TSTP Solution File: GRP650+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP650+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:14:55 EDT 2023
% Result : Theorem 245.00s 53.37s
% Output : Refutation 248.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2548
% Syntax : Number of formulae : 5808 ( 842 unt; 436 typ; 0 def)
% Number of atoms : 31814 (4500 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 108064 (5115 ~;1569 |;13784 &;76757 @)
% ( 434 <=>;10405 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 870 ( 870 >; 0 *; 0 +; 0 <<)
% Number of symbols : 438 ( 436 usr; 49 con; 0-9 aty)
% Number of variables : 13903 ( 0 ^;13279 !; 624 ?;13903 :)
% 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(k3_latsubgr_type,type,
k3_latsubgr: $i > $i > $i > $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k11_group_4_type,type,
k11_group_4: $i > $i ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(v3_filter_0_type,type,
v3_filter_0: $i > $o ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v3_lattice4_type,type,
v3_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_type,type,
r1_lattice4: $i > $i > $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(v2_lattice4_type,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r4_lattice4_type,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k8_filter_1_type,type,
k8_filter_1: $i > $i > $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_finseq_1_type,type,
v1_finseq_1: $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(k3_finseq_1_type,type,
k3_finseq_1: $i > $i ).
thf(k1_nat_1_type,type,
k1_nat_1: $i > $i > $i ).
thf(np__1_type,type,
np__1: $i ).
thf(r1_xreal_0_type,type,
r1_xreal_0: $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k2_finseq_3_type,type,
k2_finseq_3: $i > $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k4_filter_0_type,type,
k4_filter_0: $i > $i > $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k7_filter_1_type,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_type,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k6_xcmplx_0_type,type,
k6_xcmplx_0: $i > $i > $i ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(k7_filter_0_type,type,
k7_filter_0: $i > $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(r1_binop_1_type,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_finseq_3_type,type,
k1_finseq_3: $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k4_finseq_1_type,type,
k4_finseq_1: $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(r2_wellord2_type,type,
r2_wellord2: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(v4_lattice3_type,type,
v4_lattice3: $i > $o ).
thf(r4_lattice3_type,type,
r4_lattice3: $i > $i > $i > $o ).
thf(r1_lattices_type,type,
r1_lattices: $i > $i > $i > $o ).
thf(m1_filter_1_type,type,
m1_filter_1: $i > $i > $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(m1_orders_1_type,type,
m1_orders_1: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k4_card_1_type,type,
k4_card_1: $i > $i ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(v1_lattice4_type,type,
v1_lattice4: $i > $i > $i > $o ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(k2_funcop_1_type,type,
k2_funcop_1: $i > $i > $i ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(k33_binop_2_type,type,
k33_binop_2: $i ).
thf(np__0_type,type,
np__0: $i ).
thf(r3_lattice3_type,type,
r3_lattice3: $i > $i > $i > $o ).
thf(k6_finseq_1_type,type,
k6_finseq_1: $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(m2_finseq_1_type,type,
m2_finseq_1: $i > $i > $o ).
thf(r1_filter_0_type,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(r3_binop_1_type,type,
r3_binop_1: $i > $i > $i > $o ).
thf(m2_filter_1_type,type,
m2_filter_1: $i > $i > $i > $o ).
thf(m1_finseq_1_type,type,
m1_finseq_1: $i > $i > $o ).
thf(k2_card_1_type,type,
k2_card_1: $i > $i ).
thf(k1_card_1_type,type,
k1_card_1: $i > $i ).
thf(k6_filter_0_type,type,
k6_filter_0: $i > $i > $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k6_group_1_type,type,
k6_group_1: $i > $i > $i > $i ).
thf(k1_group_1_type,type,
k1_group_1: $i > $i > $i > $i ).
thf(k5_filter_0_type,type,
k5_filter_0: $i > $i > $i > $i ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m4_vectsp_8_type,type,
m4_vectsp_8: $i > $i > $i > $o ).
thf(m3_vectsp_8_type,type,
m3_vectsp_8: $i > $i > $i > $o ).
thf(k1_funct_4_type,type,
k1_funct_4: $i > $i > $i ).
thf(r2_lattice4_type,type,
r2_lattice4: $i > $i > $i > $o ).
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(v5_lattice3_type,type,
v5_lattice3: $i > $o ).
thf(k1_real_1_type,type,
k1_real_1: $i > $i ).
