_group_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(388,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_finseq_1) ).
thf(3454,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1804,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_group_3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_3) ).
thf(9699,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_group_3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(395,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(3476,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)],[395]) ).
thf(1389,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(8127,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)],[1389]) ).
thf(533,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(4148,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)],[533]) ).
thf(192,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(2634,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)],[192]) ).
thf(1486,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(8614,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(96,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2203,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1297,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(7678,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)],[1297]) ).
thf(1800,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k6_group_4 @ A ) )
& ( m1_group_2 @ ( k6_group_4 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_group_4) ).
thf(9684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k6_group_4 @ A ) )
& ( m1_group_2 @ ( k6_group_4 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(1739,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r2_hidden @ A @ ( k1_group_3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_group_3) ).
thf(9468,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r2_hidden @ A @ ( k1_group_3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(1558,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_group_2) ).
thf(8839,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( u1_struct_0 @ D )
!= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(647,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(4644,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)],[647]) ).
thf(1409,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) )
= ( k2_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_group_3) ).
thf(8205,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) )
= ( k2_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(1166,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(7052,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)],[1166]) ).
thf(1468,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(8512,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)],[1468]) ).
thf(680,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(4782,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)],[680]) ).
thf(1671,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( r6_group_3 @ A @ C @ D )
& ( r5_group_3 @ A @ D @ B ) )
=> ( r5_group_3 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_group_3) ).
thf(9269,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( r6_group_3 @ A @ C @ D )
& ( r5_group_3 @ A @ D @ B ) )
=> ( r5_group_3 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(608,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(4476,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)],[608]) ).
thf(1610,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k9_group_2 @ A @ B @ C ) )
& ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).
thf(9044,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k9_group_2 @ A @ B @ C ) )
& ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(469,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(3856,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1447,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_group_4) ).
thf(8422,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(349,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(3306,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)],[349]) ).
thf(1427,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(8279,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)],[1427]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_2) ).
thf(7414,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k3_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(419,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( ( k3_xcmplx_0 @ A @ B )
= np__1 )
<=> ( ( ( A = np__1 )
& ( B = np__1 ) )
| ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B
= ( k1_real_1 @ np__1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_int_1) ).
thf(3592,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( ( ( k3_xcmplx_0 @ A @ B )
= np__1 )
=> ( ( ( A = np__1 )
& ( B = np__1 ) )
| ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B
= ( k1_real_1 @ np__1 ) ) ) ) )
& ( ( ( ( A = np__1 )
& ( B = np__1 ) )
| ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B
= ( k1_real_1 @ np__1 ) ) ) )
=> ( ( k3_xcmplx_0 @ A @ B )
= np__1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(823,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k8_group_4 @ A @ B @ C )
= ( k5_group_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_group_4) ).
thf(5419,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k8_group_4 @ A @ B @ C )
= ( k5_group_4 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(709,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( ( k3_xcmplx_0 @ A @ B )
= ( k1_real_1 @ np__1 ) )
<=> ( ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B = np__1 ) )
| ( ( A = np__1 )
& ( B
= ( k1_real_1 @ np__1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_int_1) ).
thf(4906,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ( ( ( k3_xcmplx_0 @ A @ B )
= ( k1_real_1 @ np__1 ) )
=> ( ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B = np__1 ) )
| ( ( A = np__1 )
& ( B
= ( k1_real_1 @ np__1 ) ) ) ) )
& ( ( ( ( A
= ( k1_real_1 @ np__1 ) )
& ( B = np__1 ) )
| ( ( A = np__1 )
& ( B
= ( k1_real_1 @ np__1 ) ) ) )
=> ( ( k3_xcmplx_0 @ A @ B )
= ( k1_real_1 @ np__1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(142,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(2440,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)],[142]) ).
thf(1111,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
= ( k9_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ B @ E ) @ ( k2_group_3 @ A @ C @ D ) @ ( k2_group_3 @ A @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_group_3) ).
thf(6688,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
= ( k9_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ B @ E ) @ ( k2_group_3 @ A @ C @ D ) @ ( k2_group_3 @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1677,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_1 @ A @ ( k2_group_1 @ A ) )
= ( k2_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_group_1) ).
thf(9284,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_1 @ A @ ( k2_group_1 @ A ) )
= ( k2_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(942,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( A
= ( k1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_card_1) ).
thf(5930,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( A
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(1586,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ B @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_group_3) ).
thf(8945,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ B @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(380,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(3422,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)],[380]) ).
thf(971,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(6038,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)],[971]) ).
thf(763,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(5198,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)],[763]) ).
thf(1553,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( v1_card_1 @ ( k16_group_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_group_2) ).
thf(8824,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( v1_card_1 @ ( k16_group_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(940,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) )
=> ( ( B
= ( k10_group_4 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k9_group_2 @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_group_4) ).
thf(5909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) )
=> ( ( ( B
= ( k10_group_4 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k9_group_2 @ A @ E @ F ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k9_group_2 @ A @ E @ F ) ) ) ) ) ) )
=> ( B
= ( k10_group_4 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(795,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) )
& ( v1_funct_2 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_group_6) ).
thf(5295,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) )
& ( v1_funct_2 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1036,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k3_group_2 @ A @ C @ B ) )
= ( k3_group_2 @ A @ C @ ( k4_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_group_2) ).
thf(6311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k4_group_2 @ A @ D @ ( k3_group_2 @ A @ C @ B ) )
= ( k3_group_2 @ A @ C @ ( k4_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(728,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(4995,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)],[728]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k8_group_6 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_6) ).
thf(4572,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m1_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m1_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k8_group_6 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k8_group_6 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ A @ ( k3_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_group_2) ).
thf(6368,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( r2_hidden @ A @ ( k3_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( k3_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(43,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(2001,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)],[43]) ).
thf(311,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(3130,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)],[311]) ).
thf(1276,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( D
= ( k12_group_6 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( a_3_0_group_6 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_group_6) ).
thf(7582,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( D
= ( k12_group_6 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( a_3_0_group_6 @ A @ B @ C ) ) )
& ( ( ( u1_struct_0 @ D )
= ( a_3_0_group_6 @ A @ B @ C ) )
=> ( D
= ( k12_group_6 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(420,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(3607,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)],[420]) ).
thf(929,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) )
& ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( u1_struct_0 @ C )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_group_2) ).
thf(5855,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) )
& ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( u1_struct_0 @ C )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(953,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) @ A @ B )
=> ( ( k1_group_6 @ A @ B @ C )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_group_6) ).
thf(5960,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) @ A @ B )
=> ( ( k1_group_6 @ A @ B @ C )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1605,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_group_2 @ A ) )
& ( v1_group_1 @ ( k5_group_2 @ A ) )
& ( v2_group_1 @ ( k5_group_2 @ A ) )
& ( v3_group_1 @ ( k5_group_2 @ A ) )
& ( v4_group_1 @ ( k5_group_2 @ A ) )
& ( v1_group_3 @ ( k5_group_2 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_group_6) ).
thf(9021,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_group_2 @ A ) )
& ( v1_group_1 @ ( k5_group_2 @ A ) )
& ( v2_group_1 @ ( k5_group_2 @ A ) )
& ( v3_group_1 @ ( k5_group_2 @ A ) )
& ( v4_group_1 @ ( k5_group_2 @ A ) )
& ( v1_group_3 @ ( k5_group_2 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(584,axiom,
! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(4393,plain,
! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(958,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_tarski @ ( k12_group_2 @ A @ C @ ( k6_group_1 @ A @ np__2 @ B ) ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_group_2) ).
thf(5979,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_tarski @ ( k12_group_2 @ A @ C @ ( k6_group_1 @ A @ np__2 @ B ) ) @ ( k2_group_2 @ A @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1790,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( v6_group_1 @ B )
| ( v6_group_1 @ C ) )
=> ( v6_group_1 @ ( k9_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_group_2) ).
thf(9650,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( v6_group_1 @ B )
| ( v6_group_1 @ C ) )
=> ( v6_group_1 @ ( k9_group_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(431,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(3696,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)],[431]) ).
thf(1618,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r5_group_3 @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_group_3) ).
thf(9072,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r5_group_3 @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_finseq_1 @ B @ A )
& ( m1_finseq_1 @ C @ A ) )
=> ( m2_finseq_1 @ ( k8_finseq_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_finseq_1) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_finseq_1 @ B @ A )
& ( m1_finseq_1 @ C @ A ) )
=> ( m2_finseq_1 @ ( k8_finseq_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1356,axiom,
! [A: $i] :
( ( r2_wellord2 @ A @ k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_card_1) ).
thf(7985,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)],[1356]) ).
thf(710,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ C ) @ B ) )
= ( k1_group_1 @ A @ C @ ( k3_group_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_group_4) ).
thf(4921,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ C ) @ B ) )
= ( k1_group_1 @ A @ C @ ( k3_group_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1138,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ C @ D )
=> ( ( r1_tarski @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ D @ B ) )
& ( r1_tarski @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_group_3) ).
thf(6901,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ C @ D )
=> ( ( r1_tarski @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ D @ B ) )
& ( r1_tarski @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r4_group_3 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r4_group_3) ).
thf(8164,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r4_group_3 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(1037,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(6314,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)],[1037]) ).
thf(1074,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k12_group_2 @ A @ C @ B ) )
= ( k3_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_4) ).
thf(6507,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k12_group_2 @ A @ C @ B ) )
= ( k3_group_2 @ A @ B @ ( k7_group_4 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1700,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(9352,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(174,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(2556,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)],[174]) ).
thf(524,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(4116,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)],[524]) ).
thf(50,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 ) )
=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_4) ).
thf(2033,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 ) )
=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(79,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(2149,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)],[79]) ).
thf(641,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(4613,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)],[641]) ).
thf(1125,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
<=> ( ( k2_group_2 @ A @ B @ C )
!= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_group_2) ).
thf(6824,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) )
=> ( ( k2_group_2 @ A @ B @ C )
!= k1_xboole_0 ) )
& ( ( ( k2_group_2 @ A @ B @ C )
!= k1_xboole_0 )
=> ( ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(106,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 ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).
thf(2253,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 ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1008,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_group_3) ).
thf(6203,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ ( k2_group_3 @ A @ B @ D ) @ ( k2_group_3 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(789,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_card_1) ).
thf(5278,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(842,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(5508,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)],[842]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_group_4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ B )
& ( D
= ( u1_struct_0 @ E ) )
& ( r1_tarski @ C @ ( k7_group_2 @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_4) ).
thf(7225,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_group_4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ B )
& ( D
= ( u1_struct_0 @ E ) )
& ( r1_tarski @ C @ ( k7_group_2 @ B @ E ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ B )
& ( D
= ( u1_struct_0 @ E ) )
& ( r1_tarski @ C @ ( k7_group_2 @ B @ E ) ) ) )
=> ( r2_hidden @ A @ ( a_2_0_group_4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1187,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
<=> ( v1_binop_1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_group_3) ).
thf(7155,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_binop_1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) )
& ( ( v1_binop_1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(297,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(3079,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(590,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(4412,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)],[590]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k9_group_6 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_6) ).
thf(3985,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k9_group_6 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1122,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(6792,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)],[1122]) ).
thf(1385,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(8110,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)],[1385]) ).
thf(1311,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) )
=> ( ( B
= ( k9_group_4 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k8_group_4 @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_group_4) ).
thf(7753,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) ) @ ( k1_group_3 @ A ) ) )
=> ( ( ( B
= ( k9_group_4 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k8_group_4 @ A @ E @ F ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_group_3 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_group_3 @ A ) )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ A )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k2_binop_1 @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ ( k1_group_3 @ A ) @ B @ C @ D )
= ( k8_group_4 @ A @ E @ F ) ) ) ) ) ) )
=> ( B
= ( k9_group_4 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(1652,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ ( k6_group_3 @ A @ B @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_group_3) ).
thf(9181,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ ( k6_group_3 @ A @ B @ C ) @ B ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ ( k6_group_3 @ A @ B @ C ) @ B ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k8_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_group_3) ).
thf(5608,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k8_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = D )
& ( r4_group_3 @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( k8_group_3 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(683,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(4797,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)],[683]) ).
thf(190,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(2602,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)],[190]) ).
thf(1717,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k3_group_6 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_group_6) ).
thf(9404,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k3_group_6 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(212,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(2734,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)],[212]) ).
thf(1644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ A )
& ( ( k9_group_1 @ A )
= ( k9_group_1 @ B ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_group_2) ).
thf(9154,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v6_group_1 @ A )
& ( ( k9_group_1 @ A )
= ( k9_group_1 @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(632,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(4577,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)],[632]) ).
thf(166,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(2524,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)],[166]) ).
thf(375,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(3396,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)],[375]) ).
thf(129,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(2376,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)],[129]) ).
thf(1547,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k9_group_2 @ A @ B @ C )
= ( k9_group_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k9_group_2) ).
thf(8807,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k9_group_2 @ A @ B @ C )
= ( k9_group_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(358,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(3343,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)],[358]) ).
thf(319,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(3158,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)],[319]) ).
thf(1300,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(7709,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(833,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ ( k5_group_4 @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_latsubgr) ).
thf(5456,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ ( k5_group_4 @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(446,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(3768,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)],[446]) ).
thf(838,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) ) )
=> ( ( C
= ( k5_group_6 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k4_group_6 @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_group_6 @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D = F )
& ( E = G ) )
=> ( ( k2_binop_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ C @ D @ E )
= ( k2_group_2 @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_group_6) ).
thf(5474,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) ) )
=> ( ( ( C
= ( k5_group_6 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k4_group_6 @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_group_6 @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D = F )
& ( E = G ) )
=> ( ( k2_binop_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ C @ D @ E )
= ( k2_group_2 @ A @ F @ G ) ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k4_group_6 @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k4_group_6 @ A @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( D = F )
& ( E = G ) )
=> ( ( k2_binop_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) @ C @ D @ E )
= ( k2_group_2 @ A @ F @ G ) ) ) ) ) ) )
=> ( C
= ( k5_group_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(227,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(2789,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)],[227]) ).
thf(179,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(2568,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)],[179]) ).
thf(345,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(3272,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)],[345]) ).
thf(273,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 @ B )
= ( k1_relat_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_4) ).
thf(2991,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 @ B )
= ( k1_relat_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_group_2) ).
thf(5503,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(200,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(2695,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)],[200]) ).
thf(1412,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ B @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ C @ D ) )
= ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ C ) @ ( k2_group_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_group_2) ).
thf(8217,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ B @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ C @ D ) )
= ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ C ) @ ( k2_group_2 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1240,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_1 @ A @ B )
= ( k2_group_1 @ A ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_group_1) ).
thf(7411,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_group_1 @ A @ B )
= ( k2_group_1 @ A ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(499,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k6_subset_1 @ k5_numbers @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k2_finseq_1 @ A ) )
= ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_3) ).
thf(4000,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k6_subset_1 @ k5_numbers @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k2_finseq_1 @ A ) )
= ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(729,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).
thf(4998,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(326,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(3187,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)],[326]) ).
thf(1301,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(7714,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)],[1301]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_group_1 @ A @ B ) )
& ( v1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_group_1) ).
thf(4341,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g1_group_1 @ A @ B ) )
& ( v1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(943,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(5933,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)],[943]) ).
thf(1345,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_latsubgr @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_latsubgr @ A @ B @ C ) @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) )
& ( m2_relset_1 @ ( k3_latsubgr @ A @ B @ C ) @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_latsubgr) ).
thf(7938,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_latsubgr @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_latsubgr @ A @ B @ C ) @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) )
& ( m2_relset_1 @ ( k3_latsubgr @ A @ B @ C ) @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(211,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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).
thf(2727,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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1144,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) @ D )
= ( k2_group_2 @ A @ B @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_group_2) ).
thf(6916,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) @ D )
= ( k2_group_2 @ A @ B @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(234,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(2859,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)],[234]) ).
thf(559,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(4283,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)],[559]) ).
thf(613,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(4494,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(342,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(3255,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)],[342]) ).
thf(1075,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( v1_finset_1 @ ( k8_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k8_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_group_3) ).
thf(6510,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( ( v1_finset_1 @ ( k8_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k8_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(817,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k2_group_1 @ B ) )
= ( k2_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_group_1) ).
thf(5395,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k2_group_1 @ B ) )
= ( k2_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(339,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(3240,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(925,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ ( k1_nat_1 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ C ) )
& ( ( k6_group_1 @ B @ ( k1_nat_1 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_group_1) ).
thf(5844,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ ( k1_nat_1 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ C ) )
& ( ( k6_group_1 @ B @ ( k1_nat_1 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1306,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_group_6 @ C @ B @ A )
=> ( r1_group_6 @ B @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_6) ).
thf(7736,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_group_6 @ C @ B @ A )
=> ( r1_group_6 @ B @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(90,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(2188,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)],[90]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k8_rlvect_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_1) ).
thf(4309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k8_rlvect_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1182,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k4_group_1 @ A ) )
& ( v1_funct_2 @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_group_1) ).
thf(7134,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k4_group_1 @ A ) )
& ( v1_funct_2 @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(742,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(5121,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)],[742]) ).
thf(134,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(2393,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)],[134]) ).
thf(1645,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_group_6 @ A @ B )
=> ( r2_group_6 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_group_6) ).
thf(9157,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_group_6 @ A @ B )
=> ( r2_group_6 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1393,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k5_group_3 @ A @ D @ B ) @ C )
= ( k5_group_3 @ A @ ( k4_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_3) ).
thf(8139,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k5_group_3 @ A @ D @ B ) @ C )
= ( k5_group_3 @ A @ ( k4_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(1204,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(7223,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_setfam_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1516,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_group_4) ).
thf(8711,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k7_group_4 @ A @ B @ C )
= ( k7_group_4 @ A @ C @ B ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(1310,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(7751,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)],[1310]) ).
thf(298,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(3081,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)],[298]) ).
thf(483,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(3945,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1366,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_finseq_1) ).
thf(8027,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(605,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(4465,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)],[605]) ).
thf(1434,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ C @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ C ) @ ( k2_group_3 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_group_3) ).
thf(8332,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ C @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_3 @ A @ B @ C ) @ ( k2_group_3 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(1401,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(8167,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)],[1401]) ).
thf(1527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k2_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k2_group_6 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k2_group_6 @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_6) ).
thf(8740,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k2_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k2_group_6 @ A @ B @ C ) @ B )
& ( m1_group_6 @ ( k2_group_6 @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(1480,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( u1_struct_0 @ ( k6_group_3 @ A @ C @ B ) )
= ( k4_group_2 @ A @ B @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_group_3) ).
thf(8581,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( u1_struct_0 @ ( k6_group_3 @ A @ C @ B ) )
= ( k4_group_2 @ A @ B @ ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(135,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(2398,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)],[135]) ).
thf(571,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_rlvect_1 @ A @ B )
<=> ( r2_hidden @ B @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rlvect_1) ).
thf(4328,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ( r1_rlvect_1 @ A @ B )
=> ( r2_hidden @ B @ ( u1_struct_0 @ A ) ) )
& ( ( r2_hidden @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finseq_1) ).
thf(2716,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1598,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_group_1) ).
thf(8993,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(581,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(4381,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)],[581]) ).
thf(788,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k2_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_group_3) ).
thf(5271,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k2_group_3 @ A @ C @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k2_group_3 @ A @ C @ D ) ) )
=> ( r1_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1093,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(6606,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)],[1093]) ).
thf(967,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r2_hidden @ A @ ( k13_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_group_2) ).
thf(6019,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r2_hidden @ A @ ( k13_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ C ) )
& ( r1_rlvect_1 @ D @ E ) )
=> ( r2_hidden @ A @ ( k13_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(778,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) )
& ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_group_2) ).
thf(5239,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) )
& ( r1_tarski @ ( k7_group_2 @ A @ C ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(1695,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k5_group_2 @ B )
= ( k5_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_group_2) ).
thf(9339,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k5_group_2 @ B )
= ( k5_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(675,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(4769,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)],[675]) ).
thf(1321,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(7815,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)],[1321]) ).
thf(75,axiom,
! [A: $i] :
( ? [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
& ( r1_tarski @ A @ ( k2_finseq_1 @ B ) ) )
=> ( ( ( k14_finseq_1 @ A )
= k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_finseq_1) ).
thf(2134,plain,
! [A: $i] :
( ? [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
& ( r1_tarski @ A @ ( k2_finseq_1 @ B ) ) )
=> ( ( ( ( k14_finseq_1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( k14_finseq_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1784,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( D = B )
=> ( ( k3_group_1 @ C @ D )
= ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_2) ).
thf(9627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( D = B )
=> ( ( k3_group_1 @ C @ D )
= ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(263,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ ( k2_finseq_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_finseq_3) ).
thf(2959,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ ( k2_finseq_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(849,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ ( k3_group_1 @ A @ B ) )
= ( k2_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ B ) ) )
= ( k2_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_group_6) ).
thf(5535,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ ( k3_group_1 @ A @ B ) )
= ( k2_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ B ) ) )
= ( k2_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1372,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ D )
= ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_group_2) ).
thf(8064,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ D )
= ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(277,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 ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).
thf(3002,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 ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1348,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ ( k2_finseq_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_finseq_1) ).
thf(7951,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ ( k2_finseq_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1294,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(7671,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)],[1294]) ).
thf(555,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_finseq_1 @ A )
= ( k4_xboole_0 @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_finseq_1) ).
thf(4273,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_finseq_1 @ A )
= ( k4_xboole_0 @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(962,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k1_group_2 @ A @ B ) @ C )
= ( k1_group_2 @ A @ ( k3_group_3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_group_3) ).
thf(5997,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k1_group_2 @ A @ B ) @ C )
= ( k1_group_2 @ A @ ( k3_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1408,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_3) ).
thf(8202,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k5_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(1027,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(6281,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1535,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r2_hidden @ ( k2_group_1 @ A ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
thf(8767,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r2_hidden @ ( k2_group_1 @ A ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(852,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(5546,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)],[852]) ).
thf(92,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(2193,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)],[92]) ).
thf(1473,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(8534,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)],[1473]) ).
thf(1774,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ C @ ( k8_group_4 @ A @ C @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_group_4) ).
thf(9587,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ C @ ( k8_group_4 @ A @ C @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(527,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(4127,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)],[527]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r1_tarski @ A @ ( k2_finseq_1 @ B ) )
=> ( v2_funct_1 @ ( k14_finseq_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_finseq_3) ).
thf(2029,plain,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r1_tarski @ A @ ( k2_finseq_1 @ B ) )
=> ( v2_funct_1 @ ( k14_finseq_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1635,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r1_group_6 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_group_6) ).
thf(9125,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r1_group_6 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1055,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k4_group_3 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_group_3) ).
thf(6403,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k4_group_3 @ A @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k4_group_3 @ A @ B @ D ) ) )
=> ( r3_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1477,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(8549,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)],[1477]) ).
thf(837,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k7_group_4 @ A @ C @ D ) @ B )
= ( k11_group_2 @ A @ C @ ( k11_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_group_4) ).
thf(5471,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k7_group_4 @ A @ C @ D ) @ B )
= ( k11_group_2 @ A @ C @ ( k11_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1217,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k10_group_2 @ A @ C @ B ) )
= ( k2_group_2 @ A @ B @ ( k11_group_2 @ A @ C @ ( k7_group_2 @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_group_2) ).
thf(7270,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k10_group_2 @ A @ C @ B ) )
= ( k2_group_2 @ A @ B @ ( k11_group_2 @ A @ C @ ( k7_group_2 @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(296,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(3077,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)],[296]) ).
thf(1420,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_group_3 @ A @ B @ ( k2_group_1 @ A ) )
| ( r2_group_3 @ A @ ( k2_group_1 @ A ) @ B ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_group_3) ).
thf(8249,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_group_3 @ A @ B @ ( k2_group_1 @ A ) )
| ( r2_group_3 @ A @ ( k2_group_1 @ A ) @ B ) )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(1302,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_group_3) ).
thf(7719,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1801,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k10_group_3 @ A @ B ) )
& ( m1_group_2 @ ( k10_group_3 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_group_3) ).
thf(9687,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_group_1 @ ( k10_group_3 @ A @ B ) )
& ( m1_group_2 @ ( k10_group_3 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(333,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(3208,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)],[333]) ).
thf(790,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k4_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_group_3) ).
thf(5282,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k4_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(16,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).
thf(1865,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(357,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(3340,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)],[357]) ).
thf(1463,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( m1_group_2 @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_group_4) ).