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(k2_enumset1_type,type,
k2_enumset1: $i > $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k10_relset_1_type,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(k15_lattice3_type,type,
k15_lattice3: $i > $i > $i ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
thf(k10_filter_1_type,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(k3_setfam_1_type,type,
k3_setfam_1: $i > $i > $i ).
thf(k2_xcmplx_0_type,type,
k2_xcmplx_0: $i > $i > $i ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(k8_filter_0_type,type,
k8_filter_0: $i > $i > $i ).
thf(k2_filter_0_type,type,
k2_filter_0: $i > $i > $i ).
thf(k7_group_1_type,type,
k7_group_1: $i > $i > $i ).
thf(k3_group_1_type,type,
k3_group_1: $i > $i > $i ).
thf(k2_group_1_type,type,
k2_group_1: $i > $i ).
thf(r1_lattice3_type,type,
r1_lattice3: $i > $i > $i > $o ).
thf(k3_lattice3_type,type,
k3_lattice3: $i > $i ).
thf(k4_lattice3_type,type,
k4_lattice3: $i > $i > $i ).
thf(k7_lattices_type,type,
k7_lattices: $i > $i > $i ).
thf(a_2_0_lattice3_type,type,
a_2_0_lattice3: $i > $i > $i ).
thf(k3_filter_0_type,type,
k3_filter_0: $i > $i > $i ).
thf(a_3_1_filter_0_type,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(v2_filter_0_type,type,
v2_filter_0: $i > $i > $o ).
thf(k1_filter_0_type,type,
k1_filter_0: $i > $i ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_5_lattice3_type,type,
a_2_5_lattice3: $i > $i > $i ).
thf(k16_lattice3_type,type,
k16_lattice3: $i > $i > $i ).
thf(a_2_6_lattice3_type,type,
a_2_6_lattice3: $i > $i > $i ).
thf(k12_finseq_1_type,type,
k12_finseq_1: $i > $i > $i ).
thf(m3_lattice4_type,type,
m3_lattice4: $i > $i > $o ).
thf(k3_lattice4_type,type,
k3_lattice4: $i > $i > $i ).
thf(k5_group_1_type,type,
k5_group_1: $i > $i ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(r3_orders_2_type,type,
r3_orders_2: $i > $i > $i > $o ).
thf(v7_group_1_type,type,
v7_group_1: $i > $o ).
thf(k4_finseq_4_type,type,
k4_finseq_4: $i > $i > $i > $i > $i ).
thf(k3_group_4_type,type,
k3_group_4: $i > $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(k5_lattice4_type,type,
k5_lattice4: $i > $i ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(k9_filter_0_type,type,
k9_filter_0: $i > $i > $i > $i ).
thf(k4_funct_2_type,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k3_lattices_type,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_binop_2_type,type,
k7_binop_2: $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(v6_ordinal1_type,type,
v6_ordinal1: $i > $o ).
thf(a_2_2_lattice3_type,type,
a_2_2_lattice3: $i > $i > $i ).
thf(k3_xcmplx_0_type,type,
k3_xcmplx_0: $i > $i > $i ).
thf(k8_finseq_1_type,type,
k8_finseq_1: $i > $i > $i > $i ).
thf(v6_lattice3_type,type,
v6_lattice3: $i > $o ).
thf(a_3_5_lattice3_type,type,
a_3_5_lattice3: $i > $i > $i > $i ).
thf(k4_lattice4_type,type,
k4_lattice4: $i > $i > $i ).
thf(g4_vectsp_1_type,type,
g4_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(k4_numbers_type,type,
k4_numbers: $i ).
thf(r2_setfam_1_type,type,
r2_setfam_1: $i > $i > $o ).
thf(m1_group_2_type,type,
m1_group_2: $i > $i > $o ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(v3_funct_2_type,type,
v3_funct_2: $i > $i > $i > $o ).
thf(m2_lattice4_type,type,
m2_lattice4: $i > $i > $o ).
thf(r3_lattice4_type,type,
r3_lattice4: $i > $i > $i > $o ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_2_0_lattice4_type,type,
a_2_0_lattice4: $i > $i > $i ).
thf(k3_binop_1_type,type,
k3_binop_1: $i > $i > $i ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(v1_card_1_type,type,
v1_card_1: $i > $o ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k9_filter_1_type,type,
k9_filter_1: $i > $i ).
thf(k1_int_2_type,type,
k1_int_2: $i > $i ).
thf(r1_rlvect_1_type,type,
r1_rlvect_1: $i > $i > $o ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k2_struct_0_type,type,
k2_struct_0: $i > $i > $i > $i ).