thf(8492,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( m1_group_2 @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(143,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(2442,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)],[143]) ).
thf(220,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(2759,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)],[220]) ).
thf(1436,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ ( k7_group_1 @ A @ B ) @ B )
= ( k2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_1) ).
thf(8344,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ ( k7_group_1 @ A @ B ) @ B )
= ( k2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(399,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(3487,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)],[399]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k2_group_2 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_group_2) ).
thf(7145,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k2_group_2 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
=> ( r2_hidden @ A @ ( k2_group_2 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(462,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).
thf(3832,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(85,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(2166,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)],[85]) ).
thf(1264,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k10_group_1 @ B @ C @ D ) )
= ( k10_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_group_1) ).
thf(7536,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k10_group_1 @ B @ C @ D ) )
= ( k10_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(695,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(4854,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)],[695]) ).
thf(1465,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(8497,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)],[1465]) ).
thf(995,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(6123,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)],[995]) ).
thf(1498,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(8656,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(1326,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(7843,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)],[1326]) ).
thf(1275,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
& ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) )
=> ( C
= ( k3_group_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_group_1) ).
thf(7579,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k2_group_1 @ A ) )
& ( ( k1_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) ) )
=> ( C
= ( k3_group_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(1115,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v3_group_1 @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ C @ D )
= B )
& ( ( k1_group_1 @ A @ D @ C )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_1) ).
thf(6757,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( v3_group_1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ C @ D )
= B )
& ( ( k1_group_1 @ A @ D @ C )
= B ) ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ C @ D )
= B )
& ( ( k1_group_1 @ A @ D @ C )
= B ) ) ) ) )
=> ( v3_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(702,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(4887,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1223,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k12_group_2 @ A @ B @ D ) )
& ( C
= ( k13_group_2 @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_group_6) ).
thf(7315,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( C
= ( k12_group_2 @ A @ B @ D ) )
& ( C
= ( k13_group_2 @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(826,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(5432,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)],[826]) ).
thf(1624,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_lattices @ ( k11_group_4 @ A ) )
= ( k6_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_group_4) ).
thf(9089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_lattices @ ( k11_group_4 @ A ) )
= ( k6_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(180,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(2573,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)],[180]) ).
thf(1666,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] : ( m1_group_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_group_2) ).
thf(9258,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] : ( m1_group_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(966,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k12_group_2 @ A @ B @ C )
= ( k3_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_group_2) ).
thf(6016,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k12_group_2 @ A @ B @ C )
= ( k3_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(323,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(3170,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)],[323]) ).
thf(1254,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_group_3) ).
thf(7482,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_group_2) ).
thf(9390,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(975,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(6048,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)],[975]) ).
thf(1452,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_card_1 @ ( k7_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_group_3) ).
thf(8436,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_card_1 @ ( k7_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k10_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(1072,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ ( k6_group_4 @ A ) @ B )
<=> ~ ( v1_group_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_group_4) ).
thf(6478,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ ( k6_group_4 @ A ) @ B )
=> ~ ( v1_group_4 @ B @ A ) )
& ( ~ ( v1_group_4 @ B @ A )
=> ( r1_rlvect_1 @ ( k6_group_4 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(209,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(2721,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)],[209]) ).
thf(1086,axiom,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_card_1) ).
thf(6572,plain,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(615,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(4498,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)],[615]) ).
thf(844,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r4_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
<=> ( r2_group_3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_group_3) ).
thf(5520,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r4_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( r2_group_3 @ A @ B @ C ) )
& ( ( r2_group_3 @ A @ B @ C )
=> ( r4_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1611,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k3_group_1 @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_group_1) ).
thf(9047,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k3_group_1 @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(1041,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_group_6) ).
thf(6340,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(977,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ( ( C = E )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ D @ A @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_group_4) ).
thf(6061,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ( ( C = E )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ D @ A @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1089,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( r1_tarski @ ( k3_group_2 @ A @ B @ C ) @ ( k3_group_2 @ A @ B @ D ) )
& ( r1_tarski @ ( k4_group_2 @ A @ B @ C ) @ ( k4_group_2 @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_group_3) ).
thf(6585,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( r1_tarski @ ( k3_group_2 @ A @ B @ C ) @ ( k3_group_2 @ A @ B @ D ) )
& ( r1_tarski @ ( k4_group_2 @ A @ B @ C ) @ ( k4_group_2 @ A @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(3101,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(165,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r1_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).
thf(2521,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1426,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(8276,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)],[1426]) ).
thf(1725,axiom,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(9422,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(1181,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ( ( C = E )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ D @ A @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_group_4) ).
thf(7130,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ( ( C = E )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k6_group_1 @ D @ A @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(80,axiom,
( ( k14_finseq_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_finseq_3) ).
thf(2151,plain,
( ( k14_finseq_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1289,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= B ) ) )
=> ( v7_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_group_3) ).
thf(7643,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ C )
= B ) ) )
=> ( v7_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(318,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(3155,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)],[318]) ).
thf(1706,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v7_group_1 @ ( k5_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_group_3) ).
thf(9375,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v7_group_1 @ ( k5_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(284,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(3038,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)],[284]) ).
thf(1707,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k8_group_1 @ C )
= ( k8_group_1 @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_group_3) ).
thf(9377,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k8_group_1 @ C )
= ( k8_group_1 @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1062,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(6443,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)],[1062]) ).
thf(429,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(3683,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)],[429]) ).
thf(690,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(4828,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)],[690]) ).
thf(404,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(3515,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)],[404]) ).
thf(920,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(5827,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(928,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(5853,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)],[928]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5901,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(639,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(4601,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)],[639]) ).
thf(1421,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(8254,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)],[1421]) ).
thf(1634,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ B @ ( k6_group_3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_group_3) ).
thf(9118,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ B @ ( k6_group_3 @ A @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( m1_group_2 @ B @ ( k6_group_3 @ A @ B @ C ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(305,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r1_xreal_0 @ ( k2_xcmplx_0 @ A @ np__1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_int_1) ).
thf(3106,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r1_xreal_0 @ ( k2_xcmplx_0 @ A @ np__1 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1219,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(7282,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)],[1219]) ).
thf(686,axiom,
? [A: $i] :
( ( l1_vectsp_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_vectsp_1) ).
thf(4805,plain,
? [A: $i] :
( ( l1_vectsp_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v8_vectsp_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1371,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ ( k3_group_1 @ A @ C ) )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ ( k3_group_1 @ A @ C ) ) @ C )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ C ) @ B )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ C ) ) @ B )
= B )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ C ) ) )
= B )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ C ) )
= B )
& ( ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k1_group_1 @ A @ C @ B ) )
= B )
& ( ( k1_group_1 @ A @ C @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_group_3) ).
thf(8047,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ ( k3_group_1 @ A @ C ) )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ ( k3_group_1 @ A @ C ) ) @ C )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ C ) @ B )
= B )
& ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ C ) ) @ B )
= B )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ ( k3_group_1 @ A @ C ) ) )
= B )
& ( ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ C ) )
= B )
& ( ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k1_group_1 @ A @ C @ B ) )
= B )
& ( ( k1_group_1 @ A @ C @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(771,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(5222,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)],[771]) ).
thf(1216,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k11_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k11_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
& ( v1_group_6 @ ( k11_group_6 @ A @ B ) @ A @ ( k6_group_6 @ A @ B ) )
& ( m2_relset_1 @ ( k11_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_group_6) ).
thf(7265,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k11_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k11_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
& ( v1_group_6 @ ( k11_group_6 @ A @ B ) @ A @ ( k6_group_6 @ A @ B ) )
& ( m2_relset_1 @ ( k11_group_6 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(259,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(2945,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)],[259]) ).
thf(549,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(4213,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)],[549]) ).
thf(642,axiom,
! [A: $i] :
( ( v4_finsub_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A ) )
=> ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
& ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(4616,plain,
! [A: $i] :
( ( ( v4_finsub_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A ) )
=> ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
& ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A ) )
=> ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
& ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) )
=> ( v4_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(330,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( ( A
= ( k2_xcmplx_0 @ B @ np__1 ) )
& ( r2_hidden @ C @ ( k2_finseq_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ C ) ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_finseq_3) ).
thf(3197,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( ( A
= ( k2_xcmplx_0 @ B @ np__1 ) )
& ( r2_hidden @ C @ ( k2_finseq_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ C ) ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1604,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v1_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v2_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v3_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v4_group_1 @ ( k6_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_group_6) ).
thf(9015,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v1_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v2_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v3_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v4_group_1 @ ( k6_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(516,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(4073,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)],[516]) ).
thf(233,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(2856,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)],[233]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(886,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ~ ( r1_xreal_0 @ np__0 @ A )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_group_1) ).
thf(5689,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ~ ( r1_xreal_0 @ np__0 @ A )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(562,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_group_4) ).
thf(4300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ ( k12_finseq_1 @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k1_group_1 @ A @ ( k3_group_4 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(868,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(5616,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(618,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ B )
= ( k2_finsop_1 @ ( u1_struct_0 @ A ) @ B @ ( u1_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_4) ).
thf(4509,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ B )
= ( k2_finsop_1 @ ( u1_struct_0 @ A ) @ B @ ( u1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(94,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(2197,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)],[94]) ).
thf(1121,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(6789,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)],[1121]) ).
thf(59,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(2065,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)],[59]) ).
thf(582,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(4388,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)],[582]) ).
thf(1342,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_4) ).
thf(7928,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(1327,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k13_group_2 @ A @ B @ C ) @ ( k12_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_group_3) ).
thf(7869,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k13_group_2 @ A @ B @ C ) @ ( k12_group_2 @ A @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( k13_group_2 @ A @ B @ C ) @ ( k12_group_2 @ A @ B @ C ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(254,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(2928,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)],[254]) ).
thf(33,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(1952,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)],[33]) ).
thf(1718,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( v3_realset2 @ A )
& ( v3_realset2 @ B ) )
=> ( r2_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_group_6) ).
thf(9407,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( v3_realset2 @ A )
& ( v3_realset2 @ B ) )
=> ( r2_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(389,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(3456,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)],[389]) ).
thf(657,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(4694,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)],[657]) ).
thf(547,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(4203,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)],[547]) ).
thf(916,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(5816,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)],[916]) ).
thf(1488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( m2_relset_1 @ ( k8_relset_1 @ A @ C @ D @ B ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relset_1) ).
thf(8620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( m2_relset_1 @ ( k8_relset_1 @ A @ C @ D @ B ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1554,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_group_6 @ A @ B )
<=> ( r1_group_6 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_group_6) ).
thf(8826,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_group_6 @ A @ B )
=> ( r1_group_6 @ A @ B ) )
& ( ( r1_group_6 @ A @ B )
=> ( r2_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(21,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(1877,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)],[21]) ).
thf(1406,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ B )
=> ( r1_xreal_0 @ ( k9_group_1 @ ( k13_group_6 @ B @ A @ C ) ) @ ( k9_group_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_6) ).
thf(8192,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ B )
=> ( r1_xreal_0 @ ( k9_group_1 @ ( k13_group_6 @ B @ A @ C ) ) @ ( k9_group_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(312,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i,C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r1_xreal_0 @ D @ A )
=> ( ( k1_funct_1 @ ( k16_finseq_1 @ B @ C @ A ) @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_finseq_3) ).
thf(3133,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i,C: $i] :
( ( m2_finseq_1 @ C @ B )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r1_xreal_0 @ D @ A )
=> ( ( k1_funct_1 @ ( k16_finseq_1 @ B @ C @ A ) @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(290,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).
thf(3055,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(73,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_4) ).
thf(2129,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1176,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(7113,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1398,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k8_group_6 @ A @ B @ C @ ( k10_group_6 @ A @ B ) @ E )
= ( k10_group_6 @ A @ C ) )
& ( ( k8_group_6 @ A @ B @ C @ D @ ( k10_group_6 @ B @ C ) )
= ( k10_group_6 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_group_6) ).
thf(8156,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k8_group_6 @ A @ B @ C @ ( k10_group_6 @ A @ B ) @ E )
= ( k10_group_6 @ A @ C ) )
& ( ( k8_group_6 @ A @ B @ C @ D @ ( k10_group_6 @ B @ C ) )
= ( k10_group_6 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(604,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(4462,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)],[604]) ).
thf(70,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(2111,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)],[70]) ).
thf(1384,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) )
=> ( ( k1_group_2 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_group_2) ).
thf(8103,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) )
=> ( ( k1_group_2 @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(224,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(2780,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(667,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(4731,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)],[667]) ).
thf(505,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( D
= ( k1_nat_1 @ C @ np__1 ) )
& ( r2_hidden @ B @ ( k2_finseq_1 @ D ) )
& ( r2_hidden @ A @ ( k2_finseq_1 @ C ) ) )
=> ( ( ( r1_xreal_0 @ np__1 @ A )
=> ( ( r1_xreal_0 @ B @ A )
| ( ( k1_funct_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ D ) @ ( k1_tarski @ B ) ) ) @ A )
= A ) ) )
& ( ( ( r1_xreal_0 @ B @ A )
& ( r1_xreal_0 @ A @ C ) )
=> ( ( k1_funct_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ D ) @ ( k1_tarski @ B ) ) ) @ A )
= ( k1_nat_1 @ A @ np__1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_finseq_3) ).
thf(4028,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( ( D
= ( k1_nat_1 @ C @ np__1 ) )
& ( r2_hidden @ B @ ( k2_finseq_1 @ D ) )
& ( r2_hidden @ A @ ( k2_finseq_1 @ C ) ) )
=> ( ( ( r1_xreal_0 @ np__1 @ A )
=> ( ( r1_xreal_0 @ B @ A )
| ( ( k1_funct_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ D ) @ ( k1_tarski @ B ) ) ) @ A )
= A ) ) )
& ( ( ( r1_xreal_0 @ B @ A )
& ( r1_xreal_0 @ A @ C ) )
=> ( ( k1_funct_1 @ ( k14_finseq_1 @ ( k4_xboole_0 @ ( k2_finseq_1 @ D ) @ ( k1_tarski @ B ) ) ) @ A )
= ( k1_nat_1 @ A @ np__1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(108,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(2261,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)],[108]) ).
thf(828,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(5439,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)],[828]) ).
thf(1045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_wellord2 @ ( k7_group_2 @ A @ C ) @ ( k12_group_2 @ A @ C @ B ) )
& ( r2_wellord2 @ ( k7_group_2 @ A @ C ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_group_2) ).
thf(6353,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_wellord2 @ ( k7_group_2 @ A @ C ) @ ( k12_group_2 @ A @ C @ B ) )
& ( r2_wellord2 @ ( k7_group_2 @ A @ C ) @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(706,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(4897,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(725,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r2_wellord2 @ A @ B )
=> ( ( k4_card_1 @ A )
= ( k4_card_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_card_1) ).
thf(4985,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( r2_wellord2 @ A @ B )
=> ( ( k4_card_1 @ A )
= ( k4_card_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1529,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_group_2) ).
thf(8750,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( u1_struct_0 @ B )
= ( u1_struct_0 @ C ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ C ) @ ( u1_group_1 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(145,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(2446,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)],[145]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(3165,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(15,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(1862,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)],[15]) ).
thf(542,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(4181,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)],[542]) ).
thf(1173,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k2_group_1 @ A ) )
= ( k2_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_group_6) ).
thf(7098,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k2_group_1 @ A ) )
= ( k2_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(252,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(2923,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)],[252]) ).
thf(11,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(1838,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)],[11]) ).
thf(1291,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v2_group_1 @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_1) ).
thf(7654,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( v2_group_1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C ) ) ) )
=> ( v2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r1_xreal_0 @ ( k3_finseq_1 @ B ) @ C )
=> ( ( k16_finseq_1 @ A @ B @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_finseq_1) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r1_xreal_0 @ ( k3_finseq_1 @ B ) @ C )
=> ( ( k16_finseq_1 @ A @ B @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(387,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_funct_1 @ ( k1_funct_4 @ C @ D ) )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_4) ).
thf(3451,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_funct_1 @ ( k1_funct_4 @ C @ D ) )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(879,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(5656,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)],[879]) ).
thf(1184,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( m1_subset_1 @ ( u1_vectsp_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_vectsp_1) ).
thf(7141,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( m1_subset_1 @ ( u1_vectsp_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(346,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(3298,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)],[346]) ).
thf(397,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(3483,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)],[397]) ).
thf(1194,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_group_1) ).
thf(7186,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(170,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(2542,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)],[170]) ).
thf(973,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ B @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ C @ D ) ) @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ C ) @ ( k2_group_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_group_2) ).
thf(6044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ B @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ C @ D ) ) @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ C ) @ ( k2_group_2 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(113,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(2289,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)],[113]) ).
thf(759,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).
thf(5180,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1619,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k14_group_2 @ A @ B )
= ( k15_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_group_3) ).
thf(9074,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k14_group_2 @ A @ B )
= ( k15_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(1658,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r1_group_2 @ B @ ( k13_group_6 @ A @ B @ ( k10_group_6 @ A @ B ) ) @ ( k5_group_2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_group_6) ).
thf(9228,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( r1_group_2 @ B @ ( k13_group_6 @ A @ B @ ( k10_group_6 @ A @ B ) ) @ ( k5_group_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(1222,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(7297,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)],[1222]) ).
thf(821,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_6 @ D @ A @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( ( E = C )
=> ( ( ( k12_group_2 @ B @ D @ E )
= ( k12_group_2 @ A @ D @ C ) )
& ( ( k13_group_2 @ B @ D @ E )
= ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_group_6) ).
thf(5410,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_6 @ D @ A @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( ( E = C )
=> ( ( ( k12_group_2 @ B @ D @ E )
= ( k12_group_2 @ A @ D @ C ) )
& ( ( k13_group_2 @ B @ D @ E )
= ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1607,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_group_3) ).
thf(9030,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(1270,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k18_group_2 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_latsubgr) ).
thf(7561,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k18_group_2 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(247,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(2911,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)],[247]) ).
thf(627,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(4554,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)],[627]) ).
thf(5,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(1820,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)],[5]) ).
thf(1690,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k3_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k3_group_6 @ A @ B @ C ) @ C )
& ( m1_group_6 @ ( k3_group_6 @ A @ B @ C ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_group_6) ).
thf(9327,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k3_group_6 @ A @ B @ C ) )
& ( v1_group_3 @ ( k3_group_6 @ A @ B @ C ) @ C )
& ( m1_group_6 @ ( k3_group_6 @ A @ B @ C ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(1049,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_group_1) ).
thf(6376,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_xcmplx_0 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1782,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ B @ C )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
thf(9619,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r1_group_2 @ A @ B @ C )
=> ( B = C ) )
& ( ( B = C )
=> ( r1_group_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(1391,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(8131,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)],[1391]) ).
thf(1733,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r6_group_3 @ A @ B @ C )
<=> ( r5_group_3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_group_3) ).
thf(9450,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r6_group_3 @ A @ B @ C )
=> ( r5_group_3 @ A @ B @ C ) )
& ( ( r5_group_3 @ A @ B @ C )
=> ( r6_group_3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(1013,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k10_group_1 @ A @ B @ C ) )
= ( k10_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_group_1) ).
thf(6223,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_1 @ A @ ( k10_group_1 @ A @ B @ C ) )
= ( k10_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(781,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(5248,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)],[781]) ).
thf(1338,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(7911,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)],[1338]) ).
thf(1225,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(7324,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(103,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(2244,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)],[103]) ).
thf(926,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(5849,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)],[926]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_group_6 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_group_6) ).
thf(6100,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_group_6 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1715,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( ( k9_group_1 @ A )
= ( k2_nat_1 @ ( k9_group_1 @ B ) @ ( k17_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_group_2) ).
thf(9398,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( ( k9_group_1 @ A )
= ( k2_nat_1 @ ( k9_group_1 @ B ) @ ( k17_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(37,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(1973,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)],[37]) ).
thf(713,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(4933,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)],[713]) ).
thf(1020,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(6255,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)],[1020]) ).
thf(1042,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ ( k7_binop_2 @ np__1 ) @ B )
= ( k3_group_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_group_1) ).
thf(6345,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ ( k7_binop_2 @ np__1 ) @ B )
= ( k3_group_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1087,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ A @ ( k4_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ D ) )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_group_2) ).
thf(6574,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( r2_hidden @ A @ ( k4_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ D ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ D ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( k4_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(125,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(2365,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)],[125]) ).
thf(264,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(2962,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)],[264]) ).
thf(906,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ D @ C )
=> ( r1_rlvect_1 @ D @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_group_4) ).
thf(5775,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ D @ C )
=> ( r1_rlvect_1 @ D @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(100,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 @ ( k1_funct_4 @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_4) ).
thf(2212,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 @ ( k1_funct_4 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1456,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v3_realset2 @ A )
<=> ( ( ( k9_group_1 @ A )
= np__1 )
& ( v6_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_group_6) ).
thf(8456,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( v3_realset2 @ A )
=> ( ( ( k9_group_1 @ A )
= np__1 )
& ( v6_group_1 @ A ) ) )
& ( ( ( ( k9_group_1 @ A )
= np__1 )
& ( v6_group_1 @ A ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(463,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(3838,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)],[463]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r2_hidden @ A @ ( k12_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ C @ E ) )
& ( r1_rlvect_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_group_2) ).
thf(5377,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r2_hidden @ A @ ( k12_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ C @ E ) )
& ( r1_rlvect_1 @ D @ E ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ C @ E ) )
& ( r1_rlvect_1 @ D @ E ) )
=> ( r2_hidden @ A @ ( k12_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1519,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r5_group_3 @ A @ B @ C )
=> ( r5_group_3 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_group_3) ).
thf(8719,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r5_group_3 @ A @ B @ C )
=> ( r5_group_3 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(1680,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k8_group_4 @ A @ B @ C ) )
& ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_4) ).
thf(9294,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k8_group_4 @ A @ B @ C ) )
& ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(62,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(2086,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)],[62]) ).
thf(1552,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_group_6 @ A @ B )
& ( v6_group_1 @ A ) )
=> ( ( k9_group_1 @ A )
= ( k9_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_group_6) ).
thf(8821,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_group_6 @ A @ B )
& ( v6_group_1 @ A ) )
=> ( ( k9_group_1 @ A )
= ( k9_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(578,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(4362,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)],[578]) ).
thf(1704,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ B @ ( k9_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k9_group_3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_group_3) ).
thf(9371,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r2_hidden @ B @ ( k9_group_3 @ A @ C ) )
=> ( r2_hidden @ C @ ( k9_group_3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(255,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(2931,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)],[255]) ).
thf(858,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(5575,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)],[858]) ).
thf(659,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(4703,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)],[659]) ).
thf(1648,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_group_3 @ A @ B @ C )
& ( r2_group_3 @ A @ C @ D ) )
=> ( r2_group_3 @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_group_3) ).
thf(9165,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_group_3 @ A @ B @ C )
& ( r2_group_3 @ A @ C @ D ) )
=> ( r2_group_3 @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(67,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(2101,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)],[67]) ).
thf(1697,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_group_2) ).
thf(9345,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(1608,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ( ( k9_group_3 @ A @ B )
= ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_group_3) ).
thf(9033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k9_group_3 @ A @ B )
= ( k1_tarski @ B ) ) )
& ( ( ( k9_group_3 @ A @ B )
= ( k1_tarski @ B ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(1269,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(7558,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)],[1269]) ).
thf(266,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(2967,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)],[266]) ).
thf(133,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(2390,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(882,axiom,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_card_1) ).
thf(5667,plain,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r2_hidden @ A @ ( k11_group_2 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r1_rlvect_1 @ D @ E )
& ( r2_hidden @ F @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_group_2) ).
thf(6325,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r2_hidden @ A @ ( k11_group_2 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r1_rlvect_1 @ D @ E )
& ( r2_hidden @ F @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_group_1 @ B @ E @ F ) )
& ( r1_rlvect_1 @ D @ E )
& ( r2_hidden @ F @ C ) ) )
=> ( r2_hidden @ A @ ( k11_group_2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1030,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ D @ B ) @ C )
= ( k4_group_3 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_group_3) ).
thf(6293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ D @ B ) @ C )
= ( k4_group_3 @ A @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(968,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_group_2) ).
thf(6027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1095,axiom,
~ ( v1_xboole_0 @ k4_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_numbers) ).
thf(6614,plain,
~ ( v1_xboole_0 @ k4_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(643,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(4626,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)],[643]) ).
thf(514,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( r1_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_3) ).
thf(4067,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( r1_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(98,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(2207,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)],[98]) ).
thf(801,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( m1_group_2 @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_2) ).
thf(5326,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( m1_group_2 @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u1_group_1 @ B )
= ( k1_realset1 @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_group_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(745,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(5139,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)],[745]) ).
thf(199,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(2693,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)],[199]) ).
thf(719,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(4965,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)],[719]) ).
thf(237,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(2867,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)],[237]) ).
thf(1071,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_2 @ A ) @ B ) @ ( k6_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_3) ).
thf(6476,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_2 @ A ) @ B ) @ ( k6_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(161,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).
thf(2506,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) )
& ( ( r5_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(607,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(4473,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)],[607]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ C )
= ( k1_finsub_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).
thf(3380,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k1_finsub_1 @ A @ B @ C )
= ( k1_finsub_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1510,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k14_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_group_2) ).
thf(8689,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k14_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(1165,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r1_xreal_0 @ A @ np__0 )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_1) ).
thf(7049,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r1_xreal_0 @ A @ np__0 )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ ( k1_int_2 @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1524,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k6_group_2 @ A ) )
& ( m1_group_2 @ ( k6_group_2 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_group_2) ).
thf(8731,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_1 @ ( k6_group_2 @ A ) )
& ( m1_group_2 @ ( k6_group_2 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(656,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(4690,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)],[656]) ).
thf(381,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(3427,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)],[381]) ).
thf(481,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(3936,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)],[481]) ).
thf(1106,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k16_group_2 @ A @ B )
= ( k8_group_1 @ A ) ) )
=> ( ( v6_group_1 @ A )
& ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_group_2) ).
thf(6672,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
& ( ( k16_group_2 @ A @ B )
= ( k8_group_1 @ A ) ) )
=> ( ( v6_group_1 @ A )
& ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1079,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ ( k6_group_1 @ B @ A @ D ) )
= ( k6_group_1 @ C @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_group_6) ).
thf(6542,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ ( k6_group_1 @ B @ A @ D ) )
= ( k6_group_1 @ C @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(623,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(4529,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)],[623]) ).
thf(1265,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_2 @ A @ B @ C )
= ( k11_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_group_3) ).
thf(7539,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_2 @ A @ B @ C )
= ( k11_group_2 @ A @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_2 @ A @ B @ C )
= ( k11_group_2 @ A @ B @ C ) ) )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(1335,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_group_3) ).
thf(7897,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_group_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(1357,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(7992,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(477,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(3921,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)],[477]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ( ( ( r1_tarski @ A @ ( k2_finseq_1 @ C ) )
& ( r1_tarski @ B @ ( k2_finseq_1 @ D ) ) )
=> ( ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ! [F: $i] :
( ( m2_subset_1 @ F @ k1_numbers @ k5_numbers )
=> ~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( r1_xreal_0 @ F @ E ) ) ) )
<=> ( ( k14_finseq_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k8_finseq_1 @ k5_numbers @ ( k14_finseq_1 @ A ) @ ( k14_finseq_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_finseq_3) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ( ( ( r1_tarski @ A @ ( k2_finseq_1 @ C ) )
& ( r1_tarski @ B @ ( k2_finseq_1 @ D ) ) )
=> ( ( ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ! [F: $i] :
( ( m2_subset_1 @ F @ k1_numbers @ k5_numbers )
=> ~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( r1_xreal_0 @ F @ E ) ) ) )
=> ( ( k14_finseq_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k8_finseq_1 @ k5_numbers @ ( k14_finseq_1 @ A ) @ ( k14_finseq_1 @ B ) ) ) )
& ( ( ( k14_finseq_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k8_finseq_1 @ k5_numbers @ ( k14_finseq_1 @ A ) @ ( k14_finseq_1 @ B ) ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
=> ! [F: $i] :
( ( m2_subset_1 @ F @ k1_numbers @ k5_numbers )
=> ~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( r1_xreal_0 @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(903,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(5763,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)],[903]) ).
thf(1631,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r1_rlvect_1 @ B @ ( k2_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_group_2) ).
thf(9111,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r1_rlvect_1 @ B @ ( k2_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(827,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(5435,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)],[827]) ).
thf(596,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(4441,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(65,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(2096,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)],[65]) ).
thf(687,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(4813,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)],[687]) ).
thf(633,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(4580,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)],[633]) ).
thf(274,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ ( k2_xcmplx_0 @ B @ C ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) )
=> ( ( r1_xreal_0 @ B @ np__0 )
| ( ( r2_hidden @ B @ ( k2_finseq_1 @ A ) )
& ( r2_hidden @ B @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_finseq_1) ).
thf(2994,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ ( k2_xcmplx_0 @ B @ C ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) )
=> ( ( r1_xreal_0 @ B @ np__0 )
| ( ( r2_hidden @ B @ ( k2_finseq_1 @ A ) )
& ( r2_hidden @ B @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1236,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(7371,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)],[1236]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k2_group_6 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_group_6) ).
thf(9069,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k2_group_6 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(1766,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ B @ D )
| ( r1_rlvect_1 @ C @ D ) )
=> ( r1_rlvect_1 @ ( k8_group_4 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_latsubgr) ).
thf(9563,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_rlvect_1 @ B @ D )
| ( r1_rlvect_1 @ C @ D ) )
=> ( r1_rlvect_1 @ ( k8_group_4 @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(151,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(2471,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)],[151]) ).
thf(909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v1_group_6 @ D @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v4_group_6 @ D @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) )
& ( C
= ( k8_group_6 @ B @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) @ ( k11_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_group_6) ).
thf(5785,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v1_group_6 @ D @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v4_group_6 @ D @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) )
& ( C
= ( k8_group_6 @ B @ ( k6_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ ( k13_group_6 @ B @ A @ C ) @ ( k11_group_6 @ B @ ( k12_group_6 @ B @ A @ C ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(638,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(4598,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)],[638]) ).
thf(1245,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) ) @ ( k5_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_group_4) ).
thf(7447,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r1_group_2 @ A @ ( k5_group_4 @ A @ ( k1_subset_1 @ ( u1_struct_0 @ A ) ) ) @ ( k5_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k8_group_2 @ A @ B @ C ) )
& ( m1_group_2 @ ( k8_group_2 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_group_2) ).
thf(8804,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( v1_group_1 @ ( k8_group_2 @ A @ B @ C ) )
& ( m1_group_2 @ ( k8_group_2 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(1386,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k12_group_2 @ A @ D @ B ) @ C )
= ( k3_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_group_3) ).
thf(8116,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k12_group_2 @ A @ D @ B ) @ C )
= ( k3_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(950,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k12_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_group_2) ).
thf(5952,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k12_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(41,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(1990,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)],[41]) ).
thf(287,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(3048,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)],[287]) ).
thf(198,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(2684,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)],[198]) ).
thf(630,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).
thf(4566,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1373,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k3_group_1 @ B @ C ) )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_group_1) ).
thf(8067,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k3_group_1 @ B @ C ) )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(1494,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_4 @ A @ ( k6_finseq_1 @ ( u1_struct_0 @ A ) ) )
= ( k2_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_group_4) ).
thf(8637,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_4 @ A @ ( k6_finseq_1 @ ( u1_struct_0 @ A ) ) )
= ( k2_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(655,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4688,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k13_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_group_2) ).
thf(6564,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k13_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(523,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(4113,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)],[523]) ).
thf(1124,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(6821,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)],[1124]) ).
thf(1461,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_group_4 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ B )
& ( C
= ( u1_struct_0 @ D ) )
& ( v2_group_4 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_group_4) ).
thf(8477,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_group_4 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ B )
& ( C
= ( u1_struct_0 @ D ) )
& ( v2_group_4 @ D @ B ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ B )
& ( C
= ( u1_struct_0 @ D ) )
& ( v2_group_4 @ D @ B ) ) )
=> ( r2_hidden @ A @ ( a_1_0_group_4 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_group_3 @ A @ B @ C )
<=> ( r1_group_3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_group_3) ).
thf(5358,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_group_3 @ A @ B @ C )
=> ( r1_group_3 @ A @ B @ C ) )
& ( ( r1_group_3 @ A @ B @ C )
=> ( r2_group_3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1407,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k4_group_3 @ B @ D @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r2_hidden @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_group_3) ).
thf(8194,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k4_group_3 @ B @ D @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ C ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( k4_group_3 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(665,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(4722,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)],[665]) ).
thf(1355,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k4_group_2 @ A @ D @ B ) @ C )
= ( k2_group_2 @ A @ B @ ( k3_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_group_2) ).
thf(7982,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k4_group_2 @ A @ D @ B ) @ C )
= ( k2_group_2 @ A @ B @ ( k3_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(573,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( u1_struct_0 @ A ) )
& ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_group_6) ).
thf(4336,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
=> ( ( ( k1_relat_1 @ C )
= ( u1_struct_0 @ A ) )
& ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1657,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k1_group_3 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_group_3) ).
thf(9202,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k1_group_3 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) ) )
& ( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) ) )
& ( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_group_3 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(537,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4168,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1167,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k12_group_2 @ A @ ( k6_group_2 @ A ) @ B )
= ( u1_struct_0 @ A ) )
& ( ( k13_group_2 @ A @ ( k6_group_2 @ A ) @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_group_2) ).
thf(7070,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k12_group_2 @ A @ ( k6_group_2 @ A ) @ B )
= ( u1_struct_0 @ A ) )
& ( ( k13_group_2 @ A @ ( k6_group_2 @ A ) @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1132,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ C ) @ ( k3_group_1 @ A @ C ) )
= B )
& ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ ( k3_group_1 @ A @ C ) ) @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_group_3) ).
thf(6875,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ C ) @ ( k3_group_1 @ A @ C ) )
= B )
& ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ ( k3_group_1 @ A @ C ) ) @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1688,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_1_group_4 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A = C )
& ~ ( v1_group_4 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_group_4) ).
thf(9317,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_1_group_4 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A = C )
& ~ ( v1_group_4 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( A = C )
& ~ ( v1_group_4 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_1_group_4 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(774,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k4_group_3 @ A @ C @ B ) @ D )
= ( k3_group_3 @ A @ C @ ( k3_group_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_group_3) ).
thf(5229,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k4_group_3 @ A @ C @ B ) @ D )
= ( k3_group_3 @ A @ C @ ( k3_group_2 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1361,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r5_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( k6_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_group_3) ).
thf(8003,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( r5_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( k6_group_3 @ A @ C @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( k6_group_3 @ A @ C @ D ) ) )
=> ( r5_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(941,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_group_3 @ A @ D @ ( k2_group_3 @ A @ B @ C ) )
= ( k5_group_3 @ A @ ( k3_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_group_3) ).
thf(5927,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_group_3 @ A @ D @ ( k2_group_3 @ A @ B @ C ) )
= ( k5_group_3 @ A @ ( k3_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1317,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k11_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_group_2) ).
thf(7801,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k11_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(335,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3214,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1756,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_2 @ A @ B @ C ) @ ( k8_group_2 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_group_2) ).
thf(9535,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_2 @ A @ B @ C ) @ ( k8_group_2 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(84,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 ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2160,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 ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1528,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ? [D: $i] :
( ( v1_group_1 @ D )
& ( v1_group_3 @ D @ A )
& ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_group_3) ).
thf(8744,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ? [D: $i] :
( ( v1_group_1 @ D )
& ( v1_group_3 @ D @ A )
& ( m1_group_2 @ D @ A )
& ( ( u1_struct_0 @ D )
= ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(508,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(4045,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)],[508]) ).
thf(258,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(2942,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)],[258]) ).
thf(164,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_binop_1) ).
thf(2513,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1785,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ C )
& ( v2_group_4 @ D @ C ) )
=> ( ( r1_rlvect_1 @ ( k6_group_4 @ C ) @ B )
<=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ C ) )
=> ( ( v2_group_4 @ D @ C )
=> ( r1_rlvect_1 @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_group_4) ).
thf(9631,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ( ? [D: $i] :
( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ C )
& ( v2_group_4 @ D @ C ) )
=> ( ( ( r1_rlvect_1 @ ( k6_group_4 @ C ) @ B )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ C ) )
=> ( ( v2_group_4 @ D @ C )
=> ( r1_rlvect_1 @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ C ) )
=> ( ( v2_group_4 @ D @ C )
=> ( r1_rlvect_1 @ D @ B ) ) )
=> ( r1_rlvect_1 @ ( k6_group_4 @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(856,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(5570,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)],[856]) ).
thf(1575,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_group_6) ).
thf(8905,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(831,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( ( v1_group_3 @ D @ A )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( r2_hidden @ B @ ( k4_group_6 @ A @ D ) )
& ( r2_hidden @ C @ ( k4_group_6 @ A @ D ) ) )
=> ( r2_hidden @ ( k2_group_2 @ A @ B @ C ) @ ( k4_group_6 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_group_6) ).
thf(5452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( ( v1_group_3 @ D @ A )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( r2_hidden @ B @ ( k4_group_6 @ A @ D ) )
& ( r2_hidden @ C @ ( k4_group_6 @ A @ D ) ) )
=> ( r2_hidden @ ( k2_group_2 @ A @ B @ C ) @ ( k4_group_6 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(736,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(5047,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)],[736]) ).
thf(1483,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(8592,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)],[1483]) ).
thf(438,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(3737,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)],[438]) ).
thf(368,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(3376,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)],[368]) ).
thf(994,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k11_group_2 @ A @ D @ B ) @ C )
= ( k11_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_group_2) ).
thf(6120,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k2_group_2 @ A @ ( k11_group_2 @ A @ D @ B ) @ C )
= ( k11_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1537,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_finseqop @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( k4_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_group_1) ).
thf(8772,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_finseqop @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) )
= ( k4_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(1017,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_group_3) ).
thf(6238,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ ( k2_group_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1286,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ C @ B )
= ( k4_group_2 @ A @ B @ ( k3_group_2 @ A @ ( k3_group_1 @ A @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_3) ).
thf(7635,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_3 @ A @ C @ B )
= ( k4_group_2 @ A @ B @ ( k3_group_2 @ A @ ( k3_group_1 @ A @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1346,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_group_2) ).
thf(7942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_finsub_1) ).
thf(6472,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(506,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(4035,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)],[506]) ).
thf(1109,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(6683,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)],[1109]) ).
thf(1640,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_group_6 @ D @ A @ B )
=> ( ( k9_group_2 @ A @ C @ D )
= ( k9_group_2 @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_group_6) ).
thf(9138,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_group_6 @ D @ A @ B )
=> ( ( k9_group_2 @ A @ C @ D )
= ( k9_group_2 @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(782,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k8_group_1 @ C )
= ( k1_card_1 @ ( k12_group_2 @ A @ C @ B ) ) )
& ( ( k8_group_1 @ C )
= ( k1_card_1 @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_group_2) ).
thf(5250,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( k8_group_1 @ C )
= ( k1_card_1 @ ( k12_group_2 @ A @ C @ B ) ) )
& ( ( k8_group_1 @ C )
= ( k1_card_1 @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(464,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(3842,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)],[464]) ).
thf(611,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(4490,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)],[611]) ).
thf(715,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(4937,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)],[715]) ).
thf(269,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(2977,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)],[269]) ).
thf(1474,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ ( k6_group_1 @ B @ A @ D ) )
= ( k6_group_1 @ C @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_group_6) ).
thf(8537,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ B @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ ( k6_group_1 @ B @ A @ D ) )
= ( k6_group_1 @ C @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1198,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k13_group_2 @ A @ B @ C )
= ( k4_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_2) ).
thf(7196,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k13_group_2 @ A @ B @ C )
= ( k4_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(442,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(3754,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)],[442]) ).
thf(756,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(5171,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)],[756]) ).
thf(1146,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_rlvect_1 @ ( k12_group_6 @ A @ B @ D ) @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C )
= ( k2_group_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_group_6) ).
thf(6921,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r1_rlvect_1 @ ( k12_group_6 @ A @ B @ D ) @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C )
= ( k2_group_1 @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C )
= ( k2_group_1 @ B ) )
=> ( r1_rlvect_1 @ ( k12_group_6 @ A @ B @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1662,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k1_group_2 @ A @ ( k7_group_2 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_group_2) ).
thf(9238,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k1_group_2 @ A @ ( k7_group_2 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_group_1) ).
thf(5944,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(625,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(4534,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)],[625]) ).
thf(1616,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_group_1) ).
thf(9061,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(845,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ C @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ C ) @ ( k1_group_1 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_group_2) ).
thf(5523,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ C @ D ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ C ) @ ( k1_group_1 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(646,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k1_group_4 @ ( u1_struct_0 @ A ) @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) )
= ( k3_group_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_group_4) ).
thf(4641,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_group_4 @ A @ ( k1_group_4 @ ( u1_struct_0 @ A ) @ B @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) )
= ( k3_group_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(893,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k1_card_1 @ ( k2_finseq_1 @ A ) )
= ( k1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_finseq_1) ).
thf(5721,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k1_card_1 @ ( k2_finseq_1 @ A ) )
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1248,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_subset_1 @ ( k13_group_2 @ A @ C @ B ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
& ( m1_subset_1 @ ( k12_group_2 @ A @ C @ B ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
& ( m1_subset_1 @ ( k7_group_2 @ A @ C ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_group_6) ).
thf(7462,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_subset_1 @ ( k13_group_2 @ A @ C @ B ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
& ( m1_subset_1 @ ( k12_group_2 @ A @ C @ B ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
& ( m1_subset_1 @ ( k7_group_2 @ A @ C ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1382,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(8096,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)],[1382]) ).
thf(453,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(3786,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(717,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(4961,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)],[717]) ).
thf(291,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k7_group_2 @ A @ B ) )
=> ( r1_rlvect_1 @ B @ ( k3_group_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_group_4) ).
thf(3058,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k7_group_2 @ A @ B ) )
=> ( r1_rlvect_1 @ B @ ( k3_group_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(472,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
<=> ( ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) )
& ( v2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_group_6) ).
thf(3872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_group_6 @ C @ A @ B )
=> ( ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) )
& ( v2_funct_1 @ C ) ) )
& ( ( ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) )
& ( v2_funct_1 @ C ) )
=> ( v4_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(580,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(4377,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)],[580]) ).
thf(1073,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(6481,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)],[1073]) ).
thf(739,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ A @ ( k2_finseq_1 @ B ) )
=> ( ( r1_xreal_0 @ A @ C )
| ( r2_hidden @ ( k6_xcmplx_0 @ A @ C ) @ ( k2_finseq_1 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finseq_3) ).
thf(5079,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r2_hidden @ A @ ( k2_finseq_1 @ B ) )
=> ( ( r1_xreal_0 @ A @ C )
| ( r2_hidden @ ( k6_xcmplx_0 @ A @ C ) @ ( k2_finseq_1 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(242,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(2882,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(734,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(5018,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)],[734]) ).
thf(1324,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(7832,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)],[1324]) ).
thf(885,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k8_group_3 @ A @ B )
= ( k8_group_3 @ A @ C ) )
<=> ~ ( r1_xboole_0 @ ( k8_group_3 @ A @ B ) @ ( k8_group_3 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_group_3) ).
thf(5684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k8_group_3 @ A @ B )
= ( k8_group_3 @ A @ C ) )
=> ~ ( r1_xboole_0 @ ( k8_group_3 @ A @ B ) @ ( k8_group_3 @ A @ C ) ) )
& ( ~ ( r1_xboole_0 @ ( k8_group_3 @ A @ B ) @ ( k8_group_3 @ A @ C ) )
=> ( ( k8_group_3 @ A @ B )
= ( k8_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(341,axiom,
( ! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k4_card_1 @ ( k2_finseq_1 @ A ) )
= A ) )
& ! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( ( k4_card_1 @ A )
= A )
& ( ( k4_card_1 @ ( k1_card_1 @ A ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_1) ).
thf(3246,plain,
( ! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k4_card_1 @ ( k2_finseq_1 @ A ) )
= A ) )
& ! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( ( k4_card_1 @ A )
= A )
& ( ( k4_card_1 @ ( k1_card_1 @ A ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(586,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(4398,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)],[586]) ).
thf(355,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(3334,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)],[355]) ).
thf(1080,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(6545,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)],[1080]) ).
thf(733,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 ) )
=> ( ( v1_group_1 @ ( g1_group_1 @ A @ B ) )
& ( l1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_group_1) ).
thf(5015,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 ) )
=> ( ( v1_group_1 @ ( g1_group_1 @ A @ B ) )
& ( l1_group_1 @ ( g1_group_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1490,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(8625,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)],[1490]) ).
thf(1315,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(7796,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)],[1315]) ).
thf(724,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(4982,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)],[724]) ).
thf(1155,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_rlvect_1 @ ( k5_group_4 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_group_4) ).
thf(6994,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_rlvect_1 @ ( k5_group_4 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1133,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k5_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k5_group_6 @ A @ B ) @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) )
& ( m2_relset_1 @ ( k5_group_6 @ A @ B ) @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_6) ).
thf(6880,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k5_group_6 @ A @ B ) )
& ( v1_funct_2 @ ( k5_group_6 @ A @ B ) @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) )
& ( m2_relset_1 @ ( k5_group_6 @ A @ B ) @ ( k2_zfmisc_1 @ ( k4_group_6 @ A @ B ) @ ( k4_group_6 @ A @ B ) ) @ ( k4_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(567,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(4314,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)],[567]) ).
thf(386,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(3448,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)],[386]) ).
thf(621,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(4522,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)],[621]) ).
thf(776,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(5235,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)],[776]) ).
thf(1443,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(8396,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)],[1443]) ).
thf(422,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(3642,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)],[422]) ).
thf(628,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(4561,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)],[628]) ).
thf(1676,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_2 @ A @ B )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_group_2) ).
thf(9281,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k7_group_2 @ A @ B )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(1440,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k12_group_2 @ A @ ( k9_group_2 @ A @ C @ D ) @ B )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_group_2) ).
thf(8377,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k12_group_2 @ A @ ( k9_group_2 @ A @ C @ D ) @ B )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k12_group_2 @ A @ C @ B ) @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v4_finsub_1 @ C ) )
=> ( ( ( m1_subset_1 @ A @ C )
& ( m1_subset_1 @ B @ C ) )
=> ( m1_subset_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finsub_1) ).
thf(4003,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v4_finsub_1 @ C ) )
=> ( ( ( m1_subset_1 @ A @ C )
& ( m1_subset_1 @ B @ C ) )
=> ( m1_subset_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1272,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_group_6 @ C @ A @ B )
<=> ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_group_6) ).
thf(7568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_group_6 @ C @ A @ B )
=> ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) ) )
& ( ( ( k9_group_6 @ A @ B @ C )
= ( u1_struct_0 @ B ) )
=> ( v3_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(1058,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k13_group_2 @ A @ C @ B )
= ( k11_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_group_3) ).
thf(6421,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k13_group_2 @ A @ C @ B )
= ( k11_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1612,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r2_group_6 @ A @ ( k6_group_6 @ A @ ( k5_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_group_6) ).
thf(9050,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r2_group_6 @ A @ ( k6_group_6 @ A @ ( k5_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(1329,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(7879,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)],[1329]) ).
thf(39,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(1980,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)],[39]) ).
thf(1622,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( u1_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k5_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_group_6) ).
thf(9082,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( u1_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k5_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(8,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(1830,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)],[8]) ).
thf(310,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(3127,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)],[310]) ).
thf(1432,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(8327,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)],[1432]) ).
thf(851,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k13_group_2 @ A @ C @ B ) )
= ( k11_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_group_3) ).
thf(5543,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k13_group_2 @ A @ C @ B ) )
= ( k11_group_2 @ A @ C @ ( k12_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(750,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(5152,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)],[750]) ).
thf(202,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(2701,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)],[202]) ).
thf(1721,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r1_tarski @ ( k8_group_1 @ B ) @ ( k8_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_group_2) ).
thf(9413,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( r1_tarski @ ( k8_group_1 @ B ) @ ( k8_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(669,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(4737,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)],[669]) ).
thf(1180,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k13_group_2 @ A @ ( k9_group_2 @ A @ C @ D ) @ B )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_group_2) ).
thf(7127,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k13_group_2 @ A @ ( k9_group_2 @ A @ C @ D ) @ B )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k13_group_2 @ A @ C @ B ) @ ( k13_group_2 @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(830,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(5450,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1009,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_group_3 @ A @ B @ C ) @ ( k2_group_2 @ A @ ( k2_group_2 @ A @ ( k1_group_2 @ A @ C ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_group_3) ).