thf(v1_group_6_type,type,
v1_group_6: $i > $i > $i > $o ).
thf(k2_nat_1_type,type,
k2_nat_1: $i > $i > $i ).
thf(k17_group_2_type,type,
k17_group_2: $i > $i > $i ).
thf(k2_group_3_type,type,
k2_group_3: $i > $i > $i > $i ).
thf(k7_rlvect_1_type,type,
k7_rlvect_1: $i > $i > $i > $i ).
thf(v5_group_1_type,type,
v5_group_1: $i > $i > $o ).
thf(k2_group_4_type,type,
k2_group_4: $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k14_group_2_type,type,
k14_group_2: $i > $i > $i ).
thf(a_1_0_filter_1_type,type,
a_1_0_filter_1: $i > $i ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(v2_group_6_type,type,
v2_group_6: $i > $i > $i > $o ).
thf(r2_lattice3_type,type,
r2_lattice3: $i > $i > $i > $o ).
thf(k2_vectsp_1_type,type,
k2_vectsp_1: $i > $i ).
thf(u1_vectsp_1_type,type,
u1_vectsp_1: $i > $i ).
thf(a_3_3_lattice3_type,type,
a_3_3_lattice3: $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(a_3_9_lattice3_type,type,
a_3_9_lattice3: $i > $i > $i > $i ).
thf(a_3_10_lattice3_type,type,
a_3_10_lattice3: $i > $i > $i > $i ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(a_3_6_lattice3_type,type,
a_3_6_lattice3: $i > $i > $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(l2_struct_0_type,type,
l2_struct_0: $i > $o ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(a_2_0_filter_0_type,type,
a_2_0_filter_0: $i > $i > $i ).
thf(a_3_7_lattice3_type,type,
a_3_7_lattice3: $i > $i > $i > $i ).
thf(a_3_8_lattice3_type,type,
a_3_8_lattice3: $i > $i > $i > $i ).
thf(k1_group_3_type,type,
k1_group_3: $i > $i ).
thf(v1_group_1_type,type,
v1_group_1: $i > $o ).
thf(k2_latsubgr_type,type,
k2_latsubgr: $i > $i > $i ).
thf(k1_latsubgr_type,type,
k1_latsubgr: $i > $i ).
thf(k9_group_1_type,type,
k9_group_1: $i > $i ).
thf(a_2_7_lattice3_type,type,
a_2_7_lattice3: $i > $i > $i ).
thf(a_3_3_domain_1_type,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(k10_group_1_type,type,
k10_group_1: $i > $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(a_2_3_lattice3_type,type,
a_2_3_lattice3: $i > $i > $i ).
thf(a_2_4_lattice3_type,type,
a_2_4_lattice3: $i > $i > $i ).
thf(k5_int_1_type,type,
k5_int_1: $i > $i > $i ).
thf(r1_group_2_type,type,
r1_group_2: $i > $i > $i > $o ).
thf(k8_group_4_type,type,
k8_group_4: $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(k7_group_2_type,type,
k7_group_2: $i > $i > $i ).
thf(v1_group_3_type,type,
v1_group_3: $i > $i > $o ).
thf(v3_group_6_type,type,
v3_group_6: $i > $i > $i > $o ).
thf(k11_group_6_type,type,
k11_group_6: $i > $i > $i ).
thf(k6_group_6_type,type,
k6_group_6: $i > $i > $i ).
thf(k2_group_2_type,type,
k2_group_2: $i > $i > $i > $i ).
thf(k13_group_2_type,type,
k13_group_2: $i > $i > $i > $i ).
thf(k6_group_2_type,type,
k6_group_2: $i > $i ).
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(k16_group_2_type,type,
k16_group_2: $i > $i > $i ).
thf(k13_group_6_type,type,
k13_group_6: $i > $i > $i > $i ).
thf(k8_relset_1_type,type,
k8_relset_1: $i > $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(u1_group_1_type,type,
u1_group_1: $i > $i ).
thf(k2_group_6_type,type,
k2_group_6: $i > $i > $i > $i ).
thf(m1_group_6_type,type,
m1_group_6: $i > $i > $i > $o ).
thf(a_3_0_filter_0_type,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(k1_group_6_type,type,
k1_group_6: $i > $i > $i > $i ).
thf(k9_group_2_type,type,
k9_group_2: $i > $i > $i > $i ).
thf(k5_group_4_type,type,
k5_group_4: $i > $i > $i ).