thf(6206,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_group_3 @ A @ B @ C ) @ ( k2_group_2 @ A @ ( k2_group_2 @ A @ ( k1_group_2 @ A @ C ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(285,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(3041,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)],[285]) ).
thf(1802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ A )
= C )
& ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ B )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_4) ).
thf(9690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ A )
= C )
& ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(436,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( r1_tarski @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finseq_3) ).
thf(3715,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( r1_tarski @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( r2_group_6 @ ( k6_group_6 @ ( k8_group_4 @ A @ B @ C ) @ ( k1_group_6 @ A @ ( k8_group_4 @ A @ B @ C ) @ C ) ) @ ( k6_group_6 @ B @ ( k2_group_6 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_group_6) ).
thf(9445,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( r2_group_6 @ ( k6_group_6 @ ( k8_group_4 @ A @ B @ C ) @ ( k1_group_6 @ A @ ( k8_group_4 @ A @ B @ C ) @ C ) ) @ ( k6_group_6 @ B @ ( k2_group_6 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(121,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(2354,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)],[121]) ).
thf(748,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(5147,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)],[748]) ).
thf(766,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k1_nat_1 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_group_1) ).
thf(5208,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k1_nat_1 @ A @ B ) @ D )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(268,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(2975,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)],[268]) ).
thf(872,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( B
= ( k4_card_1 @ A ) )
<=> ( ( k1_card_1 @ B )
= ( k1_card_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_card_1) ).
thf(5633,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( B
= ( k4_card_1 @ A ) )
=> ( ( k1_card_1 @ B )
= ( k1_card_1 @ A ) ) )
& ( ( ( k1_card_1 @ B )
= ( k1_card_1 @ A ) )
=> ( B
= ( k4_card_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(372,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(3388,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)],[372]) ).
thf(261,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ~ ( ~ ( v1_xboole_0 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ A )
=> ~ ( ( C
= ( k1_funct_1 @ B @ np__1 ) )
& ( B
= ( k8_finseq_1 @ A @ ( k12_finseq_1 @ A @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_finseq_3) ).
thf(2949,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ~ ( ~ ( v1_xboole_0 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ A )
=> ~ ( ( C
= ( k1_funct_1 @ B @ np__1 ) )
& ( B
= ( k8_finseq_1 @ A @ ( k12_finseq_1 @ A @ C ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1523,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ B @ C )
=> ( r1_group_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_group_2) ).
thf(8729,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A )
& ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ B @ C )
=> ( r1_group_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(1513,axiom,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( k10_finseq_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_finseq_3) ).
thf(8696,plain,
! [A: $i,B: $i] :
( k1_xboole_0
!= ( k10_finseq_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(1328,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_group_1 @ A )
=> ( A
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
thf(7876,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( ( v1_group_1 @ A )
=> ( A
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1249,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(7466,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)],[1249]) ).
thf(1743,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_finseqop @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_group_1) ).
thf(9486,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v1_finseqop @ ( u1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(685,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(4802,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)],[685]) ).
thf(1430,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k3_group_2 @ A @ B @ C ) )
= ( k3_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_group_3) ).
thf(8316,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k10_group_2 @ A @ D @ ( k3_group_2 @ A @ B @ C ) )
= ( k3_group_2 @ A @ B @ ( k10_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(1746,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k5_group_2 @ B )
= ( k5_group_2 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_group_2) ).
thf(9495,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k5_group_2 @ B )
= ( k5_group_2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1040,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k7_group_2 @ A @ ( k8_group_2 @ A @ B @ C ) )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_group_2) ).
thf(6337,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k7_group_2 @ A @ ( k8_group_2 @ A @ B @ C ) )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1749,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k1_group_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_group_2) ).
thf(9505,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k1_group_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(23,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 ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1898,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 ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1454,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(8448,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(229,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 ) )
=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_4) ).
thf(2838,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 ) )
=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1137,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(6899,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)],[1137]) ).
thf(175,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(2558,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)],[175]) ).
thf(461,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(3829,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)],[461]) ).
thf(898,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(5736,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(309,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_finseq_1 @ A )
!= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finseq_3) ).
thf(3124,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_finseq_1 @ A )
!= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(529,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(4133,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)],[529]) ).
thf(1260,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ A @ ( k7_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( D = A )
& ( r2_group_3 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_group_3) ).
thf(7515,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r2_hidden @ A @ ( k7_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( D = A )
& ( r2_group_3 @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( D = A )
& ( r2_group_3 @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( k7_group_3 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(130,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(2379,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)],[130]) ).
thf(1748,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k12_group_2 @ A @ B @ ( k2_group_1 @ A ) )
= ( k7_group_2 @ A @ B ) )
& ( ( k13_group_2 @ A @ B @ ( k2_group_1 @ A ) )
= ( k7_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_group_2) ).
thf(9500,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k12_group_2 @ A @ B @ ( k2_group_1 @ A ) )
= ( k7_group_2 @ A @ B ) )
& ( ( k13_group_2 @ A @ B @ ( k2_group_1 @ A ) )
= ( k7_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(1022,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(6262,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)],[1022]) ).
thf(723,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).
thf(4976,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(122,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(2357,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)],[122]) ).
thf(34,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(1955,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)],[34]) ).
thf(231,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(2843,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)],[231]) ).
thf(206,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ A @ k1_xboole_0 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_4) ).
thf(2711,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ A @ k1_xboole_0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(520,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(4106,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)],[520]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( k3_group_3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_group_3) ).
thf(7163,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( k3_group_3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
=> ( r2_hidden @ A @ ( k3_group_3 @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(532,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(4143,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)],[532]) ).
thf(337,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k5_group_1 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ np__0 )
= ( k2_group_1 @ A ) )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ ( k1_nat_1 @ D @ np__1 ) )
= ( k1_group_1 @ A @ ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_group_1) ).
thf(3224,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ k5_numbers ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k5_group_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ np__0 )
= ( k2_group_1 @ A ) )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ ( k1_nat_1 @ D @ np__1 ) )
= ( k1_group_1 @ A @ ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ np__0 )
= ( k2_group_1 @ A ) )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ ( k1_nat_1 @ D @ np__1 ) )
= ( k1_group_1 @ A @ ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ B @ C @ D ) @ C ) ) ) ) )
=> ( B
= ( k5_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1560,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_2 @ A @ B @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_group_2) ).
thf(8850,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k8_group_2 @ A @ B @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(163,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(2511,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)],[163]) ).
thf(282,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(3024,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)],[282]) ).
thf(1455,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(8449,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)],[1455]) ).
thf(1525,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k4_group_4 @ A @ ( k6_finseq_1 @ k4_numbers ) @ ( k6_finseq_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_group_4) ).
thf(8734,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k4_group_4 @ A @ ( k6_finseq_1 @ k4_numbers ) @ ( k6_finseq_1 @ ( u1_struct_0 @ A ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1200,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_card_1) ).
thf(7202,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1786,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_lattices @ ( k11_group_4 @ A ) )
= ( k10_group_4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_group_4) ).
thf(9637,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_lattices @ ( k11_group_4 @ A ) )
= ( k10_group_4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(257,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(2939,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)],[257]) ).
thf(1196,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(7192,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)],[1196]) ).
thf(1069,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(6467,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)],[1069]) ).
thf(1451,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r1_xreal_0 @ A @ B )
<=> ( r1_ordinal1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_card_1) ).
thf(8433,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( r1_xreal_0 @ A @ B )
=> ( r1_ordinal1 @ A @ B ) )
& ( ( r1_ordinal1 @ A @ B )
=> ( r1_xreal_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(1770,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( v6_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_group_2) ).
thf(9574,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( v6_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1673,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v1_group_1 @ ( k6_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_group_6) ).
thf(9274,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v1_group_1 @ ( k6_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(1019,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(6245,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)],[1019]) ).
thf(1149,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(6960,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)],[1149]) ).
thf(1544,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C )
<=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_group_4) ).
thf(8798,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ C ) @ B ) )
& ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ C ) @ B )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(863,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_2 @ A @ B @ C )
= ( k4_group_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_group_2) ).
thf(5596,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_group_2 @ A @ B @ C )
= ( k4_group_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(232,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).
thf(2848,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(534,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(4150,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)],[534]) ).
thf(935,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(5895,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)],[935]) ).
thf(1337,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( v6_group_1 @ C )
=> ( ( k9_group_1 @ C )
= ( k9_group_1 @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_group_3) ).
thf(7908,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( v6_group_1 @ C )
=> ( ( k9_group_1 @ C )
= ( k9_group_1 @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(654,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(4671,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)],[654]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k7_rlvect_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_rlvect_1) ).
thf(4111,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k7_rlvect_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(1734,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) )
<=> ~ ( r1_xboole_0 @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_group_2) ).
thf(9453,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) )
=> ~ ( r1_xboole_0 @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) )
& ( ~ ( r1_xboole_0 @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) )
=> ( ( k12_group_2 @ A @ D @ B )
= ( k12_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_group_3) ).
thf(6992,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_group_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(591,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(4414,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)],[591]) ).
thf(689,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(4819,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)],[689]) ).
thf(1012,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_group_2 @ A )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_group_2) ).
thf(6220,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k6_group_2 @ A )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1097,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(6622,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)],[1097]) ).
thf(140,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(2435,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)],[140]) ).
thf(148,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(2458,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)],[148]) ).
thf(1597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B != k1_xboole_0 )
& ( ( k1_group_2 @ A @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k1_group_2 @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_group_2) ).
thf(8987,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B != k1_xboole_0 )
& ( ( k1_group_2 @ A @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k1_group_2 @ A @ B )
!= k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(294,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 )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(3067,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 )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1795,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k9_group_2 @ A @ B @ C ) @ D ) @ ( k9_group_2 @ A @ B @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_group_2) ).
thf(9665,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k9_group_2 @ A @ B @ C ) @ D ) @ ( k9_group_2 @ A @ B @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(907,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
<=> ( ( k3_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_group_1) ).
thf(5777,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
=> ( ( k3_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) )
& ( ( ( k3_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k8_relset_1 @ A @ B @ D @ C ) )
& ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ D @ C ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_partfun1) ).
thf(7288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k8_relset_1 @ A @ B @ D @ C ) )
& ( m2_relset_1 @ ( k8_relset_1 @ A @ B @ D @ C ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(679,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(4780,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)],[679]) ).
thf(543,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(4185,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)],[543]) ).
thf(99,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 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_4) ).
thf(2209,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 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1533,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_group_2) ).
thf(8761,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k2_group_2 @ A @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ B ) )
= ( k7_group_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B )
!= k1_xboole_0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1807,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_finseq_1 @ B @ k4_numbers )
& ( m1_finseq_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k4_group_4 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_group_4) ).
thf(5832,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_finseq_1 @ B @ k4_numbers )
& ( m1_finseq_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m2_finseq_1 @ ( k4_group_4 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1549,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r2_group_3 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_group_3) ).
thf(8812,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r2_group_3 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(239,axiom,
? [A: $i] : ( l1_rlvect_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_rlvect_1) ).
thf(2875,plain,
? [A: $i] : ( l1_rlvect_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1028,axiom,
( ~ ( v3_struct_0 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v3_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v4_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v7_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( l1_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_group_1) ).
thf(6284,plain,
( ~ ( v3_struct_0 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v3_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v4_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( v7_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
& ( l1_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1233,axiom,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(7363,plain,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1267,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_4 @ A )
= ( g3_lattices @ ( k1_group_3 @ A ) @ ( k9_group_4 @ A ) @ ( k10_group_4 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_group_4) ).
thf(7552,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_4 @ A )
= ( g3_lattices @ ( k1_group_3 @ A ) @ ( k9_group_4 @ A ) @ ( k10_group_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( 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 ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(3400,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( 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 ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(382,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(3433,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)],[382]) ).
thf(557,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(4278,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(417,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(3584,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)],[417]) ).
thf(1129,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( C
= ( k5_group_4 @ A @ B ) )
<=> ( ( r1_tarski @ B @ ( u1_struct_0 @ C ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( r1_tarski @ B @ ( u1_struct_0 @ D ) )
=> ( m1_group_2 @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_4) ).
thf(6850,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( C
= ( k5_group_4 @ A @ B ) )
=> ( ( r1_tarski @ B @ ( u1_struct_0 @ C ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( r1_tarski @ B @ ( u1_struct_0 @ D ) )
=> ( m1_group_2 @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ ( u1_struct_0 @ C ) )
& ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( r1_tarski @ B @ ( u1_struct_0 @ D ) )
=> ( m1_group_2 @ C @ D ) ) ) )
=> ( C
= ( k5_group_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(650,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(4651,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)],[650]) ).
thf(1675,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_group_2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_group_2) ).
thf(9279,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_group_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(959,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_group_3 @ A @ B @ C )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k4_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_group_3) ).
thf(5981,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_group_3 @ A @ B @ C )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k4_group_3 @ A @ C @ D ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( B
= ( k4_group_3 @ A @ C @ D ) ) )
=> ( r3_group_3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1296,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(7676,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(154,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(2479,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)],[154]) ).
thf(640,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(4606,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)],[640]) ).
thf(418,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(3589,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)],[418]) ).
thf(54,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(2045,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)],[54]) ).
thf(1285,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
& ( v1_group_6 @ C @ A @ ( k6_group_6 @ A @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) )
=> ( ( C
= ( k11_group_6 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) @ C @ D )
= ( k12_group_2 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_group_6) ).
thf(7627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) )
& ( v1_group_6 @ C @ A @ ( k6_group_6 @ A @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) ) )
=> ( ( ( C
= ( k11_group_6 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) @ C @ D )
= ( k12_group_2 @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k6_group_6 @ A @ B ) ) @ C @ D )
= ( k12_group_2 @ A @ B @ D ) ) )
=> ( C
= ( k11_group_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1684,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k2_group_1 @ B ) )
= ( k2_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_group_1) ).
thf(9306,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k2_group_1 @ B ) )
= ( k2_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(1625,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_group_1) ).
thf(9092,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(32,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 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_4) ).
thf(1949,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 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(673,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(4763,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(238,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(2870,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)],[238]) ).
thf(716,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(4944,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)],[716]) ).
thf(698,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(4873,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)],[698]) ).
thf(9,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(1834,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)],[9]) ).
thf(652,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( 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',t3_lattice4) ).
thf(4656,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( 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)],[652]) ).
thf(407,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(3533,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)],[407]) ).
thf(1723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( r1_rlvect_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_group_2) ).
thf(9417,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( r1_rlvect_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_1) ).
thf(5966,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(12,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 )
<=> ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_4) ).
thf(1844,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 )
=> ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) )
& ( ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) )
=> ( r1_partfun1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(857,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(5573,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)],[857]) ).
thf(648,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(4646,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)],[648]) ).
thf(1332,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_tarski @ ( k4_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_group_2) ).
thf(7889,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r1_tarski @ ( k4_group_2 @ A @ C @ ( k13_group_2 @ A @ D @ B ) ) @ ( k2_group_2 @ A @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(797,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(5308,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)],[797]) ).
thf(215,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(2743,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)],[215]) ).
thf(275,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(2997,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)],[275]) ).
thf(518,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(4102,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)],[518]) ).
thf(1415,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v5_group_1 @ B @ A )
<=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
=> ( C = np__0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_group_1) ).
thf(8228,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( v5_group_1 @ B @ A )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
=> ( C = np__0 ) ) ) )
& ( ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( k6_group_1 @ A @ C @ B )
= ( k2_group_1 @ A ) )
=> ( C = np__0 ) ) )
=> ( v5_group_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(118,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(2305,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)],[118]) ).
thf(1397,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_group_1) ).
thf(8153,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(1781,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) )
=> ( ( ( E = B )
& ( F = C ) )
=> ( ( k1_group_1 @ D @ E @ F )
= ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_group_2) ).
thf(9615,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) )
=> ( ( ( E = B )
& ( F = C ) )
=> ( ( k1_group_1 @ D @ E @ F )
= ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A != B )
& ( B != C )
& ( C != A ) )
<=> ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_finseq_3) ).
thf(5124,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != B )
& ( B != C )
& ( C != A ) )
=> ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) )
& ( ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) )
=> ( ( A != B )
& ( B != C )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(538,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(4170,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1641,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_group_4) ).
thf(9141,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k8_group_4 @ A @ B @ C ) )
= ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(802,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
<=> ( ( k1_group_1 @ A @ B @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_group_1) ).
thf(5332,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) )
=> ( ( k1_group_1 @ A @ B @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) ) )
& ( ( ( k1_group_1 @ A @ B @ ( k3_group_1 @ A @ C ) )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1753,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v2_group_4 @ B @ A )
<=> ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_2 @ B @ C )
=> ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= C )
| ( C
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_group_4) ).
thf(9515,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( v2_group_4 @ B @ A )
=> ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_2 @ B @ C )
=> ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= C )
| ( C
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ) ) )
& ( ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_2 @ B @ C )
=> ( ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= C )
| ( C
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ) )
=> ( v2_group_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(1376,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( m2_subset_1 @ ( k4_card_1 @ A ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_1) ).
thf(8075,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( m2_subset_1 @ ( k4_card_1 @ A ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(1114,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) ) )
=> ( ( k2_group_2 @ A @ B @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_group_2) ).
thf(6726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ B ) ) ) )
=> ( ( k2_group_2 @ A @ B @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(1789,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_3 @ ( k5_group_2 @ A ) @ A )
& ( v1_group_3 @ ( k6_group_2 @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_group_3) ).
thf(9647,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_group_3 @ ( k5_group_2 @ A ) @ A )
& ( v1_group_3 @ ( k6_group_2 @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_2) ).
thf(5315,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(204,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_4) ).
thf(2707,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1481,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_group_1 @ ( k13_group_6 @ A @ B @ C ) )
& ( m1_group_2 @ ( k13_group_6 @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_group_6) ).
thf(8584,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m1_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_group_1 @ ( k13_group_6 @ A @ B @ C ) )
& ( m1_group_2 @ ( k13_group_6 @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(1359,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( r1_rlvect_1 @ D @ B )
& ( r1_rlvect_1 @ D @ C ) )
=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_2) ).
thf(7996,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( r1_rlvect_1 @ D @ B )
& ( r1_rlvect_1 @ D @ C ) )
=> ( r1_rlvect_1 @ D @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(47,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(2026,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)],[47]) ).
thf(1143,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(6913,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)],[1143]) ).
thf(1287,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ ( k3_group_1 @ A @ C ) )
= ( k3_group_1 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_group_6) ).
thf(7638,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ ( k3_group_1 @ A @ C ) )
= ( k3_group_1 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(660,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(4705,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)],[660]) ).
thf(662,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(4710,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(272,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(2988,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)],[272]) ).
thf(1015,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_group_3 @ A @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) )
<=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_group_3) ).
thf(6230,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k7_group_3 @ A @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) )
=> ( B
= ( k2_group_1 @ A ) ) )
& ( ( B
= ( k2_group_1 @ A ) )
=> ( ( k7_group_3 @ A @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(894,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k12_group_2 @ A @ C @ B )
= ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_group_2) ).
thf(5724,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k12_group_2 @ A @ C @ B )
= ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1123,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(6818,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)],[1123]) ).
thf(1460,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(8474,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1539,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( B
= ( k5_group_2 @ A ) )
<=> ( ( u1_struct_0 @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_group_2) ).
thf(8780,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( B
= ( k5_group_2 @ A ) )
=> ( ( u1_struct_0 @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) ) )
& ( ( ( u1_struct_0 @ B )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) ) )
=> ( B
= ( k5_group_2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(1567,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ ( k8_group_4 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_group_4) ).
thf(8882,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ ( k8_group_4 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1628,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k9_group_1 @ ( k5_group_2 @ A ) )
= np__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_group_2) ).
thf(9102,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k9_group_1 @ ( k5_group_2 @ A ) )
= np__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(969,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(6030,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)],[969]) ).
thf(1164,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( k2_group_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) @ B )
= ( u1_struct_0 @ A ) )
& ( ( k2_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_group_2) ).
thf(7044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( k2_group_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) @ B )
= ( u1_struct_0 @ A ) )
& ( ( k2_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(168,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(2532,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)],[168]) ).
thf(761,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) )
= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_1) ).
thf(5191,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ( ( k2_xboole_0 @ ( k2_finseq_1 @ A ) @ ( k1_tarski @ ( k2_xcmplx_0 @ A @ np__1 ) ) )
= ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(913,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(5800,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)],[913]) ).
thf(1101,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_group_2 @ A @ ( k2_group_1 @ A ) @ B )
= B )
& ( ( k4_group_2 @ A @ ( k2_group_1 @ A ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_group_2) ).
thf(6639,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_group_2 @ A @ ( k2_group_1 @ A ) @ B )
= B )
& ( ( k4_group_2 @ A @ ( k2_group_1 @ A ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(370,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(3383,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1562,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( r1_nat_1 @ ( k9_group_1 @ B ) @ ( k9_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_group_2) ).
thf(8854,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v6_group_1 @ A )
=> ( r1_nat_1 @ ( k9_group_1 @ B ) @ ( k9_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(507,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( v8_vectsp_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_vectsp_1) ).
thf(4042,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( v8_vectsp_1 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v6_vectsp_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1577,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ B )
& ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_group_2) ).
thf(8912,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ B )
& ( m1_group_2 @ ( k9_group_2 @ A @ B @ C ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(304,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(3104,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(44,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(2004,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)],[44]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ! [E: $i] :
( ( v4_ordinal2 @ E )
=> ! [F: $i] :
( ( v4_ordinal2 @ F )
=> ~ ( ( r1_tarski @ A @ ( k2_finseq_1 @ B ) )
& ~ ( r1_xreal_0 @ D @ C )
& ( r1_xreal_0 @ np__1 @ E )
& ( r1_xreal_0 @ F @ ( k3_finseq_1 @ ( k14_finseq_1 @ A ) ) )
& ( ( k1_funct_1 @ ( k14_finseq_1 @ A ) @ F )
= C )
& ( ( k1_funct_1 @ ( k14_finseq_1 @ A ) @ E )
= D )
& ( r1_xreal_0 @ E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_finseq_3) ).
thf(3991,plain,
! [A: $i,B: $i] :
( ( v4_ordinal2 @ B )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ! [D: $i] :
( ( v4_ordinal2 @ D )
=> ! [E: $i] :
( ( v4_ordinal2 @ E )
=> ! [F: $i] :
( ( v4_ordinal2 @ F )
=> ~ ( ( r1_tarski @ A @ ( k2_finseq_1 @ B ) )
& ~ ( r1_xreal_0 @ D @ C )
& ( r1_xreal_0 @ np__1 @ E )
& ( r1_xreal_0 @ F @ ( k3_finseq_1 @ ( k14_finseq_1 @ A ) ) )
& ( ( k1_funct_1 @ ( k14_finseq_1 @ A ) @ F )
= C )
& ( ( k1_funct_1 @ ( k14_finseq_1 @ A ) @ E )
= D )
& ( r1_xreal_0 @ E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(915,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(5813,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)],[915]) ).
thf(1484,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_group_6 @ C @ A @ B )
<=> ( ( k13_group_6 @ A @ B @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_group_6) ).
thf(8606,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_group_6 @ C @ A @ B )
=> ( ( k13_group_6 @ A @ B @ C )
= B ) )
& ( ( ( k13_group_6 @ A @ B @ C )
= B )
=> ( v3_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(811,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_group_2) ).
thf(5368,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(354,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(3331,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)],[354]) ).
thf(313,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3136,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1113,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) )
=> ( ( C
= ( k9_group_3 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( D = E )
& ( r5_group_3 @ A @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_group_3) ).
thf(6694,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) )
=> ( ( ( C
= ( k9_group_3 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( D = E )
& ( r5_group_3 @ A @ B @ E ) ) )
& ( ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( D = E )
& ( r5_group_3 @ A @ B @ E ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( D = E )
& ( r5_group_3 @ A @ B @ E ) ) )
& ( ? [E: $i] :
( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A )
& ( D = E )
& ( r5_group_3 @ A @ B @ E ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_group_3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(841,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k5_group_3 @ A @ B @ C )
= ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_3) ).
thf(5505,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k5_group_3 @ A @ B @ C )
= ( k3_group_3 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1487,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ ( k1_group_2 @ A @ C ) @ ( k1_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_group_2) ).