thf(k8_group_3_type,type,
k8_group_3: $i > $i > $i ).
thf(r4_group_3_type,type,
r4_group_3: $i > $i > $i > $o ).
thf(k7_group_3_type,type,
k7_group_3: $i > $i > $i ).
thf(k5_group_3_type,type,
k5_group_3: $i > $i > $i > $i ).
thf(np__2_type,type,
np__2: $i ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k4_group_6_type,type,
k4_group_6: $i > $i > $i ).
thf(k5_group_2_type,type,
k5_group_2: $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(k7_domain_1_type,type,
k7_domain_1: $i > $i > $i > $i ).
thf(a_1_0_group_2_type,type,
a_1_0_group_2: $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(v4_group_6_type,type,
v4_group_6: $i > $i > $i > $o ).
thf(k8_group_6_type,type,
k8_group_6: $i > $i > $i > $i > $i > $i ).
thf(r2_group_6_type,type,
r2_group_6: $i > $i > $o ).
thf(k9_group_6_type,type,
k9_group_6: $i > $i > $i > $i ).
thf(k1_group_2_type,type,
k1_group_2: $i > $i > $i ).
thf(k3_finsub_1_type,type,
k3_finsub_1: $i > $i > $i > $i ).
thf(a_3_4_lattice3_type,type,
a_3_4_lattice3: $i > $i > $i > $i ).
thf(k9_group_4_type,type,
k9_group_4: $i > $i ).
thf(k8_group_2_type,type,
k8_group_2: $i > $i > $i > $i ).
thf(r1_nat_1_type,type,
r1_nat_1: $i > $i > $o ).
thf(k12_group_6_type,type,
k12_group_6: $i > $i > $i > $i ).
thf(v2_group_4_type,type,
v2_group_4: $i > $i > $o ).
thf(k6_group_4_type,type,
k6_group_4: $i > $i ).
thf(k10_group_4_type,type,
k10_group_4: $i > $i ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_group_4_type,type,
k1_group_4: $i > $i > $i > $i ).
thf(k9_group_3_type,type,
k9_group_3: $i > $i > $i ).
thf(a_3_2_lattice3_type,type,
a_3_2_lattice3: $i > $i > $i > $i ).
thf(k15_group_2_type,type,
k15_group_2: $i > $i > $i ).
thf(k9_group_5_type,type,
k9_group_5: $i > $i ).
thf(k7_group_6_type,type,
k7_group_6: $i > $i > $i > $i ).
thf(k10_group_3_type,type,
k10_group_3: $i > $i > $i ).
thf(a_1_0_group_4_type,type,
a_1_0_group_4: $i > $i ).
thf(r6_group_3_type,type,
r6_group_3: $i > $i > $i > $o ).
thf(k11_group_3_type,type,
k11_group_3: $i > $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(v1_group_4_type,type,
v1_group_4: $i > $i > $o ).
thf(p1_s2_card_1_type,type,
p1_s2_card_1: $i > $o ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $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(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(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k3_finseq_4_type,type,
k3_finseq_4: $i > $i > $i > $i > $i ).
thf(k8_rlvect_1_type,type,
k8_rlvect_1: $i > $i > $i > $i > $i ).
thf(a_2_0_group_4_type,type,
a_2_0_group_4: $i > $i > $i ).
thf(k10_group_6_type,type,
k10_group_6: $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $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(k9_domain_1_type,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(k3_group_6_type,type,
k3_group_6: $i > $i > $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(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(k2_group_5_type,type,
k2_group_5: $i > $i > $i > $i ).
thf(a_2_3_group_3_type,type,
a_2_3_group_3: $i > $i > $i ).
thf(a_2_1_group_3_type,type,
a_2_1_group_3: $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $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(k4_xcmplx_0_type,type,
k4_xcmplx_0: $i > $i ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
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(k6_eqrel_1_type,type,
k6_eqrel_1: $i > $i > $i > $i ).
thf(a_1_0_group_6_type,type,
a_1_0_group_6: $i > $i ).
thf(r3_group_3_type,type,
r3_group_3: $i > $i > $i > $o ).
thf(r1_group_3_type,type,
r1_group_3: $i > $i > $i > $o ).