thf(8617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ ( k1_group_2 @ A @ C ) @ ( k1_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(622,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
thf(4527,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(707,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(4900,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)],[707]) ).
thf(1606,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_6) ).
thf(9028,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_group_6 @ C @ A @ B )
=> ( m1_group_2 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(1387,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( u1_struct_0 @ ( k5_group_4 @ A @ B ) )
= ( k1_setfam_1 @ ( a_2_0_group_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_group_4) ).
thf(8119,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( u1_struct_0 @ ( k5_group_4 @ A @ B ) )
= ( k1_setfam_1 @ ( a_2_0_group_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(600,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k2_card_1 @ ( k1_card_1 @ A ) )
= ( k1_card_1 @ ( k1_nat_1 @ A @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_card_1) ).
thf(4451,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k2_card_1 @ ( k1_card_1 @ A ) )
= ( k1_card_1 @ ( k1_nat_1 @ A @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(864,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( a_3_0_group_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_2) ).
thf(5600,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( a_3_0_group_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1243,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v1_group_4 @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k5_group_4 @ A @ C )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ( ( k5_group_4 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_group_4) ).
thf(7437,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( v1_group_4 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k5_group_4 @ A @ C )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ( ( k5_group_4 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( ( k5_group_4 @ A @ C )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) )
& ( ( k5_group_4 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) )
!= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) )
=> ( v1_group_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(754,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(5164,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)],[754]) ).
thf(1805,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ C @ D )
= B )
& ( ( k1_group_1 @ A @ D @ C )
= B ) ) ) ) )
| ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_group_1) ).
thf(9701,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_group_1 @ A @ C @ B )
= C )
& ( ( k1_group_1 @ A @ B @ C )
= C )
& ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k1_group_1 @ A @ C @ D )
= B )
& ( ( k1_group_1 @ A @ D @ C )
= B ) ) ) ) )
| ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(1757,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] :
( ( m1_group_2 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v2_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_2) ).
thf(9537,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ? [B: $i] :
( ( m1_group_2 @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v2_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(747,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(5144,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)],[747]) ).
thf(954,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_group_1) ).
thf(5963,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( ( k1_group_1 @ C @ D @ E )
= ( k1_group_1 @ C @ E @ D ) )
=> ( ( k1_group_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) )
= ( k1_group_1 @ C @ ( k6_group_1 @ C @ B @ E ) @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_4) ).
thf(2956,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(324,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(3181,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)],[324]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_4 @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(2475,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_4 @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(226,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(2786,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)],[226]) ).
thf(352,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(3324,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)],[352]) ).
thf(649,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(4649,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)],[649]) ).
thf(1740,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( m1_group_2 @ B @ ( k6_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_group_2) ).
thf(9470,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( m1_group_2 @ B @ ( k6_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(848,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5532,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(1768,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k10_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_group_2) ).
thf(9569,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k10_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(1003,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(6181,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)],[1003]) ).
thf(1797,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k5_lattices @ ( k11_group_4 @ A ) )
= ( k5_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_group_4) ).
thf(9669,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k5_lattices @ ( k11_group_4 @ A ) )
= ( k5_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(540,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(4175,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)],[540]) ).
thf(402,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(3497,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)],[402]) ).
thf(535,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(4153,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)],[535]) ).
thf(1580,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ ( k6_group_2 @ A ) ) @ B )
& ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k6_group_2 @ A ) @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_group_2) ).
thf(8925,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ B @ ( k6_group_2 @ A ) ) @ B )
& ( r1_group_2 @ A @ ( k9_group_2 @ A @ ( k6_group_2 @ A ) @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(1029,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(6290,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(1751,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k5_group_2 @ A ) )
=> ( r1_group_2 @ A @ C @ ( k5_group_2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_group_3) ).
thf(9510,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k5_group_2 @ A ) )
=> ( r1_group_2 @ A @ C @ ( k5_group_2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(465,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(3844,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)],[465]) ).
thf(1713,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( k1_card_1 @ ( k9_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_group_3) ).
thf(9393,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( k1_card_1 @ ( k9_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(887,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(5692,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)],[887]) ).
thf(677,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ B )
& ( ( k3_finseq_1 @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finseq_1) ).
thf(4774,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ B )
& ( ( k3_finseq_1 @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1728,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( D
= ( k8_group_2 @ A @ B @ C ) )
<=> ( ( u1_struct_0 @ D )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_group_2) ).
thf(9434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( D
= ( k8_group_2 @ A @ B @ C ) )
=> ( ( u1_struct_0 @ D )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) )
& ( ( ( u1_struct_0 @ D )
= ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k7_group_2 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) )
=> ( D
= ( k8_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(1354,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_group_2) ).
thf(7979,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_rlvect_1 @ ( k13_group_6 @ B @ A @ D ) @ C )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_group_6) ).
thf(5837,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_rlvect_1 @ ( k13_group_6 @ B @ A @ D ) @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ D @ E ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ D @ E ) ) )
=> ( r1_rlvect_1 @ ( k13_group_6 @ B @ A @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1446,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) @ ( u1_group_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_group_1) ).
thf(8420,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k2_group_1 @ A ) @ ( u1_group_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(1242,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(7416,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)],[1242]) ).
thf(406,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(3529,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)],[406]) ).
thf(1076,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(6521,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)],[1076]) ).
thf(426,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_finseq_3) ).
thf(3677,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(124,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r5_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).
thf(2362,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r5_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1026,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(6277,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)],[1026]) ).
thf(853,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ ( k2_group_3 @ A @ B @ C ) @ ( k7_group_3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_group_3) ).
thf(5549,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ ( k2_group_3 @ A @ B @ C ) @ ( k7_group_3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1543,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ B @ D ) )
| ( ( k1_group_1 @ A @ C @ B )
= ( k1_group_1 @ A @ D @ B ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_group_1) ).
thf(8793,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ B @ D ) )
| ( ( k1_group_1 @ A @ C @ B )
= ( k1_group_1 @ A @ D @ B ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(89,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(2183,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)],[89]) ).
thf(1637,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m2_subset_1 @ ( k17_group_2 @ A @ B ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_group_2) ).
thf(9130,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m2_subset_1 @ ( k17_group_2 @ A @ B ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(1651,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
<=> ( ( k11_group_3 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t163_group_3) ).
thf(9173,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( k11_group_3 @ A @ B )
= A ) )
& ( ( ( k11_group_3 @ A @ B )
= A )
=> ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(1764,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v3_realset2 @ ( k5_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_group_6) ).
thf(9559,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v3_realset2 @ ( k5_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k7_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_group_2) ).
thf(7017,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k7_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(361,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(3351,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)],[361]) ).
thf(244,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(2902,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1793,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
thf(9660,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_1 @ A @ B @ C )
= ( k10_group_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k10_group_1) ).
thf(5211,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k10_group_1 @ A @ B @ C )
= ( k10_group_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(861,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_group_6 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_group_6) ).
thf(5590,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_group_6 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1085,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k6_group_1 @ B @ A @ ( k1_group_1 @ B @ C @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_group_1) ).
thf(6569,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k6_group_1 @ B @ A @ ( k1_group_1 @ B @ C @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1520,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( v3_group_6 @ ( k11_group_6 @ A @ B ) @ A @ ( k6_group_6 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_group_6) ).
thf(8721,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( v3_group_6 @ ( k11_group_6 @ A @ B ) @ A @ ( k6_group_6 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(51,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(2036,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)],[51]) ).
thf(1423,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(8267,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)],[1423]) ).
thf(1699,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ D ) @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_group_2) ).
thf(9350,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ D ) @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(1686,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k3_group_1 @ A @ B ) ) @ C )
& ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_group_3) ).
thf(9311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ C @ B ) @ ( k3_group_1 @ A @ B ) ) @ C )
& ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k6_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(1318,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(7804,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(1647,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(9162,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)],[1647]) ).
thf(1470,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(8520,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(564,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_group_6 @ D @ A @ B )
=> ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_group_6) ).
thf(4306,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_group_6 @ D @ A @ B )
=> ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ D @ C ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1068,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ C @ B ) @ ( k3_group_1 @ A @ B ) )
= C )
& ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_group_3) ).
thf(6462,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ C @ B ) @ ( k3_group_1 @ A @ B ) )
= C )
& ( ( k4_group_3 @ A @ ( k4_group_3 @ A @ C @ ( k3_group_1 @ A @ B ) ) @ B )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(762,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5194,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1006,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(6198,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)],[1006]) ).
thf(1593,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v3_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v4_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v7_group_1 @ ( k6_group_6 @ A @ B ) )
& ( l1_group_1 @ ( k6_group_6 @ A @ B ) ) )
<=> ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_group_6) ).
thf(8969,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v3_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v4_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v7_group_1 @ ( k6_group_6 @ A @ B ) )
& ( l1_group_1 @ ( k6_group_6 @ A @ B ) ) )
=> ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B ) )
& ( ( m1_group_6 @ ( k9_group_5 @ A ) @ A @ B )
=> ( ~ ( v3_struct_0 @ ( k6_group_6 @ A @ B ) )
& ( v3_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v4_group_1 @ ( k6_group_6 @ A @ B ) )
& ( v7_group_1 @ ( k6_group_6 @ A @ B ) )
& ( l1_group_1 @ ( k6_group_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(1668,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k5_group_4 @ A @ ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_group_4) ).
thf(9262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k5_group_4 @ A @ ( k7_group_4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(379,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(3420,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)],[379]) ).
thf(701,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).
thf(4880,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1232,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(7355,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)],[1232]) ).
thf(184,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(2587,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)],[184]) ).
thf(1330,axiom,
? [A: $i] : ( v1_card_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_1) ).
thf(7883,plain,
? [A: $i] : ( v1_card_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1536,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k14_group_2 @ A @ B )
= ( a_1_0_group_2 @ A ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t170_group_2) ).
thf(8769,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k14_group_2 @ A @ B )
= ( a_1_0_group_2 @ A ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(1014,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
=> ( ( D
= ( k12_group_2 @ A @ C @ B ) )
=> ( ( k3_group_1 @ ( k6_group_6 @ A @ C ) @ D )
= ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_group_6) ).
thf(6226,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k6_group_6 @ A @ C ) ) )
=> ( ( D
= ( k12_group_2 @ A @ C @ B ) )
=> ( ( k3_group_1 @ ( k6_group_6 @ A @ C ) @ D )
= ( k12_group_2 @ A @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1462,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(8489,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(102,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(2218,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)],[102]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k1_finsub_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
thf(4125,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k1_finsub_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_rlvect_1 @ A @ B @ C @ D )
= ( k11_finseq_1 @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_rlvect_1) ).
thf(4816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_rlvect_1 @ A @ B @ C @ D )
= ( k11_finseq_1 @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1761,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( r5_group_3 @ A @ C @ B )
<=> ( r4_group_3 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_group_3) ).
thf(9551,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( r5_group_3 @ A @ C @ B )
=> ( r4_group_3 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) ) )
& ( ( r4_group_3 @ A @ ( k7_group_2 @ A @ C ) @ ( k7_group_2 @ A @ B ) )
=> ( r5_group_3 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(117,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(2302,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)],[117]) ).
thf(731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_4 @ A @ ( k1_finsop_1 @ k4_numbers @ ( k3_finseq_1 @ B ) @ ( k2_group_4 @ np__0 ) ) @ B )
= ( k1_finsop_1 @ ( u1_struct_0 @ A ) @ ( k3_finseq_1 @ B ) @ ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_group_4) ).
thf(5009,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_group_4 @ A @ ( k1_finsop_1 @ k4_numbers @ ( k3_finseq_1 @ B ) @ ( k2_group_4 @ np__0 ) ) @ B )
= ( k1_finsop_1 @ ( u1_struct_0 @ A ) @ ( k3_finseq_1 @ B ) @ ( k2_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(682,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( A != np__0 )
=> ( r2_hidden @ A @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finseq_3) ).
thf(4794,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( A != np__0 )
=> ( r2_hidden @ A @ ( k2_finseq_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(895,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(5728,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1374,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ B )
=> ! [G: $i] :
( ( m1_group_2 @ G @ B )
=> ( ( ( ( u1_struct_0 @ F )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ A @ E ) )
=> ( m1_group_6 @ F @ B @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_latsubgr) ).
thf(8070,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ! [E: $i] :
( ( m1_group_2 @ E @ A )
=> ! [F: $i] :
( ( m1_group_2 @ F @ B )
=> ! [G: $i] :
( ( m1_group_2 @ G @ B )
=> ( ( ( ( u1_struct_0 @ F )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ D ) ) )
& ( ( u1_struct_0 @ G )
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
& ( m1_group_6 @ D @ A @ E ) )
=> ( m1_group_6 @ F @ B @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(434,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(3705,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)],[434]) ).
thf(131,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(2385,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)],[131]) ).
thf(471,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(3860,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)],[471]) ).
thf(82,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_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
=> ( r1_partfun1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_4) ).
thf(2155,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_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
=> ( r1_partfun1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(169,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 @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).
thf(2534,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 @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(498,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(3997,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(911,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(5796,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1120,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k4_group_4 @ C @ ( k2_finseq_4 @ k4_numbers @ ( k2_group_4 @ A ) @ ( k2_group_4 @ B ) ) @ ( k7_rlvect_1 @ C @ D @ E ) )
= ( k7_rlvect_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_group_4) ).
thf(6786,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k4_group_4 @ C @ ( k2_finseq_4 @ k4_numbers @ ( k2_group_4 @ A ) @ ( k2_group_4 @ B ) ) @ ( k7_rlvect_1 @ C @ D @ E ) )
= ( k7_rlvect_1 @ C @ ( k6_group_1 @ C @ A @ D ) @ ( k6_group_1 @ C @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(271,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(2983,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)],[271]) ).
thf(1772,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) )
<=> ~ ( r1_xboole_0 @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_group_2) ).
thf(9579,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) )
=> ~ ( r1_xboole_0 @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) ) )
& ( ~ ( r1_xboole_0 @ ( k13_group_2 @ A @ D @ B ) @ ( k13_group_2 @ A @ D @ C ) )
=> ( ( k13_group_2 @ A @ D @ B )
= ( k13_group_2 @ A @ D @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v2_group_6 @ D @ A @ B )
& ( r1_rlvect_1 @ ( k13_group_6 @ A @ B @ D ) @ C ) )
=> ( ( k1_funct_1 @ D @ ( k1_funct_1 @ ( k2_funct_1 @ D ) @ C ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_group_6) ).
thf(5268,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ D @ A @ B )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v2_group_6 @ D @ A @ B )
& ( r1_rlvect_1 @ ( k13_group_6 @ A @ B @ D ) @ C ) )
=> ( ( k1_funct_1 @ D @ ( k1_funct_1 @ ( k2_funct_1 @ D ) @ C ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(951,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_group_1 @ A @ B )
= np__1 )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_group_1) ).
thf(5954,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_group_1 @ A @ B )
= np__1 )
=> ( B
= ( k2_group_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(1214,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_hidden @ B @ ( k12_group_2 @ A @ C @ B ) )
& ( r2_hidden @ B @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_group_2) ).
thf(7259,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_hidden @ B @ ( k12_group_2 @ A @ C @ B ) )
& ( r2_hidden @ B @ ( k13_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(775,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(5232,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1208,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7242,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(494,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(3987,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)],[494]) ).
thf(1256,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(7489,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)],[1256]) ).
thf(391,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( r1_xreal_0 @ A @ B )
<=> ( r1_tarski @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_finseq_1) ).
thf(3464,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ! [B: $i] :
( ( v4_ordinal2 @ B )
=> ( ( ( r1_xreal_0 @ A @ B )
=> ( r1_tarski @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) ) )
& ( ( r1_tarski @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) )
=> ( r1_xreal_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1162,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(7029,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)],[1162]) ).
thf(1522,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( ( v1_group_3 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) )
& ( m1_group_2 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_group_6) ).
thf(8726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( ( v1_group_3 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) )
& ( m1_group_2 @ ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) @ ( k6_group_6 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(1574,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ D )
=> ( r1_rlvect_1 @ C @ D ) ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_group_2) ).
thf(8901,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_rlvect_1 @ B @ D )
=> ( r1_rlvect_1 @ C @ D ) ) )
=> ( m1_group_2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(1178,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ C ) @ D )
= ( k2_group_3 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_group_3) ).
thf(7121,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ ( k2_group_3 @ A @ B @ C ) @ D )
= ( k2_group_3 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(930,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_group_2) ).
thf(5884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_domain_1 @ ( u1_struct_0 @ A ) @ ( k3_group_1 @ A @ B ) @ ( k3_group_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(356,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(3337,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)],[356]) ).
thf(812,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(5371,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)],[812]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(6906,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r1_xreal_0 @ C @ ( k3_finseq_1 @ B ) )
=> ( ( k3_finseq_1 @ ( k16_finseq_1 @ A @ B @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_1) ).
thf(2050,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ! [C: $i] :
( ( v4_ordinal2 @ C )
=> ( ( r1_xreal_0 @ C @ ( k3_finseq_1 @ B ) )
=> ( ( k3_finseq_1 @ ( k16_finseq_1 @ A @ B @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1479,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(8574,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)],[1479]) ).
thf(1691,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r1_group_6 @ A @ B )
& ( v6_group_1 @ A ) )
=> ( v6_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_group_6) ).
thf(9331,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( ( r1_group_6 @ A @ B )
& ( v6_group_1 @ A ) )
=> ( v6_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(818,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(5398,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)],[818]) ).
thf(332,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(3203,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)],[332]) ).
thf(1583,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_6) ).
thf(8933,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v2_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(1349,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
= ( k9_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ D ) @ ( k1_group_1 @ A @ B @ E ) @ ( k1_group_1 @ A @ C @ D ) @ ( k1_group_1 @ A @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_group_2) ).
thf(7955,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_2 @ A @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k7_domain_1 @ ( u1_struct_0 @ A ) @ D @ E ) )
= ( k9_domain_1 @ ( u1_struct_0 @ A ) @ ( k1_group_1 @ A @ B @ D ) @ ( k1_group_1 @ A @ B @ E ) @ ( k1_group_1 @ A @ C @ D ) @ ( k1_group_1 @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(1545,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_group_3) ).
thf(8801,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_group_3 @ A @ B @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_4) ).
thf(3015,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(217,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(2751,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)],[217]) ).
thf(3,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(1816,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)],[3]) ).
thf(720,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(4968,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)],[720]) ).
thf(203,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(2704,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)],[203]) ).
thf(1021,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_card_1 @ A ) )
=> ? [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
& ( A
= ( k1_card_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_card_1) ).
thf(6258,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_card_1 @ A ) )
=> ? [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
& ( A
= ( k1_card_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(248,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).
thf(2913,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(207,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(2714,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)],[207]) ).
thf(445,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(3765,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)],[445]) ).
thf(421,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(3633,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)],[421]) ).
thf(1221,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(7291,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)],[1221]) ).
thf(1709,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k4_group_1 @ B )
= ( k8_relset_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_group_2) ).
thf(9382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( k4_group_1 @ B )
= ( k8_relset_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_group_1 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(1416,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k10_group_1 @ B @ C @ D ) )
= ( k10_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_group_1) ).
thf(8236,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ A @ ( k10_group_1 @ B @ C @ D ) )
= ( k10_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1803,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_rlvect_1 @ C @ B )
=> ( r1_rlvect_1 @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_2) ).
thf(9697,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r1_rlvect_1 @ C @ B )
=> ( r1_rlvect_1 @ C @ ( k3_group_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).
thf(492,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(3982,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)],[492]) ).
thf(541,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(4178,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)],[541]) ).
thf(1199,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_card_1 @ ( k8_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_group_3) ).
thf(7199,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_card_1 @ ( k8_group_3 @ A @ B ) )
= ( k16_group_2 @ A @ ( k10_group_3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(353,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(3328,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)],[353]) ).
thf(1738,axiom,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_setfam_1) ).
thf(9466,plain,
! [A: $i] : ( r1_setfam_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(563,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(4303,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)],[563]) ).
thf(510,axiom,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_card_1) ).
thf(4051,plain,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_group_3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r2_group_3 @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_group_3) ).
thf(5300,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_group_3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r2_group_3 @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r2_group_3 @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_group_3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1497,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( ( k9_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k17_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_group_6) ).
thf(8653,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( ( v1_finset_1 @ ( k14_group_2 @ A @ B ) )
=> ( ( k9_group_1 @ ( k6_group_6 @ A @ B ) )
= ( k17_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(820,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(5404,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)],[820]) ).
thf(1193,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(7184,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)],[1193]) ).
thf(889,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ ( k1_group_2 @ A @ B ) @ ( k1_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_group_2) ).
thf(5709,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_group_2 @ A @ ( k2_group_2 @ A @ B @ C ) )
= ( k2_group_2 @ A @ ( k1_group_2 @ A @ B ) @ ( k1_group_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(705,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(4895,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)],[705]) ).
thf(558,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(4281,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)],[558]) ).
thf(359,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(3347,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)],[359]) ).
thf(992,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( m1_subset_1 @ ( k2_group_4 @ A ) @ k4_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_4) ).
thf(6114,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( m1_subset_1 @ ( k2_group_4 @ A ) @ k4_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1526,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_2 @ C @ B )
<=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ C @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_group_2) ).
thf(8737,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( m1_group_2 @ C @ B )
=> ( r1_group_2 @ A @ ( k9_group_2 @ A @ C @ B ) @ C ) )
& ( ( r1_group_2 @ A @ ( k9_group_2 @ A @ C @ B ) @ C )
=> ( m1_group_2 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(414,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(3558,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)],[414]) ).
thf(1672,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k9_group_2 @ A @ ( k6_group_2 @ A ) @ ( k6_group_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_group_2) ).
thf(9271,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k9_group_2 @ A @ ( k6_group_2 @ A ) @ ( k6_group_2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(1102,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_group_2) ).
thf(6644,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(1448,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k4_group_4 @ B @ ( k12_finseq_1 @ k4_numbers @ ( k2_group_4 @ A ) ) @ ( k12_finseq_1 @ ( u1_struct_0 @ B ) @ C ) )
= ( k12_finseq_1 @ ( u1_struct_0 @ B ) @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_group_4) ).
thf(8424,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k4_group_4 @ B @ ( k12_finseq_1 @ k4_numbers @ ( k2_group_4 @ A ) ) @ ( k12_finseq_1 @ ( u1_struct_0 @ B ) @ C ) )
= ( k12_finseq_1 @ ( u1_struct_0 @ B ) @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(874,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_group_1) ).
thf(5642,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k6_group_1 @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ k5_numbers @ ( u1_struct_0 @ A ) @ ( k5_group_1 @ A ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(1054,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ ( k2_xcmplx_0 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ C ) )
& ( ( k6_group_1 @ B @ ( k2_xcmplx_0 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_1) ).
thf(6398,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k6_group_1 @ B @ ( k2_xcmplx_0 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ C ) )
& ( ( k6_group_1 @ B @ ( k2_xcmplx_0 @ A @ np__1 ) @ C )
= ( k1_group_1 @ B @ C @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1727,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) )
<=> ( r1_rlvect_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).
thf(9431,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) )
=> ( r1_rlvect_1 @ B @ C ) )
& ( ( r1_rlvect_1 @ B @ C )
=> ( r2_hidden @ C @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(1719,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_group_2) ).
thf(9409,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( m1_group_2 @ B @ C )
=> ( m1_group_2 @ ( k9_group_2 @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_group_6 @ C @ A @ B )
<=> ( ( v3_group_6 @ C @ A @ B )
& ( v2_group_6 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_6) ).
thf(6273,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_group_6 @ C @ A @ B )
=> ( ( v3_group_6 @ C @ A @ B )
& ( v2_group_6 @ C @ A @ B ) ) )
& ( ( ( v3_group_6 @ C @ A @ B )
& ( v2_group_6 @ C @ A @ B ) )
=> ( v4_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(45,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(2021,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)],[45]) ).
thf(58,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(2063,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)],[58]) ).
thf(1035,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6309,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1078,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_group_2) ).
thf(6537,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_group_2 @ A @ B @ ( k2_subset_1 @ ( u1_struct_0 @ A ) ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(225,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(2783,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)],[225]) ).
thf(1290,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(7648,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)],[1290]) ).
thf(1298,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_group_3 @ A @ ( k2_group_2 @ A @ B @ C ) @ D ) @ ( k2_group_2 @ A @ ( k3_group_3 @ A @ B @ D ) @ ( k3_group_3 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_group_3) ).