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(k6_finseqop_type,type,
k6_finseqop: $i > $i > $i ).
thf(v1_setwiseo_type,type,
v1_setwiseo: $i > $i > $o ).
thf(r1_finseqop_type,type,
r1_finseqop: $i > $i > $i > $o ).
thf(a_2_2_group_3_type,type,
a_2_2_group_3: $i > $i > $i ).
thf(a_1_1_group_4_type,type,
a_1_1_group_4: $i > $i ).
thf(k2_finsop_1_type,type,
k2_finsop_1: $i > $i > $i > $i ).
thf(np__3_type,type,
np__3: $i ).
thf(v1_finseqop_type,type,
v1_finseqop: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk24_type,type,
sk24: $i ).
thf(sk27_type,type,
sk27: $i ).
thf(sk37_type,type,
sk37: $i > $i ).
thf(sk48_type,type,
sk48: $i ).
thf(sk81_type,type,
sk81: $i > $i ).
thf(sk110_type,type,
sk110: $i ).
thf(sk111_type,type,
sk111: $i > $i > $i ).
thf(sk118_type,type,
sk118: $i > $i > $i ).
thf(sk145_type,type,
sk145: $i ).
thf(sk150_type,type,
sk150: $i > $i ).
thf(sk152_type,type,
sk152: $i ).
thf(sk167_type,type,
sk167: $i ).
thf(sk179_type,type,
sk179: $i ).
thf(sk180_type,type,
sk180: $i > $i > $i ).
thf(sk196_type,type,
sk196: $i ).
thf(sk235_type,type,
sk235: $i ).
thf(sk253_type,type,
sk253: $i ).
thf(sk259_type,type,
sk259: $i ).
thf(sk261_type,type,
sk261: $i ).
thf(sk272_type,type,
sk272: $i ).
thf(sk280_type,type,
sk280: $i ).
thf(sk297_type,type,
sk297: $i > $i ).
thf(sk305_type,type,
sk305: $i > $i ).
thf(sk330_type,type,
sk330: $i > $i ).
thf(sk335_type,type,
sk335: $i ).
thf(sk348_type,type,
sk348: $i > $i ).
thf(sk370_type,type,
sk370: $i ).
thf(sk378_type,type,
sk378: $i > $i ).
thf(sk385_type,type,
sk385: $i ).
thf(sk388_type,type,
sk388: $i ).
thf(sk464_type,type,
sk464: $i ).
thf(sk510_type,type,
sk510: $i ).
thf(sk522_type,type,
sk522: $i ).
thf(sk524_type,type,
sk524: $i > $i ).
thf(sk537_type,type,
sk537: $i ).
thf(sk544_type,type,
sk544: $i ).
thf(sk545_type,type,
sk545: $i ).
thf(sk555_type,type,
sk555: $i ).
thf(sk581_type,type,
sk581: $i ).
thf(sk593_type,type,
sk593: $i ).
thf(sk605_type,type,
sk605: $i ).
thf(sk607_type,type,
sk607: $i ).
thf(sk608_type,type,
sk608: $i ).
thf(sk610_type,type,
sk610: $i ).
thf(sk611_type,type,
sk611: $i ).
thf(sk612_type,type,
sk612: $i ).
thf(sk636_type,type,
sk636: $i ).
thf(1189,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(7373,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)],[1189]) ).
thf(672,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(5116,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)],[672]) ).
thf(1550,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(9180,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)],[1550]) ).
thf(723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
<=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_1) ).
thf(5320,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v13_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v13_lattices @ A )
& ( v13_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1366,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_0) ).
thf(8200,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1518,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(9032,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)],[1518]) ).
thf(739,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(5385,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(207,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(2911,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(2912,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2911]) ).
thf(2913,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2912]) ).
thf(26,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(2219,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)],[26]) ).
thf(2220,plain,
( ! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= A )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[2219]) ).
thf(2221,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= A )
| ( r1_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[2220]) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= A )
| ( r1_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[2221]) ).
thf(2224,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= A )
| ( r1_xboole_0 @ A @ B ) ),
inference(simp,[status(thm)],[2223]) ).
thf(20847,plain,
! [C: $i,B: $i,A: $i] :
( ( k1_xboole_0 != B )
| ( r1_xboole_0 @ B @ C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2913,2224]) ).
thf(20848,plain,
! [A: $i] :
( ( k1_xboole_0 != k1_xboole_0 )
| ( r1_xboole_0 @ k1_xboole_0 @ A ) ),
inference(pattern_uni,[status(thm)],[20847:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(20849,plain,
! [A: $i] : ( r1_xboole_0 @ k1_xboole_0 @ A ),
inference(simp,[status(thm)],[20848]) ).
thf(13,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(2174,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)],[13]) ).
thf(2175,plain,
! [B: $i,A: $i] :
( ~ ( r1_xboole_0 @ A @ B )
| ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
inference(cnf,[status(esa)],[2174]) ).
thf(2176,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A )
| ~ ( r1_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[2175]) ).
thf(21282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ C )
= B )
| ( ( r1_xboole_0 @ k1_xboole_0 @ A )
!= ( r1_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20849,2176]) ).
thf(21283,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ A ) @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[21282:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(237,axiom,
r1_tarski @ k5_numbers @ k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).
thf(3020,plain,
r1_tarski @ k5_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(25,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(2216,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)],[25]) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(miniscope,[status(thm)],[2216]) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(cnf,[status(esa)],[2217]) ).
thf(19246,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) )
| ( ( r1_tarski @ k5_numbers @ k1_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3020,2218]) ).
thf(19247,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) ),
inference(pattern_uni,[status(thm)],[19246:[bind(A,$thf( k5_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(19271,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) ),
inference(simp,[status(thm)],[19247]) ).
thf(33605,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ k1_numbers ) @ k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ A ) @ A )
!= ( k4_xboole_0 @ B @ k5_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[21283,19271]) ).
thf(33606,plain,
r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k1_numbers ) @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[33605:[bind(A,$thf( k5_numbers )),bind(B,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ))]]) ).
thf(15,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(2179,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)],[15]) ).
thf(2180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
| ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[2179]) ).
thf(33817,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k1_numbers ) @ k1_xboole_0 )
!= ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33606,2180]) ).
thf(33818,plain,
r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ ( k2_xboole_0 @ k1_numbers @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[33817:[bind(A,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers )),bind(B,$thf( k1_numbers )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(661,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(5080,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(5081,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[5080]) ).
thf(5082,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[5081]) ).
thf(33905,plain,
r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k1_numbers,
inference(rewrite,[status(thm)],[33818,5082]) ).
thf(22,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(2201,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)],[22]) ).
thf(2202,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(miniscope,[status(thm)],[2201]) ).
thf(2203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[2202]) ).
thf(33919,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k1_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33905,2203]) ).
thf(33920,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ A ) @ k1_numbers ),
inference(pattern_uni,[status(thm)],[33919:[bind(A,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers )),bind(B,$thf( k1_numbers )),bind(C,$thf( C ))]]) ).
thf(33952,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ A ) @ k1_numbers ),
inference(simp,[status(thm)],[33920]) ).
thf(60,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(2340,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)],[60]) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[2340]) ).
thf(2342,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[2341]) ).
thf(2343,plain,
! [B: $i,A: $i] :
( ( sk12 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk12])]) ).
thf(41084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ A ) @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21283,2343]) ).
thf(41085,plain,
! [A: $i] :
( ( sk12 @ A @ k1_xboole_0 )
= ( k2_xboole_0 @ k1_xboole_0 @ A ) ),
inference(pattern_uni,[status(thm)],[41084:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k2_xboole_0 @ k1_xboole_0 @ E ))]]) ).
thf(41107,plain,
! [A: $i] :
( ( sk12 @ A @ k1_xboole_0 )
= ( k2_xboole_0 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[41085]) ).
thf(41090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2913,2343]) ).
thf(41091,plain,
! [A: $i] :
( ( sk12 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[41090:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(41649,plain,
! [A: $i] :
( ( k2_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[41107,41091]) ).
thf(41657,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k1_xboole_0 @ A ) @ k1_numbers ),
inference(rewrite,[status(thm)],[33952,41649]) ).
thf(42983,plain,
r1_tarski @ k1_xboole_0 @ k1_numbers,
inference(rewrite,[status(thm)],[41657,2913]) ).
thf(238,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(3021,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)],[238]) ).
thf(21,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(2195,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)],[21]) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( ( k1_binop_1 @ C @ B @ ( sk2 @ C @ B @ A ) )
!= ( sk2 @ C @ B @ A ) )
| ( r1_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2195]) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ C @ B @ ( sk2 @ C @ B @ A ) )
!= ( sk2 @ C @ B @ A ) )
| ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[2197]) ).
thf(1332,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(8062,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)],[1332]) ).
thf(1722,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(9982,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)],[1722]) ).
thf(189,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_xreal_0 @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_finseq_1) ).
thf(2822,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_xreal_0 @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1169,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(7304,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)],[1169]) ).
thf(1957,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(10917,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)],[1957]) ).
thf(487,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_0) ).