thf(7684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k3_group_3 @ A @ ( k2_group_2 @ A @ B @ C ) @ D ) @ ( k2_group_2 @ A @ ( k3_group_3 @ A @ B @ D ) @ ( k3_group_3 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(1262,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(7525,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)],[1262]) ).
thf(1341,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(7925,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)],[1341]) ).
thf(1702,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( v2_group_4 @ B @ A )
=> ( m1_group_2 @ ( k6_group_4 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_group_4) ).
thf(9367,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( v2_group_4 @ B @ A )
=> ( m1_group_2 @ ( k6_group_4 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(1661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k9_group_2 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_group_2) ).
thf(9235,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( k9_group_2 @ A @ B @ C )
= ( k8_group_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(525,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(4118,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)],[525]) ).
thf(236,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ k1_xboole_0 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_4) ).
thf(2864,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ k1_xboole_0 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1693,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k8_group_4 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_group_4) ).
thf(9335,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( r1_group_2 @ A @ ( k8_group_4 @ A @ B @ C ) @ ( k8_group_4 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(476,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(3918,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)],[476]) ).
thf(552,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(4221,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)],[552]) ).
thf(1505,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_card_1) ).
thf(8675,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( k1_card_1 @ A )
= ( k1_card_1 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(1689,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k1_group_3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_group_3) ).
thf(9325,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( k1_group_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(1759,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_group_2) ).
thf(9547,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( r2_wellord2 @ ( k12_group_2 @ A @ D @ B ) @ ( k12_group_2 @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(1511,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k11_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_group_2) ).
thf(8692,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k11_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(410,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(3543,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)],[410]) ).
thf(433,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(3701,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)],[433]) ).
thf(1228,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(7338,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)],[1228]) ).
thf(1570,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( v4_group_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_group_2) ).
thf(8889,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( v4_group_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(1799,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k14_group_2 @ A @ B ) ) )
& ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k15_group_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_group_2) ).
thf(9679,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k14_group_2 @ A @ B ) ) )
& ( ( k16_group_2 @ A @ B )
= ( k1_card_1 @ ( k15_group_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(684,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(4799,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)],[684]) ).
thf(189,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(2600,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)],[189]) ).
thf(914,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(5806,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)],[914]) ).
thf(156,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(2485,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)],[156]) ).
thf(721,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(4972,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)],[721]) ).
thf(448,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(3772,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)],[448]) ).
thf(699,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r1_xreal_0 @ A @ ( k6_xcmplx_0 @ B @ np__1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_int_1) ).
thf(4876,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( v1_int_1 @ B )
=> ( ~ ( r1_xreal_0 @ B @ A )
=> ( r1_xreal_0 @ A @ ( k6_xcmplx_0 @ B @ np__1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1532,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( m1_group_2 @ B @ ( k8_group_4 @ A @ B @ C ) )
& ( m1_group_2 @ C @ ( k8_group_4 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_group_4) ).
thf(8758,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( m1_group_2 @ B @ ( k8_group_4 @ A @ B @ C ) )
& ( m1_group_2 @ C @ ( k8_group_4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(1381,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(8093,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)],[1381]) ).
thf(617,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(4506,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)],[617]) ).
thf(1687,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_group_1 @ ( k6_group_3 @ A @ B @ C ) )
& ( m1_group_2 @ ( k6_group_3 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_group_3) ).
thf(9314,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_group_1 @ ( k6_group_3 @ A @ B @ C ) )
& ( m1_group_2 @ ( k6_group_3 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(183,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r6_binop_1 @ A @ B @ C )
<=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).
thf(2583,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r6_binop_1 @ A @ B @ C )
=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) )
& ( ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) )
=> ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1308,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k5_group_3 @ A @ C @ B ) @ D )
= ( k5_group_3 @ A @ ( k2_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_group_3) ).
thf(7740,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k5_group_3 @ A @ C @ B ) @ D )
= ( k5_group_3 @ A @ ( k2_group_2 @ A @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(400,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(3489,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)],[400]) ).
thf(1282,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(7616,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)],[1282]) ).
thf(490,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(3965,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)],[490]) ).
thf(884,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ ( k7_binop_2 @ A ) @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_group_1) ).
thf(5681,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ ( k7_binop_2 @ A ) @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(589,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(4410,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)],[589]) ).
thf(281,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( v2_funct_1 @ B )
& ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ B )
= ( k2_relat_1 @ C ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_group_4) ).
thf(3020,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A )
& ( v2_funct_1 @ B )
& ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ B )
= ( k2_relat_1 @ C ) ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1655,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k12_group_6 @ A @ ( k6_group_6 @ A @ B ) @ ( k11_group_6 @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_group_6) ).
thf(9193,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ( r1_group_2 @ A @ ( k12_group_6 @ A @ ( k6_group_6 @ A @ B ) @ ( k11_group_6 @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(981,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(6082,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)],[981]) ).
thf(870,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k6_group_1 @ B @ A @ ( k1_group_1 @ B @ C @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_group_1) ).
thf(5623,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( ( k1_group_1 @ B @ C @ D )
= ( k1_group_1 @ B @ D @ C ) )
=> ( ( k6_group_1 @ B @ A @ ( k1_group_1 @ B @ C @ D ) )
= ( k1_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) @ ( k6_group_1 @ B @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1043,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r4_group_3 @ A @ B @ C )
& ( r4_group_3 @ A @ C @ D ) )
=> ( r4_group_3 @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_group_3) ).
thf(6348,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r4_group_3 @ A @ B @ C )
& ( r4_group_3 @ A @ C @ D ) )
=> ( r4_group_3 @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1614,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u2_lattices @ ( k11_group_4 @ A ) )
= ( k9_group_4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_group_4) ).
thf(9055,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u2_lattices @ ( k11_group_4 @ A ) )
= ( k9_group_4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(663,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(4713,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)],[663]) ).
thf(1065,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k7_group_3 @ A @ C ) )
<=> ( r2_group_3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_group_3) ).
thf(6452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k7_group_3 @ A @ C ) )
=> ( r2_group_3 @ A @ B @ C ) )
& ( ( r2_group_3 @ A @ B @ C )
=> ( r2_hidden @ B @ ( k7_group_3 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(475,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(3886,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)],[475]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k12_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_group_2) ).
thf(5821,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k12_group_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1313,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(7791,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(989,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( v7_group_1 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_group_6) ).
thf(6104,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( v7_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( v7_group_1 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(585,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ k4_numbers )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ k4_numbers )
=> ( ( ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ D ) )
& ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ E ) ) )
=> ( ( k4_group_4 @ A @ ( k8_finseq_1 @ k4_numbers @ D @ E ) @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ ( k4_group_4 @ A @ D @ B ) @ ( k4_group_4 @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_group_4) ).
thf(4395,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_finseq_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m2_finseq_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ k4_numbers )
=> ! [E: $i] :
( ( m2_finseq_1 @ E @ k4_numbers )
=> ( ( ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ D ) )
& ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ E ) ) )
=> ( ( k4_group_4 @ A @ ( k8_finseq_1 @ k4_numbers @ D @ E ) @ ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k8_finseq_1 @ ( u1_struct_0 @ A ) @ ( k4_group_4 @ A @ D @ B ) @ ( k4_group_4 @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1405,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) )
= ( k11_group_2 @ A @ D @ ( k4_group_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_group_3) ).
thf(8189,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( k4_group_2 @ A @ B @ ( k11_group_2 @ A @ D @ C ) )
= ( k11_group_2 @ A @ D @ ( k4_group_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(1507,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(8680,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)],[1507]) ).
thf(933,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( m1_group_2 @ ( k5_group_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k9_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_group_4) ).
thf(5891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( m1_group_2 @ ( k5_group_4 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k9_group_2 @ A @ ( k5_group_4 @ A @ B ) @ ( k5_group_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1142,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_hidden @ B @ ( k7_group_2 @ A @ C ) )
=> ( r2_hidden @ ( k3_group_1 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_group_2) ).
thf(6911,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( r2_hidden @ B @ ( k7_group_2 @ A @ C ) )
=> ( r2_hidden @ ( k3_group_1 @ A @ B ) @ ( k7_group_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1117,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(6778,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)],[1117]) ).
thf(1190,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k3_group_2 @ A @ D @ B ) @ C )
= ( k3_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_group_2) ).
thf(7176,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( v4_group_1 @ A )
=> ( ( k2_group_2 @ A @ ( k3_group_2 @ A @ D @ B ) @ C )
= ( k3_group_2 @ A @ D @ ( k2_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1081,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ~ ( ( ( v1_finset_1 @ ( k9_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k9_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_group_3) ).
thf(6548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ~ ( ( ( v1_finset_1 @ ( k9_group_3 @ A @ B ) )
| ( v1_finset_1 @ ( k14_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) )
& ! [C: $i] :
( ( v1_finset_1 @ C )
=> ~ ( ( C
= ( k9_group_3 @ A @ B ) )
& ( ( k4_card_1 @ C )
= ( k17_group_2 @ A @ ( k11_group_3 @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(875,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k12_group_2 @ A @ C @ B )
= ( k10_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_group_3) ).
thf(5645,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( k12_group_2 @ A @ C @ B )
= ( k10_group_2 @ A @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1449,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ ( k4_xcmplx_0 @ A ) @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_group_1) ).
thf(8427,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( k6_group_1 @ B @ ( k4_xcmplx_0 @ A ) @ C )
= ( k3_group_1 @ B @ ( k6_group_1 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(1212,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ B )
=> ( v6_group_1 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_6) ).
thf(7252,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ B )
=> ( v6_group_1 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(996,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v7_group_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_group_1) ).
thf(6126,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( v7_group_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ B @ C )
= ( k1_group_1 @ A @ C @ B ) ) ) )
=> ( v7_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(616,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(4501,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)],[616]) ).
thf(1777,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( v6_group_1 @ C )
<=> ( v6_group_1 @ ( k6_group_3 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_group_3) ).
thf(9600,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( ( v6_group_1 @ C )
=> ( v6_group_1 @ ( k6_group_3 @ A @ C @ B ) ) )
& ( ( v6_group_1 @ ( k6_group_3 @ A @ C @ B ) )
=> ( v6_group_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(805,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(5344,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)],[805]) ).
thf(1059,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k3_group_3 @ A @ B @ C ) @ D )
= ( k3_group_3 @ A @ B @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_group_3) ).
thf(6424,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_group_3 @ A @ ( k3_group_3 @ A @ B @ C ) @ D )
= ( k3_group_3 @ A @ B @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(241,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(2879,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)],[241]) ).
thf(390,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(3461,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)],[390]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
& ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finseq_1) ).
thf(1944,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
& ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(478,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 ) )
=> ( ( k1_funct_4 @ B @ C )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_4) ).
thf(3924,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 ) )
=> ( ( k1_funct_4 @ B @ C )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1104,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ A @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ B @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_group_6) ).
thf(6663,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ D @ B @ A )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ E @ A @ C )
& ( m2_relset_1 @ E @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
& ( v1_group_6 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ B @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ C ) @ D @ E ) @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(334,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(3212,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)],[334]) ).
thf(1670,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( m1_group_2 @ B @ C )
& ( m1_group_2 @ B @ D ) )
=> ( m1_group_2 @ B @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_group_2) ).
thf(9267,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( m1_group_2 @ D @ A )
=> ( ( ( m1_group_2 @ B @ C )
& ( m1_group_2 @ B @ D ) )
=> ( m1_group_2 @ B @ ( k9_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(1780,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( r1_rlvect_1 @ ( k8_group_2 @ B @ C @ D ) @ A )
<=> ( ( r1_rlvect_1 @ C @ A )
& ( r1_rlvect_1 @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_group_2) ).
thf(9611,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ! [D: $i] :
( ( m1_group_2 @ D @ B )
=> ( ( ( r1_rlvect_1 @ ( k8_group_2 @ B @ C @ D ) @ A )
=> ( ( r1_rlvect_1 @ C @ A )
& ( r1_rlvect_1 @ D @ A ) ) )
& ( ( ( r1_rlvect_1 @ C @ A )
& ( r1_rlvect_1 @ D @ A ) )
=> ( r1_rlvect_1 @ ( k8_group_2 @ B @ C @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(1105,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( A = np__0 )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k2_group_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_1) ).
thf(6668,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( A = np__0 )
=> ( ( k6_group_1 @ B @ A @ C )
= ( k2_group_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1551,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_group_6 @ A @ B )
=> ( ( k8_group_1 @ A )
= ( k8_group_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_group_6) ).
thf(8818,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_group_1 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ( ( r2_group_6 @ A @ B )
=> ( ( k8_group_1 @ A )
= ( k8_group_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(1157,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ C ) )
=> ( ( k1_group_1 @ A @ D @ E )
= ( k1_group_1 @ A @ E @ D ) ) ) ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_group_2) ).
thf(7003,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ C ) )
=> ( ( k1_group_1 @ A @ D @ E )
= ( k1_group_1 @ A @ E @ D ) ) ) ) )
=> ( ( k2_group_2 @ A @ B @ C )
= ( k2_group_2 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1590,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k15_group_2 @ A @ B )
= ( a_1_0_group_2 @ A ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_group_2) ).
thf(8961,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_1 @ B )
& ( m1_group_2 @ B @ A ) )
=> ( ( ( k15_group_2 @ A @ B )
= ( a_1_0_group_2 @ A ) )
=> ( r1_group_2 @ A @ B @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(1458,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( r1_group_2 @ B @ ( k13_group_6 @ A @ B @ C ) @ ( k5_group_4 @ B @ ( k9_group_6 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_group_6) ).
thf(8465,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( v1_group_6 @ C @ A @ B )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( r1_group_2 @ B @ ( k13_group_6 @ A @ B @ C ) @ ( k5_group_4 @ B @ ( k9_group_6 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(1197,axiom,
r1_tarski @ k4_numbers @ k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_numbers) ).
thf(7195,plain,
r1_tarski @ k4_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(394,axiom,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(3474,plain,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1653,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v6_group_1 @ ( k5_group_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_group_2) ).
thf(9188,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v6_group_1 @ ( k5_group_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(218,axiom,
! [A: $i] : ( m2_finseq_1 @ ( k14_finseq_1 @ A ) @ k5_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_finseq_1) ).
thf(2754,plain,
! [A: $i] : ( m2_finseq_1 @ ( k14_finseq_1 @ A ) @ k5_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1540,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( l1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(8786,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( l1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(1404,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v1_group_6 @ C @ B @ ( k13_group_6 @ B @ A @ C ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_group_6) ).
thf(8184,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( v1_group_6 @ C @ B @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) )
& ( v1_group_6 @ C @ B @ ( k13_group_6 @ B @ A @ C ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ ( k13_group_6 @ B @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(947,axiom,
r1_tarski @ k5_numbers @ k4_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_numbers) ).
thf(5943,plain,
r1_tarski @ k5_numbers @ k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(751,axiom,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ~ ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_finseq_3) ).
thf(5155,plain,
! [A: $i] :
( ( v4_ordinal2 @ A )
=> ~ ( r2_hidden @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_finseq_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(485,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(3950,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)],[485]) ).
thf(1001,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( m1_subset_1 @ ( k2_vectsp_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_vectsp_1) ).
thf(6173,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( m1_subset_1 @ ( k2_vectsp_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(737,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(5073,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1472,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(8525,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)],[1472]) ).
thf(1601,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( r2_hidden @ A @ ( k9_group_3 @ B @ C ) )
=> ( ( v1_group_1 @ A )
& ( m1_group_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_group_3) ).
thf(9006,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ B )
=> ( ( r2_hidden @ A @ ( k9_group_3 @ B @ C ) )
=> ( ( v1_group_1 @ A )
& ( m1_group_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_group_4 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_group_4) ).
thf(8940,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A )
& ( m1_group_2 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_group_4 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ C )
= ( k3_finsub_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_finsub_1) ).
thf(7181,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_finsub_1 @ A @ B @ C )
= ( k3_finsub_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(834,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(5458,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(468,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(3854,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(869,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) @ C ) )
& ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_group_3) ).
thf(5618,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ B ) @ C ) )
& ( ( k2_group_3 @ A @ B @ C )
= ( k1_group_1 @ A @ ( k3_group_1 @ A @ C ) @ ( k1_group_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1153,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v4_group_1 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_group_1) ).
thf(6984,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ( ( ( v4_group_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_1 @ A @ ( k1_group_1 @ A @ B @ C ) @ D )
= ( k1_group_1 @ A @ B @ ( k1_group_1 @ A @ C @ D ) ) ) ) ) )
=> ( v4_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1403,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ B @ C ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_group_2) ).
thf(8179,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ B @ C ) )
=> ( ( g1_group_1 @ ( u1_struct_0 @ B ) @ ( u1_group_1 @ B ) )
= ( g1_group_1 @ ( u1_struct_0 @ A ) @ ( u1_group_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(1555,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_3 @ A @ ( k6_group_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_group_3) ).
thf(8829,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k11_group_3 @ A @ ( k6_group_2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(1485,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(8611,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)],[1485]) ).
thf(1280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_group_3 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_group_3) ).
thf(7602,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_group_1 @ B )
& ( v4_group_1 @ B )
& ( l1_group_1 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_group_3 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k2_group_3 @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_group_3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1710,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( m1_group_2 @ B @ D )
& ( m1_group_2 @ C @ D ) )
=> ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_group_4) ).
thf(9385,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( m1_group_2 @ D @ A ) )
=> ( ( ( m1_group_2 @ B @ D )
& ( m1_group_2 @ C @ D ) )
=> ( m1_group_2 @ ( k8_group_4 @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(671,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(4742,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)],[671]) ).
thf(115,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 ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( ( k5_relat_1 @ ( k1_funct_4 @ C @ D ) @ ( k1_funct_4 @ A @ B ) )
= ( k1_funct_4 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_4) ).
thf(2297,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 ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ B ) )
& ( r1_partfun1 @ A @ B ) )
=> ( ( k5_relat_1 @ ( k1_funct_4 @ C @ D ) @ ( k1_funct_4 @ A @ B ) )
= ( k1_funct_4 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r4_group_3 @ A @ B @ C )
=> ( r4_group_3 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_group_3) ).
thf(5255,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r4_group_3 @ A @ B @ C )
=> ( r4_group_3 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1425,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(8273,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1175,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ ( k3_group_1 @ A @ B ) )
= B )
& ( ( k2_group_3 @ A @ ( k3_group_1 @ A @ B ) @ B )
= ( k3_group_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_group_3) ).
thf(7108,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_group_3 @ A @ B @ ( k3_group_1 @ A @ B ) )
= B )
& ( ( k2_group_3 @ A @ ( k3_group_1 @ A @ B ) @ B )
= ( k3_group_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1683,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k6_group_4 @ A ) )
= ( a_1_1_group_4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_group_4) ).
thf(9303,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( u1_struct_0 @ ( k6_group_4 @ A ) )
= ( a_1_1_group_4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(1681,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v4_group_1 @ B )
& ( v7_group_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_group_2) ).
thf(9297,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ( ( v4_group_1 @ B )
& ( v7_group_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1252,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k14_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_group_2) ).
thf(7478,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A )
& ( m1_group_2 @ B @ A ) )
=> ( m1_subset_1 @ ( k14_group_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1592,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( ( v1_group_3 @ C @ B )
& ( m1_group_6 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_group_6) ).
thf(8966,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_group_2 @ B @ A )
=> ! [C: $i] :
( ( ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ( ( m1_group_6 @ C @ A @ B )
=> ( ( v1_group_3 @ C @ B )
& ( m1_group_6 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(512,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(4056,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)],[512]) ).
thf(289,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).
thf(3052,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(350,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(3316,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)],[350]) ).
thf(1099,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ D @ E ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_group_3) ).
thf(6632,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ D @ E ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1127,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k5_group_2 @ A ) @ B ) @ ( k5_group_2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_group_3) ).
thf(6839,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_group_2 @ A @ ( k6_group_3 @ A @ ( k5_group_2 @ A ) @ B ) @ ( k5_group_2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1441,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( B
= ( k9_group_1 @ A ) )
<=> ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( u1_struct_0 @ A ) )
& ( B
= ( k4_card_1 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_group_1) ).
thf(8380,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v6_group_1 @ A )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( B
= ( k9_group_1 @ A ) )
=> ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( u1_struct_0 @ A ) )
& ( B
= ( k4_card_1 @ C ) ) ) )
& ( ? [C: $i] :
( ( v1_finset_1 @ C )
& ( C
= ( u1_struct_0 @ A ) )
& ( B
= ( k4_card_1 @ C ) ) )
=> ( B
= ( k9_group_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(896,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ D ) @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_group_2) ).
thf(5732,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_group_2 @ A @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) @ D ) @ ( k3_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_group_2 @ A @ B @ D ) @ ( k2_group_2 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1665,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( v1_group_3 @ D @ ( k6_group_6 @ A @ C ) )
& ( m1_group_2 @ D @ ( k6_group_6 @ A @ C ) ) )
=> ( ( ( D
= ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) )
& ( m1_group_6 @ C @ A @ B ) )
=> ( r2_group_6 @ ( k6_group_6 @ ( k6_group_6 @ A @ C ) @ D ) @ ( k6_group_6 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_group_6) ).
thf(9254,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_group_3 @ B @ A )
& ( m1_group_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( v1_group_3 @ C @ A )
& ( m1_group_2 @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_group_1 @ D )
& ( v1_group_3 @ D @ ( k6_group_6 @ A @ C ) )
& ( m1_group_2 @ D @ ( k6_group_6 @ A @ C ) ) )
=> ( ( ( D
= ( k6_group_6 @ B @ ( k1_group_6 @ A @ B @ C ) ) )
& ( m1_group_6 @ C @ A @ B ) )
=> ( r2_group_6 @ ( k6_group_6 @ ( k6_group_6 @ A @ C ) @ D ) @ ( k6_group_6 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(480,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(3933,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)],[480]) ).
thf(413,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(3553,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)],[413]) ).
thf(794,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k7_group_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_group_3) ).
thf(5293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k7_group_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1503,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(8670,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(1491,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_nat_1 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_group_1) ).
thf(8628,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_group_1 @ C )
& ( v4_group_1 @ C )
& ( l1_group_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ( ( k6_group_1 @ C @ ( k2_nat_1 @ A @ B ) @ D )
= ( k6_group_1 @ C @ B @ ( k6_group_1 @ C @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(283,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(3035,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)],[283]) ).
thf(1136,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k3_group_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_group_2) ).
thf(6896,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_group_2 @ A @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k3_group_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(27,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 ) )
=> ( ( C
= ( k1_funct_4 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_4) ).
thf(1912,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 ) )
=> ( ( ( C
= ( k1_funct_4 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) )
=> ( C
= ( k1_funct_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,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(1870,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)],[18]) ).
thf(425,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 ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).
thf(3669,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 ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(668,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(4734,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)],[668]) ).