thf(4188,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) )
& ( ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B )
=> ( r2_hidden @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1067,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(6836,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)],[1067]) ).
thf(442,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(3944,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)],[442]) ).
thf(1100,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(6979,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(520,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(4331,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)],[520]) ).
thf(4334,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[4331]) ).
thf(4339,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( v1_relat_1 @ ( sk150 @ A ) ) ),
inference(lifteq,[status(thm)],[4334]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_latsubgr @ A @ A @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) )
= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_latsubgr) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_latsubgr @ A @ A @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) )
= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2113,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( k3_latsubgr @ A @ A @ ( k6_partfun1 @ ( u1_struct_0 @ A ) ) )
= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2116,plain,
l1_group_1 @ sk1,
inference(cnf,[status(esa)],[2113]) ).
thf(598,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(4718,plain,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(4719,plain,
! [A: $i] :
( ~ ( l1_group_1 @ A )
| ( l1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[4718]) ).
thf(14846,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk1 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2116,4719]) ).
thf(14847,plain,
l1_struct_0 @ sk1,
inference(pattern_uni,[status(thm)],[14846:[bind(A,$thf( sk1 ))]]) ).
thf(19539,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,14847]) ).
thf(19540,plain,
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19539:[bind(A,$thf( sk1 ))]]) ).
thf(20006,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,2116]) ).
thf(20007,plain,
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20006:[bind(A,$thf( sk1 ))]]) ).
thf(1570,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(9273,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(617,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(4835,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)],[617]) ).
thf(942,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(6355,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)],[942]) ).
thf(1796,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(10373,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)],[1796]) ).
thf(2103,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(11445,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)],[2103]) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v4_lattice3 @ A )
<=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_lattice3) ).
thf(2294,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v4_lattice3 @ A )
=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( v4_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(2295,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ( m1_subset_1 @ ( sk7 @ B @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(248,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(3053,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)],[248]) ).
thf(842,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(5857,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)],[842]) ).
thf(1698,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(9886,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)],[1698]) ).
thf(50,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v15_lattices @ A )
<=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattices) ).
thf(2306,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v15_lattices @ A )
=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) )
& ( ( ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1303,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(7890,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)],[1303]) ).
thf(1878,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(10638,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)],[1878]) ).
thf(59,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(2336,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)],[59]) ).
thf(1528,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(9077,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)],[1528]) ).
thf(234,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(3008,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)],[234]) ).
thf(775,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).
thf(5591,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(5592,plain,
k5_numbers != k1_numbers,
inference(polarity_switch,[status(thm)],[5591]) ).
thf(5593,plain,
k5_numbers != k1_numbers,
inference(lifteq,[status(thm)],[5592]) ).
thf(5,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice4) ).
thf(2130,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2131,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_lattice4 @ C @ B @ A )
| ~ ( v2_lattice4 @ C @ B @ A )
| ( r4_lattice4 @ B @ A @ C ) ),
inference(cnf,[status(esa)],[2130]) ).
thf(679,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(5136,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)],[679]) ).
thf(2041,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(11211,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)],[2041]) ).
thf(1235,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m4_vectsp_8 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m4_vectsp_8) ).
thf(7569,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m4_vectsp_8 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(852,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(5896,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)],[852]) ).
thf(1099,axiom,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_card_1) ).
thf(6976,plain,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(2031,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(11186,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)],[2031]) ).
thf(1884,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(10654,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)],[1884]) ).
thf(10658,plain,
v2_group_1 @ sk605,
inference(cnf,[status(esa)],[10654]) ).
thf(19346,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v2_group_1 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[4339,10658]) ).
thf(19347,plain,
( ( v1_relat_1 @ ( sk150 @ sk605 ) )
| ( v2_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19346:[bind(A,$thf( sk605 ))]]) ).
thf(37,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(2261,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)],[37]) ).
thf(2262,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[2261]) ).
thf(2263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ),
inference(lifteq,[status(thm)],[2262]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice3) ).
thf(6544,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(440,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(3930,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)],[440]) ).
thf(1344,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(8114,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)],[1344]) ).
thf(1665,axiom,
? [A: $i] : ( v1_int_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_int_1) ).
thf(9754,plain,
? [A: $i] : ( v1_int_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(485,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(4183,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)],[485]) ).
thf(449,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(3979,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)],[449]) ).
thf(741,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(5390,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)],[741]) ).
thf(1836,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(10495,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)],[1836]) ).
thf(1073,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(6855,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)],[1073]) ).