thf(9875,plain,
$false,
inference(e,[status(thm)],[4201,5365,1823,2263,3666,8976,2427,5205,3927,7549,2250,5385,7375,2199,6085,4188,4447,3962,5422,3883,9458,2295,9653,4005,9077,3008,2109,2131,2031,5260,6976,7445,3167,7922,8514,2921,3698,5390,7798,3581,7143,5654,2499,2544,6448,9411,6042,8887,6566,8755,1818,6527,4992,8077,9241,3681,8129,2590,3012,2114,9003,9342,5898,5454,6057,7935,2104,7083,8723,8044,5168,9373,3858,4311,3762,3813,8082,7641,7958,2908,3549,3509,5242,8402,4391,3153,2947,2248,1939,3959,2676,5793,9337,3108,2099,5224,7332,1971,5237,8928,5529,7341,7208,9135,4592,4532,7813,5361,8635,3367,3942,4058,1988,2042,2146,2195,7793,3848,6391,8101,8551,8335,9460,3745,4418,9233,8430,7573,5906,3365,9052,2740,6359,2918,8622,4026,5288,8981,8915,7115,8879,7096,3446,8667,6089,2933,5257,4638,1872,6634,9000,6078,6241,5161,4294,3481,6680,3562,6996,2580,7452,5782,3717,2360,9481,6046,7400,9672,2575,6236,2216,5227,2432,4496,6872,6887,7734,3777,7364,4198,6102,2405,3688,5342,9116,3370,9625,9443,6138,4047,8898,6268,9096,6009,9159,8239,3947,9195,7240,6904,5825,5938,5770,8866,2886,8122,9396,4137,2173,8678,8330,6306,8025,2400,4760,4963,2067,9657,3878,1904,9300,5429,2916,2698,2339,3148,8522,8208,6006,8753,4539,9447,8500,9287,7914,9099,3644,7262,4563,2039,8494,8089,8225,9561,9464,6095,9128,5188,1907,2501,4654,2444,7771,6350,7945,2274,3485,4778,8214,4130,4349,4023,2488,2562,8146,5712,9230,5706,3803,2466,8242,4428,7743,6208,3043,7665,5461,8907,4270,3470,5851,4265,4460,5076,4471,5355,3374,3385,5214,5605,2169,6455,6611,7124,6149,6626,8717,6379,4492,2373,4830,4317,6781,8367,7075,6936,3084,5829,8220,2024,6098,8037,4400,1875,8161,7509,3268,3258,7500,6382,1847,7588,8870,3788,9425,4595,5974,2178,8956,2451,8246,5761,2456,9401,5957,4988,7273,2794,8029,4583,7894,5526,4903,5084,9490,4018,2090,3393,4454,7969,7247,4297,2469,7818,2259,7369,6410,8791,6135,4847,3438,6187,2925,8659,1978,6841,3357,9415,6559,4871,2073,8664,7899,3851,8411,9309,5834,2964,5738,5648,2772,9533,9347,9108,4892,3184,2762,7473,6591,2367,2437,3537,5353,4935,7931,7613,5401,3189,3739,6685,2861,9369,2190,7807,6110,3712,9167,3808,2530,4364,2979,5321,8347,8686,4924,3756,3955,3243,5665,4519,5137,6616,4707,4211,9589,7722,3492,2205,4483,9584,5157,5012,6296,5142,2093,9252,6884,5540,4172,4700,7674,7321,9472,9556,5174,8508,7254,7533,4216,4323,9571,3301,7179,3303,8640,4407,2473,5751,7725,9440,2118,6588,5968,7885,5291,8959,7019,3995,2047,5562,3318,9009,6865,2737,9041,2905,1868,3418,6092,3679,9544,6200,9488,9549,2596,7353,5266,3989,4785,4449,4160,6582,9105,2673,5734,7042,5670,2560,6000,8091,5512,4878,6773,5044,7994,8856,5719,3742,4344,4091,5754,6107,3816,6356,5893,8714,4836,5594,7244,7565,7449,9277,7625,8847,9080,5936,1910,3799,9264,8683,9380,7237,6646,6303,9113,8810,3191,6926,7977,8948,5492,9554,8832,8672,8920,4140,8540,8788,8371,2670,3810,7555,9512,7576,9190,8700,4585,8270,9058,3403,4725,3090,8651,2565,8942,6427,5177,3349,1888,8852,8021,6972,5988,5551,3546,6833,1836,9132,8964,5201,7591,4740,3050,2547,2313,9291,7891,4104,5285,8073,7686,2769,5221,4668,6691,8319,4636,2509,2631,4840,5081,6919,7486,3968,6075,8895,7346,1936,8462,8694,2300,3784,3467,5626,6413,3782,5904,7329,5714,6677,8314,2157,9145,3122,7205,6335,7249,4512,5006,4974,9355,8009,2841,6195,8282,7623,2973,4486,6603,7173,6459,6133,7389,2709,5577,5798,8931,8041,8984,8016,9576,3518,8884,2724,4930,5889,7513,3237,9333,8662,9603,4109,7468,2268,8815,4219,3060,3087,6175,4276,3000,9508,9667,9387,7998,5337,2551,4457,9645,9530,6299,9566,4320,7101,4333,5941,3775,3141,3952,7091,8544,2877,8631,8835,7189,9640,6967,9662,5651,4772,6116,3094,4425,5992,9714,9419,8258,3441,5464,9609,2053,7841,5588,4861,4054,5662,3194,7480,9085,6395,4444,2666,8467,6271,7523,7821,5387,6065,9260,7668,5317,9012,9149,6433,6211,3390,2482,9598,1825,5947,8891,2681,5149,6033,7014,2598,7138,3354,7966,2153,2387,8764,5639,9498,7221,3770,7738,1932,8137,3222,3540,2497,4717,8439,5766,7597,7027,1852,4347,7086,8587,6450,5823,3115,6908,5217,8775,3064,6784,5603,8144,8142,3074,4069,2272,4416,2140,2756,3162,3201,2370,5245,8174,4889,4765,2748,8393,5447,9169,5417,5887,1996,8708,3454,9699,3476,8127,4148,2634,8614,2203,7678,9684,9468,8839,4644,8205,7052,8512,4782,9269,4476,9044,3856,8422,3306,8279,7414,3592,5419,4906,2440,6688,9284,5930,8945,3422,6038,5198,8824,5909,5295,6311,4995,4572,6368,2001,3130,7582,3607,5855,5960,9021,4393,5979,9650,3696,9072,2144,7985,4921,6901,8164,6314,6507,9352,2556,4116,2033,2149,4613,6824,2253,6203,5278,5508,7225,7155,3079,4412,3985,6792,8110,7753,9181,5608,4797,2602,9404,2734,9154,4577,2524,3396,2376,8807,3343,3158,7709,5456,3768,5474,2789,2568,3272,2991,5503,2695,8217,7411,4000,4998,3187,7714,4341,5933,7938,2727,6916,2859,4283,4494,3255,6510,5395,3240,5844,7736,2188,4309,7134,5121,2393,9157,8139,7223,8711,7751,3081,3945,8027,4465,8332,8167,8740,8581,2398,4328,2716,8993,4381,5271,6606,6019,5239,9339,4769,7815,2134,9627,2959,5535,8064,3002,7951,7671,4273,5997,8202,6281,8767,5546,2193,8534,9587,4127,2029,9125,6403,8549,5471,7270,3077,8249,7719,9687,3208,5282,1865,3340,8492,2442,2759,8344,3487,7145,3832,2166,7536,4854,8497,6123,8656,7843,7579,6757,4887,7315,5432,9089,2573,9258,6016,3170,7482,9390,6048,8436,6478,2721,6572,4498,5520,9047,6340,6061,6585,3101,2521,8276,9422,7130,2151,7643,3155,9375,3038,9377,6443,3683,4828,3515,5827,5853,5901,4601,8254,9118,3106,7282,4805,8047,5222,7265,2945,4213,4616,3197,9015,4073,2856,3138,5689,4300,5616,4509,2197,6789,2065,4388,7928,7869,2928,1952,9407,3456,4694,4203,5816,8620,8826,1877,8192,3133,3055,2129,7113,8156,4462,2111,8103,2780,4731,4028,2261,5439,6353,4897,4985,8750,2446,3165,1862,4181,7098,2923,1838,7654,2593,3451,5656,7141,3298,3483,7186,2542,6044,2289,5180,9074,9228,7297,5410,9030,7561,2911,4554,1820,9327,6376,9619,8131,9450,6223,5248,7911,7324,2244,5849,6100,9398,1973,4933,6255,6345,6574,2365,2962,5775,2212,8456,3838,5377,8719,9294,2086,8821,4362,9371,2931,5575,4703,9165,2101,9345,9033,7558,2967,2390,5667,6325,6293,6027,6614,4626,4067,2207,5326,5139,2693,4965,2867,6476,2506,4473,3380,8689,7049,8731,4690,3427,3936,6672,6542,4529,7539,7897,7992,3921,1958,5763,9111,5435,4441,2096,4813,4580,2994,7371,9069,9563,2471,5785,4598,7447,8804,8116,5952,1990,3048,2684,4566,8067,8637,4688,6564,4113,6821,8477,5358,8194,4722,7982,4336,9202,4168,7070,6875,9317,5229,8003,5927,7801,3214,9535,2160,8744,4045,2942,2513,9631,5570,8905,5452,5047,8592,3737,3376,6120,8772,6238,7635,7942,6472,4035,6683,9138,5250,3842,4490,4937,2977,8537,7196,3754,5171,6921,9238,5944,4534,9061,5523,4641,5721,7462,8096,3786,4961,3058,3872,4377,6481,5079,2882,5018,7832,5684,3246,4398,3334,6545,5015,8625,7796,4982,6994,6880,4314,3448,4522,5235,8396,3642,4561,9281,8377,4003,7568,6421,9050,7879,1980,9082,1830,3127,8327,5543,5152,2701,9413,4737,7127,5450,6206,3041,9690,3715,9445,2354,5147,5208,2975,5633,3388,2949,8729,8696,7876,7466,9486,4802,8316,9495,6337,9505,1898,8448,2838,6899,2558,3829,5736,3124,4133,7515,2379,9500,6262,4976,2357,1955,2843,2711,4106,7163,4143,3224,8850,2511,3024,8449,8734,7202,9637,2939,7192,6467,8433,9574,9274,6245,6960,8798,5596,2848,4150,5895,7908,4671,4111,9453,6992,4414,4819,6220,6622,2435,2458,8987,3067,9665,5777,7288,4780,4185,2209,8761,1807,5832,8812,2875,6284,7363,7552,3400,3433,4278,3584,6850,4651,9279,5981,7676,2479,4606,3589,2045,7627,9306,9092,1949,4763,2870,4944,4873,1834,4656,3533,9417,5966,1844,5573,4646,7889,5308,2743,2997,4102,8228,2305,8153,9615,5124,4170,9141,5332,9515,8075,6726,9647,5315,2707,8584,7996,2026,6913,7638,4705,4710,2988,6230,5724,6818,8474,8780,8882,9102,6030,7044,2532,5191,5800,6639,3383,8854,4042,8912,3104,2004,3991,5813,8606,5368,3331,3136,6694,5505,8617,4527,4900,9028,8119,4451,5600,7437,5164,9701,9537,5144,5963,2956,3181,2475,2786,3324,4649,9470,5532,9569,6181,9669,4175,3497,4153,8925,6290,9510,3844,9393,5692,4774,9434,7979,5837,8420,7416,3529,6521,3677,2362,6277,5549,8793,2183,9130,9173,9559,7017,3351,2902,9660,5211,5590,6569,8721,2036,8267,9350,9311,7804,9162,8520,4306,6462,5194,6198,8969,9262,3420,4880,7355,2587,7883,8769,6226,8489,2218,4125,4816,9551,2302,5009,4794,5728,8070,3705,2385,3860,2155,2534,3997,5796,6786,2983,9579,5268,5954,7259,5232,7242,3987,7489,3464,7029,8726,8901,7121,5884,3337,5371,6906,2050,8574,9331,5398,3203,8933,7955,8801,3015,2751,1816,4968,2704,6258,2913,2714,3765,3633,7291,9382,8236,9697,3982,4178,7199,3328,9466,4303,4051,5300,8653,5404,7184,5709,4895,4281,3347,6114,8737,3558,9271,6644,8424,5642,6398,9431,9409,6273,2021,2063,6309,6537,2783,7648,7684,7525,7925,9367,9235,4118,2864,9335,3918,4221,8675,9325,9547,8692,3543,3701,7338,8889,9679,4799,2600,5806,2485,4972,3772,4876,8758,8093,4506,9314,2583,7740,3489,7616,3965,5681,4410,3020,9193,6082,5623,6348,9055,4713,6452,3886,5821,7791,6104,4395,8189,8680,5891,6911,6778,7176,6548,5645,8427,7252,6126,4501,9600,5344,6424,2879,3461,1944,3924,6663,3212,9267,9611,6668,8818,7003,8961,8465,7195,3474,9188,2754,8786,8184,5943,5155,3950,6173,5073,8525,9006,8940,7181,5458,3854,5618,6984,8179,8829,8611,7602,9385,4742,2297,5255,8273,7108,9303,9297,7478,8966,4056,3052,3316,6632,6839,8380,5732,9254,3933,3553,5293,8670,8628,3035,6896,1912,1870,3669,4734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP642+2 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 16:05:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.90/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.70/1.33 % [INFO] Parsing done (517ms).
% 2.70/1.34 % [INFO] Running in sequential loop mode.
% 3.38/1.56 % [INFO] eprover registered as external prover.
% 3.38/1.56 % [INFO] cvc4 registered as external prover.
% 3.38/1.56 % [INFO] Scanning for conjecture ...
% 4.39/1.86 % [INFO] Found a conjecture and 5658 axioms. Running axiom selection ...
% 6.53/2.59 % [INFO] Axiom selection finished. Selected 1804 axioms (removed 3854 axioms).
% 8.48/3.27 % [INFO] Problem is first-order (TPTP FOF).
% 8.73/3.32 % [INFO] Type checking passed.
% 8.80/3.32 % [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 ...
% 40.79/12.55 % External prover 'e' found a proof!
% 40.95/12.55 % [INFO] Killing All external provers ...
% 40.95/12.55 % Time passed: 12042ms (effective reasoning time: 11206ms)
% 40.95/12.55 % 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)>
% 40.95/12.57 % Axioms used in derivation (1804): t23_group_3, t72_xboole_1, t107_group_3, t42_xboole_1, t76_group_4, t44_xboole_1, t60_group_2, d11_group_2, t3_group_4, t106_xboole_1, d13_group_3, t15_finset_1, t8_group_3, t62_partfun1, t56_card_1, t158_relat_1, t5_group_2, t75_finseq_1, rc3_group_1, t38_funct_4, t3_finseq_1, t133_group_3, t87_group_2, t101_group_2, t26_group_4, t55_group_2, t185_group_2, redefinition_m2_relset_1, idempotence_k1_finsub_1, fraenkel_a_1_0_domain_1, t51_partfun1, t18_finseq_3, t21_zfmisc_1, t13_zfmisc_1, t30_funct_2, t13_relset_1, t181_relat_1, t175_relat_1, t131_partfun1, t44_finseq_3, t39_group_3, t11_group_6, t48_group_2, d6_group_3, t54_rlvect_1, t19_group_3, s2_group_4, t177_relat_1, free_g1_group_1, d4_group_1, t110_group_2, t42_subset_1, dt_k3_group_3, d1_tarski, t114_group_3, t147_funct_1, t154_relat_1, t7_group_3, fraenkel_a_3_2_domain_1, t80_group_2, t12_group_3, t11_finseq_1, dt_k9_group_6, d1_group_1, t19_xboole_1, t177_orders_1, t72_group_1, t69_group_6, t169_group_2, t17_xboole_1, t17_finseq_3, t23_setfam_1, t4_funct_4, t130_partfun1, t21_int_1, d6_finseq_1, t58_group_4, t43_subset_1, t74_group_3, cc2_finset_1, t20_zfmisc_1, t4_group_4, dt_k6_group_1, t35_subset_1, t165_group_3, t135_zfmisc_1, t17_zfmisc_1, t121_group_3, fc11_finseq_1, t50_group_2, t148_funct_1, t23_card_1, t25_relset_1, d20_binop_1, t53_group_3, t66_funct_2, t143_funct_1, t67_relat_1, t18_finsub_1, dt_m1_group_6, t93_group_6, t66_partfun1, t25_card_1, t64_card_1, t49_setfam_1, t70_funct_2, t14_group_4, t182_group_2, t6_setfam_1, t35_funct_2, t14_finset_1, t154_group_2, t57_group_2, t53_subset_1, t140_zfmisc_1, rc4_finset_1, t79_funct_4, t20_funct_2, t73_xboole_1, dt_k11_group_6, t79_group_1, dt_k4_relset_1, d14_binop_1, dt_k9_domain_1, t24_group_6, t59_group_1, t105_zfmisc_1, t83_group_3, t62_group_1, commutativity_k1_finsub_1, t10_finseq_3, t109_xboole_1, idempotence_k3_xboole_0, t29_group_6, t82_group_2, t32_group_1, symmetry_r1_group_2, d10_binop_1, t10_group_2, t102_group_3, t62_relat_1, t7_subset_1, t1_boole, t70_group_4, t32_funct_2, d11_binop_1, t2_realset1, t67_group_4, t56_group_1, dt_k5_group_4, t66_xboole_1, t23_xboole_1, t16_group_1, t98_group_3, existence_m1_group_6, t27_funct_2, t14_funct_4, t50_relat_1, d10_group_1, t91_group_6, t133_group_2, t195_orders_1, d1_group_3, d3_group_1, redefinition_k5_subset_1, t9_setfam_1, t23_group_2, t3_xboole_1, t3_realset1, t137_funct_1, d3_subset_1, t40_group_2, t128_group_3, t34_xboole_1, rc7_finseq_1, t34_card_1, t68_card_1, t8_subset_1, t53_funct_2, t156_funct_1, t72_funct_4, t1_subset, t74_finseq_1, redefinition_k7_funct_2, t20_setfam_1, fc1_xboole_0, t104_group_3, t25_funct_1, t16_funct_2, t73_funct_4, t175_group_2, t113_zfmisc_1, t140_partfun1, dt_k7_domain_1, t109_group_2, t25_numbers, t27_group_3, t48_domain_1, t29_finseq_3, t44_group_4, t113_xboole_1, dt_k2_subset_1, fraenkel_a_1_0_group_4, d15_group_6, t56_partfun1, existence_l1_lattices, t84_group_4, t141_group_3, reflexivity_r1_group_2, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t31_group_6, d6_group_6, t37_funct_4, t50_group_6, rc4_group_1, t4_ordinal1, t1_group_6, t59_partfun1, t158_funct_1, t44_relat_1, t147_relat_1, t10_partfun1, t71_card_1, redefinition_k2_group_6, t124_group_3, t18_xboole_1, t90_group_1, t158_partfun1, t78_finseq_1, d5_xboole_0, t167_group_2, t29_subset_1, t24_group_2, t63_group_3, t15_numbers, t92_group_6, t24_setfam_1, d7_group_4, t151_funct_1, fc1_funct_4, t52_zfmisc_1, t144_relat_1, t57_domain_1, t18_setfam_1, t134_group_3, t48_finseq_3, t9_group_3, fc4_subset_1, t61_group_2, t22_funct_1, t79_group_6, t28_group_1, t117_finseq_3, fc1_numbers, dt_k3_funct_2, t65_group_4, t80_card_1, t31_funct_4, t168_funct_2, t43_xboole_1, t54_partfun1, t81_zfmisc_1, dt_k5_lattices, t7_funct_2, t8_group_2, rc1_group_2, t10_relset_1, t135_partfun1, t143_group_3, t146_funct_2, t3_mcart_1, t155_funct_1, d2_group_6, t44_group_3, fc3_relat_1, t96_zfmisc_1, t5_finseq_1, t28_group_4, t14_binop_1, dt_k1_subset_1, t73_group_1, dt_k9_relset_1, t119_group_3, t85_group_2, d5_group_6, t131_group_3, t90_group_6, t6_xboole_1, t132_group_3, d8_funct_1, t19_relat_1, t70_xboole_1, t28_binop_1, t13_finseq_3, dt_k13_domain_1, t100_group_3, t38_group_2, t41_funct_2, t2_boole, t72_card_1, t17_setfam_1, t69_group_4, t27_group_4, t28_group_6, t156_group_2, dt_m1_realset1, t166_funct_2, t40_group_6, t47_relat_1, t18_group_2, fc9_relat_1, t6_group_3, t148_partfun1, redefinition_k4_card_1, t77_group_6, t68_xboole_1, d7_binop_1, commutativity_k9_group_2, t19_finset_1, t71_group_1, t15_group_6, t25_xboole_1, t61_card_1, t117_zfmisc_1, t29_funct_4, t65_partfun1, t186_partfun1, t44_funct_2, t103_group_2, t49_group_1, t19_latsubgr, t14_card_1, t148_group_3, t117_funct_1, t92_group_3, t36_group_1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, t122_zfmisc_1, reflexivity_r1_group_6, t4_mcart_1, t33_group_6, dt_k8_relset_1, t178_group_2, t43_zfmisc_1, rc1_group_6, t60_group_3, t52_group_3, d7_group_2, dt_u2_struct_0, t29_numbers, t18_relat_1, rc3_funct_1, t86_group_4, t89_group_6, t18_group_6, t69_zfmisc_1, t95_zfmisc_1, t42_group_6, t63_partfun1, t153_funct_1, t15_relset_1, t61_group_6, t45_ordinal1, dt_k15_group_2, t79_group_2, t99_zfmisc_1, rc2_partfun1, t42_group_3, t46_group_3, t81_xboole_1, t47_setfam_1, existence_m1_finseq_1, dt_k7_group_3, t21_group_3, t99_group_2, t49_funct_2, d9_group_4, fc1_funct_1, t60_group_6, dt_k2_vectsp_1, d11_group_6, t88_group_3, t7_orders_1, t104_finseq_3, t171_relat_1, t78_group_6, t176_group_2, t162_partfun1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t56_group_4, t10_latsubgr, dt_k6_partfun1, symmetry_r2_group_3, d15_group_1, t63_group_6, t41_group_6, t50_funct_2, d1_struct_0, t97_group_2, dt_k7_funct_2, t8_group_4, t66_group_3, t43_group_4, t70_partfun1, t20_group_2, t26_funct_2, dt_k9_group_2, t37_xboole_1, dt_k10_group_1, t17_funct_1, t42_group_4, t9_xboole_1, t67_group_1, t6_group_6, dt_k2_group_3, t6_latsubgr, t111_group_3, t41_zfmisc_1, dt_k4_group_3, t34_group_2, t77_group_2, dt_m2_relset_1, t18_finset_1, redefinition_r6_group_3, cc1_relat_1, dt_u1_group_1, redefinition_k2_funct_2, t127_group_3, t131_zfmisc_1, t94_group_1, idempotence_k5_subset_1, t120_group_2, d7_partfun1, d11_card_1, t30_card_1, t36_subset_1, redefinition_k6_setfam_1, t49_zfmisc_1, t7_finseq_1, t76_card_1, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t140_group_3, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t79_card_1, t93_group_2, t138_funct_1, t114_group_2, t3_setfam_1, t81_card_1, t130_funct_2, t146_group_2, t39_finseq_3, t152_funct_2, t155_group_2, d8_group_4, fc11_finset_1, t17_binop_1, t33_group_4, t64_funct_2, t64_group_4, dt_k3_group_4, t115_zfmisc_1, t55_group_1, t62_funct_1, t65_funct_2, d10_group_2, t19_funct_1, redefinition_k9_group_2, t58_group_6, d12_group_2, dt_l1_rlvect_1, dt_k10_group_3, t39_group_4, t13_funct_4, existence_m1_group_2, t24_funct_2, t29_finset_1, t85_group_3, fc6_group_6, dt_k2_binop_1, t137_zfmisc_1, t82_group_6, t14_finseq_3, fraenkel_a_2_2_domain_1, d4_subset_1, t2_binop_1, t2_partfun1, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t57_group_3, rc1_funct_1, t89_xboole_1, t37_group_2, s2_card_1, t23_group_6, t25_funct_2, fc2_xboole_0, dt_l1_group_1, t102_group_2, t47_group_6, t150_group_3, fraenkel_a_2_0_group_4, d13_group_2, cc3_vectsp_1, t84_group_2, t12_group_4, t15_binop_1, dt_m2_realset1, d12_group_4, t32_subset_1, t13_group_6, t155_group_3, t107_group_2, redefinition_k3_finsub_1, t168_relat_1, d6_binop_1, t32_group_6, t126_group_2, t108_xboole_1, t34_partfun1, t147_group_2, t34_group_6, t71_group_3, t75_group_4, t30_finset_1, t68_group_6, t46_funct_2, t48_group_4, t175_partfun1, t21_funct_4, t15_relat_1, t50_group_1, t154_funct_2, t98_group_2, t48_funct_2, t173_relat_1, fraenkel_a_3_7_domain_1, t12_funct_4, t172_relat_1, t27_relat_1, t121_group_2, t156_funct_2, t65_group_1, t47_ordinal1, t78_funct_4, t43_group_3, d1_xboole_0, t53_group_2, dt_m1_eqrel_1, t49_funct_1, d3_group_6, t44_card_1, t60_group_1, dt_k4_card_1, t69_card_1, d6_group_2, t32_group_3, d1_group_2, t64_relat_1, t40_group_3, rc6_finseq_1, t25_subset_1, t138_zfmisc_1, t59_group_2, t23_funct_1, fraenkel_a_1_0_group_2, t130_zfmisc_1, t51_xboole_1, t64_group_6, t74_group_4, d5_group_4, t52_group_2, t28_funct_4, t165_funct_2, t31_finset_1, dt_l1_lattices, t29_funct_2, t14_relset_1, t39_funct_4, t85_group_6, t86_group_1, t47_funct_2, t33_card_1, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, t8_funct_2, dt_k6_finseq_1, fc10_finset_1, t79_finseq_1, t76_group_3, t113_group_3, t60_partfun1, t163_group_3, t89_group_3, existence_m1_realset1, t26_finset_1, t36_group_6, t137_group_2, t16_relset_1, t6_mcart_1, t91_group_3, t56_domain_1, t99_finseq_3, t46_zfmisc_1, t45_group_1, t181_group_2, t31_partfun1, fraenkel_a_3_0_group_3, t171_partfun1, t164_funct_2, fc2_funct_2, t72_group_4, t56_zfmisc_1, t6_boole, t12_funct_1, dt_k1_card_1, t81_group_4, t4_orders_1, t3_funct_2, t83_group_4, d2_group_2, rc2_subset_1, fc9_finset_1, t109_group_3, t35_group_3, existence_l2_lattices, t50_xboole_1, dt_k6_subset_1, t10_relat_1, commutativity_k10_group_1, t13_group_2, t59_setfam_1, t78_int_1, t55_group_6, t185_partfun1, t1_xboole_1, dt_k1_funct_4, t18_latsubgr, t2_group_6, t3_partfun1, t52_xboole_1, t160_funct_1, commutativity_k2_xboole_0, t59_group_6, t5_subset, t138_group_2, t26_relset_1, t108_group_2, d19_vectsp_1, dt_k3_finsub_1, t64_partfun1, t52_relat_1, symmetry_r4_group_3, t77_funct_2, t59_domain_1, d13_finseq_1, t20_funct_1, t154_group_3, existence_l2_struct_0, t25_group_3, t60_card_1, t55_relat_1, t7_setfam_1, t68_partfun1, t4_setfam_1, t32_partfun1, t46_card_1, t164_group_3, d2_group_1, rc8_vectsp_1, t26_binop_1, t28_subset_1, t75_xboole_1, d4_group_2, redefinition_r2_group_6, t15_group_2, t9_group_4, t13_latsubgr, dt_m1_group_2, t82_group_3, t68_group_2, d3_group_3, t39_partfun1, t149_funct_1, t57_group_6, t129_group_2, t4_xboole_0, t65_xboole_1, d2_int_1, t5_setfam_1, t33_group_1, t63_group_2, t14_latsubgr, t142_group_3, t45_funct_2, t79_zfmisc_1, t89_group_2, t84_group_3, t37_group_1, t94_zfmisc_1, fc4_numbers, d2_realset1, t41_group_2, fc17_finseq_1, t23_binop_1, d6_partfun1, t150_relat_1, existence_m1_relset_1, t68_group_1, t35_group_6, commutativity_k5_subset_1, t14_group_1, t55_setfam_1, d8_group_1, t1_zfmisc_1, t53_group_6, d7_group_3, t46_partfun1, redefinition_k8_rlvect_1, t92_group_1, t123_zfmisc_1, fc2_subset_1, t42_group_2, t46_group_4, t25_group_4, t5_funct_2, t176_relat_1, t21_group_2, dt_k8_funct_2, t54_group_4, t99_group_3, t46_finseq_3, t24_finset_1, d14_group_3, redefinition_k3_group_6, dt_k10_group_2, t33_xboole_1, t77_group_3, t122_funct_1, t52_setfam_1, t2_zfmisc_1, d6_realset1, t143_group_2, d18_group_2, t167_funct_2, t53_partfun1, t96_group_1, fc1_orders_1, dt_l2_lattices, t97_zfmisc_1, t108_group_3, t158_group_3, t11_funct_2, d2_group_4, t28_partfun1, dt_k3_realset1, t40_funct_2, t24_binop_1, fraenkel_a_3_0_group_6, dt_k3_latsubgr, t72_partfun1, dt_k2_group_4, t81_group_3, t121_funct_1, t86_card_1, t9_relat_1, t2_tarski, t16_funct_1, t14_relat_1, t142_funct_2, d4_group_6, t82_funct_2, t16_funct_4, rc1_group_3, t114_xboole_1, t67_zfmisc_1, d1_funct_4, dt_k1_partfun1, t52_subset_1, d13_funct_1, t17_group_2, t135_group_2, t4_subset, t76_xboole_1, fc3_xboole_0, t176_orders_1, t30_xboole_1, t69_group_1, cc1_funct_2, t39_subset_1, d4_tarski, t5_ordinal1, t4_boole, t36_funct_2, t53_xboole_1, redefinition_k9_group_6, t146_funct_1, t26_group_1, d2_funct_2, t75_group_1, t49_card_1, t84_xboole_1, t77_finseq_1, t125_funct_1, t21_xboole_1, t98_zfmisc_1, commutativity_k3_finsub_1, d12_group_3, t22_group_3, t44_group_6, t73_group_6, t178_relat_1, t38_subset_1, d1_int_1, t80_group_4, t62_group_4, dt_k1_finsub_1, t169_funct_2, t166_group_2, rc2_group_6, d2_xboole_0, d10_group_4, t5_group_3, t18_group_3, dt_k8_group_6, dt_k2_funct_1, t84_group_6, dt_k8_domain_1, t32_xboole_1, d13_group_6, t94_group_2, dt_k16_finseq_1, t14_funct_1, t141_zfmisc_1, t79_int_1, t174_relat_1, t20_group_3, t52_group_6, t17_funct_2, t104_group_2, t10_group_1, t179_relat_1, t59_funct_1, t132_funct_2, t6_group_1, t61_partfun1, redefinition_r4_group_3, d3_group_2, t184_group_2, d9_group_3, t80_xboole_1, t20_finsub_1, dt_k6_group_2, t58_funct_1, t25_finset_1, t3_rlvect_1, t34_group_1, t47_group_1, t148_funct_2, t79_xboole_1, t51_funct_2, t38_finseq_3, t67_xboole_1, d12_binop_1, existence_m2_realset1, d5_group_3, t67_group_6, existence_m3_realset1, cc3_int_1, t145_group_3, dt_k4_group_4, redefinition_k5_setfam_1, t35_card_1, t61_group_3, dt_k7_group_6, t6_group_4, t58_zfmisc_1, dt_k5_group_1, t161_group_3, t74_card_1, t21_finsub_1, existence_m1_ordinal1, d4_partfun1, t29_xboole_1, t5_orders_1, fc1_realset1, t29_group_4, fc5_finseq_1, t70_group_3, cc1_funct_1, t4_funct_2, t11_group_3, fc6_finseq_1, t65_group_2, t75_group_6, t139_zfmisc_1, t32_group_4, t30_finseq_3, t7_boole, t72_group_3, redefinition_r2_group_3, d14_group_6, t115_group_3, t15_group_4, d9_group_1, t136_partfun1, t16_finseq_3, t30_group_6, t11_binop_1, t54_group_2, dt_k7_group_2, t138_partfun1, dt_k6_group_3, t42_finseq_3, rc3_struct_0, t28_card_1, t70_group_6, t66_funct_4, d10_setfam_1, d2_subset_1, t53_group_1, t66_zfmisc_1, fc1_subset_1, t29_finseq_1, t13_finset_1, dt_k1_group_4, t117_group_3, t33_funct_4, dt_k10_group_4, fraenkel_a_2_2_group_3, t22_relat_1, t48_xboole_1, dt_k6_domain_1, t157_funct_1, s1_funct_2, t3_ordinal1, t25_group_2, dt_k6_group_6, t34_group_3, t15_finseq_3, cc1_group_1, t10_group_4, t149_funct_2, t129_group_3, t48_funct_1, t21_funct_2, t11_latsubgr, t61_group_4, t164_group_2, t12_finseq_3, t15_group_1, d1_rlvect_1, fc1_group_6, t71_group_2, t16_subset_1, dt_k2_partfun1, t62_group_3, t7_group_1, d12_group_1, t173_group_2, t69_partfun1, t122_group_2, t7_ordinal1, t153_relat_1, rc2_funct_1, t49_partfun1, t125_group_2, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, t158_funct_2, t116_group_3, t32_card_1, d10_group_6, t152_funct_1, dt_u1_vectsp_1, t54_setfam_1, t47_funct_1, t42_group_1, t183_group_2, t31_xboole_1, t4_subset_1, t88_xboole_1, t19_funct_2, t18_funct_4, t51_funct_1, t30_funct_4, t103_finseq_3, t122_group_3, t85_xboole_1, t10_group_6, t22_finset_1, t38_group_4, t5_group_4, t88_group_2, t85_group_4, d2_setfam_1, dt_k9_group_4, t73_group_3, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, fraenkel_a_2_0_group_3, t64_zfmisc_1, t51_setfam_1, d3_group_4, t178_orders_1, dt_k11_group_3, t151_group_2, t65_funct_1, t28_group_3, t2_latsubgr, t118_group_2, t113_funct_2, t71_partfun1, dt_k14_finseq_1, dt_k13_group_6, t69_xboole_1, t92_group_2, t116_finseq_3, t54_group_6, t30_group_3, t159_funct_2, t116_zfmisc_1, d7_xboole_0, d4_group_3, t56_group_6, fc5_relat_1, t151_relat_1, t83_xboole_1, t35_group_2, d11_group_3, t78_group_3, t45_relat_1, t14_funct_2, t155_funct_2, dt_k3_group_1, t27_binop_1, dt_k8_group_4, t20_xboole_1, t4_group_6, dt_k7_rlvect_1, t16_zfmisc_1, t101_zfmisc_1, t5_latsubgr, t30_group_2, t27_group_2, t52_finseq_3, t56_funct_1, t43_group_2, fc1_group_3, t124_zfmisc_1, fraenkel_a_3_1_domain_1, t82_finseq_1, t60_funct_2, t82_xboole_1, t35_funct_4, dt_k8_group_2, t21_card_1, t49_group_6, t20_group_4, t54_xboole_1, t10_finseq_1, t46_setfam_1, t19_finseq_3, t23_funct_4, s1_domain_1, t26_group_6, existence_m1_subset_1, t91_group_2, dt_k1_group_2, cc2_funct_1, t120_zfmisc_1, dt_k16_group_2, t169_partfun1, t51_card_1, t84_group_1, t18_funct_1, t16_group_4, t13_group_3, t55_xboole_1, t82_group_4, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, d10_group_3, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, t25_binop_1, d2_binop_1, t75_group_2, t160_group_3, t124_funct_1, t138_group_3, t2_group_3, t58_group_2, t60_group_4, t51_group_2, t55_subset_1, t79_funct_2, t46_funct_1, idempotence_k1_funct_4, dt_k6_setfam_1, t105_group_3, t41_group_3, dt_u1_lattices, t136_funct_2, fraenkel_a_2_1_domain_1, t53_group_4, t82_card_1, t17_group_4, t27_card_1, t19_group_1, t35_group_1, t41_funct_4, t95_group_3, t3_relat_1, dt_k8_rlvect_1, t35_xboole_1, t148_group_2, redefinition_k4_subset_1, t44_zfmisc_1, fc5_group_6, dt_k13_group_2, t155_relat_1, t48_setfam_1, t17_relset_1, t9_group_2, t74_group_6, d9_binop_1, t93_group_4, existence_m2_subset_1, t49_group_2, t130_group_3, t123_group_3, s1_int_1, dt_k12_group_2, t125_zfmisc_1, t30_subset_1, d17_binop_1, dt_k2_funct_2, d1_group_6, t7_finseq_3, t14_xboole_1, t44_setfam_1, t11_relset_1, dt_k4_group_1, t74_group_1, t11_funct_4, t47_xboole_1, fc3_group_6, fc4_group_6, t78_group_2, t19_numbers, t145_funct_1, t106_group_3, fc1_finset_1, t66_group_1, t15_subset_1, t54_group_3, t66_card_1, t36_group_3, t37_funct_2, t27_group_6, d5_subset_1, t14_group_2, t92_zfmisc_1, d8_group_2, t146_relat_1, t99_partfun1, t9_realset1, t58_partfun1, d8_setfam_1, t100_zfmisc_1, t79_group_4, t3_group_6, t26_group_2, rc2_relat_1, dt_k5_subset_1, d4_binop_1, existence_l1_vectsp_1, t139_group_2, d15_group_3, t116_funct_2, t121_funct_2, t49_finseq_3, t114_zfmisc_1, t31_zfmisc_1, d1_zfmisc_1, t16_xboole_1, t26_xboole_1, t63_xboole_1, t52_group_1, t15_xboole_1, t4_latsubgr, t43_funct_2, t81_finseq_1, commutativity_k4_subset_1, dt_k5_group_2, t57_setfam_1, t72_finseq_1, t73_card_1, existence_m2_relset_1, t7_group_6, d11_group_4, t51_group_6, dt_k12_finseq_1, t78_group_4, t92_group_4, t90_group_3, t40_group_4, t168_partfun1, t157_relat_1, t179_group_2, fraenkel_a_1_0_group_6, t80_group_3, t84_zfmisc_1, symmetry_r2_group_6, t29_card_1, t6_funct_2, d2_group_3, t142_group_2, fraenkel_a_2_3_group_3, fraenkel_a_3_6_domain_1, redefinition_m1_group_6, rc2_int_1, t142_funct_1, t17_numbers, dt_k8_group_1, t26_subset_1, redefinition_k2_binop_1, t21_group_1, t87_group_6, t73_partfun1, t7_latsubgr, t1_group_3, d5_group_1, t51_subset_1, t1_latsubgr, t21_subset_1, t111_xboole_1, t8_group_6, cc5_vectsp_1, t45_finseq_3, d16_group_2, involutiveness_k7_setfam_1, t22_xboole_1, t8_setfam_1, d14_group_2, t14_group_6, t41_subset_1, redefinition_k5_funct_4, symmetry_r6_group_3, t145_group_2, t6_finseq_1, t18_binop_1, t12_group_2, dt_k5_group_6, d8_realset1, rc1_relat_1, t54_funct_1, t63_group_1, t8_xboole_1, t70_group_2, t8_realset1, t78_xboole_1, t28_xboole_1, d1_relset_1, dt_k9_group_3, d3_tarski, t74_partfun1, t69_group_2, t3_latsubgr, t37_group_4, t46_subset_1, fc1_struct_0, t29_group_3, dt_l1_vectsp_1, cc6_funct_2, t59_group_3, t71_group_6, t51_group_3, t39_zfmisc_1, d1_realset1, t5_xboole_0, reflexivity_r4_group_3, t16_int_1, t64_group_2, t131_funct_2, t119_zfmisc_1, t9_finseq_3, d6_card_1, t13_xboole_1, t60_relat_1, t44_group_1, t45_group_3, t22_group_2, t11_group_4, t40_subset_1, t83_zfmisc_1, t170_relat_1, d6_group_1, t111_group_2, t149_group_3, t54_zfmisc_1, t174_group_2, t147_group_3, fraenkel_a_3_4_domain_1, t171_group_2, t33_group_2, t19_group_4, dt_k5_relat_1, d9_group_6, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, t6_orders_1, t6_zfmisc_1, t48_relat_1, d2_orders_1, t143_funct_2, t5_mcart_1, t27_finset_1, t118_group_3, dt_k9_group_1, fc6_relat_1, dt_k2_card_1, t34_funct_2, t144_group_2, dt_k11_group_2, t51_group_1, t18_funct_2, redefinition_k7_rlvect_1, t144_funct_1, t68_group_4, t121_zfmisc_1, t10_subset_1, dt_l2_struct_0, t56_setfam_1, t96_group_3, t3_group_2, redefinition_k1_partfun1, t25_group_1, dt_k1_latsubgr, t19_group_2, t1_realset1, t48_group_1, t38_group_3, t2_xboole_1, t52_group_4, t43_group_6, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_finseq_1, t9_relset_1, redefinition_k2_realset1, t17_funct_4, t15_group_3, t10_group_3, t1_partfun1, t111_finseq_3, t41_xboole_1, t150_funct_1, t168_group_2, t58_group_3, t59_group_4, d15_binop_1, d1_funct_2, t116_group_2, t3_lattice4, t55_group_3, free_g3_lattices, t2_setfam_1, d4_xboole_0, t39_group_2, t93_group_3, t101_group_3, cc2_group_2, t13_group_4, t151_funct_2, t90_xboole_1, t51_relat_1, t19_int_1, fraenkel_a_3_0_group_2, t46_relat_1, fc1_setfam_1, t141_group_2, t66_funct_1, t18_zfmisc_1, dt_k17_group_2, t8_card_1, t3_group_3, dt_k5_setfam_1, rc3_finset_1, t81_group_6, fraenkel_a_1_0_finseq_1, t22_group_6, d6_eqrel_1, t83_group_2, t76_finseq_1, t45_partfun1, d9_group_2, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, t62_group_2, t12_group_6, t27_numbers, dt_k5_group_3, t128_group_2, fraenkel_a_2_0_group_2, t22_int_1, t47_subset_1, dt_k12_domain_1, t54_group_1, dt_k7_group_1, t81_group_2, t152_group_2, t12_group_1, t64_xboole_1, dt_k7_setfam_1, t21_setfam_1, t21_funct_1, dt_k1_group_1, t26_card_1, fc1_relat_1, t27_group_1, t33_relset_1, t80_zfmisc_1, t68_zfmisc_1, t98_group_4, t16_group_2, d5_binop_1, t20_group_1, dt_m2_subset_1, dt_k5_numbers, t105_group_2, redefinition_k1_finsub_1, t77_group_4, t12_funct_2, d16_binop_1, t54_subset_1, rc1_finset_1, dt_k2_latsubgr, t127_zfmisc_1, t123_funct_1, t40_funct_4, t11_setfam_1, t44_subset_1, d1_latsubgr, t49_xboole_1, t117_group_2, t43_group_1, cc1_finset_1, d15_group_2, d8_binop_1, fc12_finset_1, t99_group_4, t136_zfmisc_1, dt_k2_group_6, t65_group_6, t77_xboole_1, t10_setfam_1, t8_boole, t169_relat_1, rc1_xboole_0, t9_group_6, t1_mcart_1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, t35_relset_1, t48_group_6, d1_orders_1, t130_group_2, t153_group_2, t121_finseq_3, reflexivity_r1_setfam_1, t67_group_3, t24_zfmisc_1, rc5_struct_0, t2_subset, d11_group_1, fc7_relat_1, t156_relat_1, t63_group_4, t162_group_3, d13_group_4, t60_domain_1, t30_group_4, t126_zfmisc_1, dt_k3_group_2, dt_m1_orders_1, t165_group_2, t182_relat_1, d5_card_1, redefinition_k3_funct_2, t59_funct_2, t12_xboole_1, t41_group_4, reflexivity_r1_partfun1, cc4_vectsp_1, t38_funct_2, t33_partfun1, t85_funct_2, t58_card_1, t64_group_1, t28_group_2, d7_group_6, t16_finset_1, t180_relat_1, t60_funct_1, reflexivity_r6_group_3, dt_k8_group_3, fc2_relat_1, t8_finseq_1, t23_group_1, redefinition_m2_finseq_1, t37_zfmisc_1, t46_group_1, t65_relat_1, t140_group_2, t21_relat_1, t152_relat_1, dt_k6_lattices, symmetry_r1_xboole_0, t7_group_2, d1_setfam_1, t134_zfmisc_1, t48_card_1, d12_group_6, t25_partfun1, t49_relat_1, t180_group_2, fc8_relat_1, t13_finsub_1, redefinition_r1_group_2, t161_funct_1, t27_funct_1, t10_realset1, t175_orders_1, fc1_group_1, t137_group_3, t25_group_6, dt_k3_binop_1, t80_group_6, t56_group_2, t16_group_6, t151_group_3, t65_group_3, dt_k2_group_1, idempotence_k3_finsub_1, t156_group_3, t146_group_3, t50_subset_1, dt_k2_group_2, fc2_realset1, t74_xboole_1, d18_binop_1, t36_group_2, t50_group_3, redefinition_k10_group_1, t58_domain_1, t115_funct_2, t11_finseq_3, idempotence_k2_xboole_0, t48_subset_1, t119_group_2, dt_k6_group_4, t44_group_2, t28_relat_1, t71_group_4, t33_group_3, t45_card_1, t44_partfun1, t34_relset_1, t23_int_1, d6_group_4, reflexivity_r2_group_6, t31_group_4, t61_group_1, t9_tarski, t24_group_1, t145_relat_1, t6_group_2, t77_group_1, t46_xboole_1, d10_xboole_0, t100_group_2, t20_int_1, cc1_int_1, existence_l1_group_1, t149_relat_1, t43_partfun1, t7_xboole_1, t29_group_2, redefinition_k18_group_2, rc1_group_1, t57_group_4, rc9_vectsp_1, t159_funct_1, t57_funct_1, t67_partfun1, redefinition_k6_subset_1, t134_group_2, t12_relset_1, dt_u2_lattices, t86_group_3, t25_relat_1, existence_l1_struct_0, t5_xboole_1, t90_group_2, t157_group_3, t49_subset_1, rc1_card_1, dt_k2_finseq_1, t7_tarski, rc2_group_1, t115_group_2, t33_funct_1, t145_funct_2, t78_card_1, rc1_partfun1, dt_k8_finseq_1, t85_group_1, t18_int_1, t66_group_6, t3_xboole_0, t27_partfun1, symmetry_r1_partfun1, d8_group_3, d13_vectsp_1, t47_card_1, d7_group_1, t3_boole, t170_group_2, t12_latsubgr, d5_funct_1, t6_ordinal1, t24_group_3, t58_setfam_1, t76_group_2, t59_card_1, dt_k12_group_6, redefinition_k4_relset_1, t46_group_6, t10_finsub_1, cc5_funct_2, dt_k1_group_6, redefinition_m2_subset_1, t22_funct_2, t94_group_4, t17_group_6, dt_k3_group_6, t13_binop_1, fraenkel_a_2_1_group_3, t149_group_2, fc2_group_6, t95_group_1, t40_zfmisc_1, existence_m1_orders_1, t26_partfun1, t40_xboole_1, dt_m3_realset1, t4_group_3, fc14_finset_1, t26_funct_4, t36_relset_1, rc4_struct_0, dt_k10_domain_1, t150_group_2, t16_binop_1, s2_funct_2, fc13_finset_1, t15_funct_4, t139_partfun1, d16_group_1, t47_group_3, t136_group_2, t139_group_3, d13_binop_1, t132_group_2, idempotence_k4_subset_1, t72_group_6, redefinition_k8_group_6, t143_partfun1, t80_finseq_1, d14_group_1, t12_finseq_1, t87_xboole_1, t22_funct_4, t177_group_2, rc2_xboole_0, t70_group_1, t67_group_2, t174_partfun1, t186_group_2, t55_funct_2, d4_group_4, fraenkel_a_3_5_domain_1, t45_xboole_1, t38_partfun1, dt_k4_group_2, d5_group_2, reflexivity_r2_group_3, t67_funct_2, t97_group_3, t172_group_2, existence_m2_finseq_1, t45_group_6, existence_l1_rlvect_1, d13_group_1, t13_card_1, cc1_group_2, d9_vectsp_1, t22_finseq_3, t26_relat_1, t127_group_2, t61_funct_2, t36_funct_4, dt_k7_group_4, t106_group_2, fc3_lattices, t10_xboole_1, d3_binop_1, t66_group_2, t28_funct_2, t26_group_3, dt_k3_subset_1, fc1_funct_2, fraenkel_a_1_1_group_4, cc1_binop_1, t6_relat_1, t22_group_1, t172_partfun1, t33_subset_1, t159_relat_1, d17_group_2, t86_group_6, free_g4_vectsp_1, t32_funct_4, t30_partfun1, t65_zfmisc_1, dt_k14_group_2, t63_subset_1, t112_partfun1, d3_xboole_0, t73_group_4, t14_group_3, t144_group_3, t38_xboole_1, t19_funct_4, dt_k10_group_6, t62_group_6, t39_xboole_1, t31_group_1, t17_group_1, t56_group_3, t83_group_6, t18_group_1, t5_group_1, t20_funct_4, antisymmetry_r2_hidden, d19_binop_1, t53_setfam_1, t79_group_3, t24_finseq_1, t55_group_4, d8_group_6, t53_relat_1, t167_relat_1, t82_group_1, t21_group_4, dt_g1_group_1, abstractness_v1_group_1, t22_subset_1, redefinition_k6_domain_1
% 40.95/12.57 % No. of inferences in proof: 3612
% 40.95/12.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12042 ms resp. 11206 ms w/o parsing
% 43.14/13.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.14/13.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------