thf(9887,plain,
( ! [A: $i] :
( ? [B: $i] :
( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ B ) ) )
=> ? [B: $i] :
( A
= ( k1_tarski @ B ) ) )
& ! [A: $i] :
( ? [B: $i] :
( A
= ( k1_tarski @ B ) )
=> ! [B: $i] :
( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[9886]) ).
thf(9888,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ C ) ) ) ),
inference(cnf,[status(esa)],[9887]) ).
thf(9890,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( ( k1_card_1 @ A )
= ( k1_card_1 @ ( k1_tarski @ C ) ) ) ),
inference(lifteq,[status(thm)],[9888]) ).
thf(9891,plain,
! [B: $i,A: $i] :
( ( k1_card_1 @ ( k1_tarski @ A ) )
= ( k1_card_1 @ ( k1_tarski @ B ) ) ),
inference(simp,[status(thm)],[9890]) ).
thf(1334,axiom,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_card_1) ).
thf(8071,plain,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(8072,plain,
( ( k1_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[8071]) ).
thf(1453,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(8703,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(8704,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[8703]) ).
thf(26166,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) )
| ( ( k1_card_1 @ k1_xboole_0 )
!= ( k1_card_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8072,8704]) ).
thf(26167,plain,
r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26166:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1001,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(6558,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(6559,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[6558]) ).
thf(26196,plain,
r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[26167,6559]) ).
thf(1526,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(9065,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)],[1526]) ).
thf(9066,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( r2_hidden @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[9065]) ).
thf(9068,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[9066]) ).
thf(9071,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[9068]) ).
thf(9072,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[9071]) ).
thf(26210,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) )
!= ( r2_hidden @ A @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[26196,9072]) ).
thf(26236,plain,
! [A: $i] :
( ( k1_xboole_0 != A )
| ( ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[26210]) ).
thf(26243,plain,
( ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26236]) ).
thf(26245,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4339,26243]) ).
thf(26246,plain,
v1_relat_1 @ ( sk150 @ ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[26245:[bind(A,$thf( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ))]]) ).
thf(26774,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ ( k1_card_1 @ ( k1_tarski @ A ) ) ) )
| ( ( k1_card_1 @ ( k1_tarski @ B ) )
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9891,26246]) ).
thf(26775,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_card_1 @ ( k1_tarski @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[26774:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1651,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(9685,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)],[1651]) ).
thf(1909,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(10743,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)],[1909]) ).
thf(446,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3968,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(3969,plain,
~ ( v3_struct_0 @ sk110 ),
inference(cnf,[status(esa)],[3968]) ).
thf(807,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(5728,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(5730,plain,
v1_xboole_0 @ k1_xboole_0,
inference(cnf,[status(esa)],[5728]) ).
thf(1272,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(7748,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(7750,plain,
~ ( v1_xboole_0 @ sk385 ),
inference(cnf,[status(esa)],[7748]) ).
thf(11540,plain,
( ( v1_xboole_0 @ sk385 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,7750]) ).
thf(11547,plain,
sk385 != k1_xboole_0,
inference(simp,[status(thm)],[11540]) ).
thf(20161,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk385 ) ),
inference(paramod_ordered,[status(thm)],[4339,11547]) ).
thf(20162,plain,
v1_relat_1 @ ( sk150 @ sk385 ),
inference(pattern_uni,[status(thm)],[20161:[bind(A,$thf( sk385 ))]]) ).
thf(699,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(5205,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)],[699]) ).
thf(895,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(6121,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)],[895]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_partfun1) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(866,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(5991,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)],[866]) ).
thf(5992,plain,
( ! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[5991]) ).
thf(5994,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[5992]) ).
thf(5998,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[5994]) ).
thf(5999,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[5998]) ).
thf(820,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(5778,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)],[820]) ).
thf(1000,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(6555,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)],[1000]) ).
thf(1105,axiom,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_group_1) ).
thf(7003,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(7004,plain,
v1_group_1 @ sk335,
inference(cnf,[status(esa)],[7003]) ).
thf(19571,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_group_1 @ k1_xboole_0 )
| ( A != sk335 ) ),
inference(paramod_ordered,[status(thm)],[4339,7004]) ).
thf(19572,plain,
( ( v1_relat_1 @ ( sk150 @ sk335 ) )
| ( v1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19571:[bind(A,$thf( sk335 ))]]) ).
thf(1899,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(10707,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)],[1899]) ).
thf(10711,plain,
l1_group_1 @ sk608,
inference(cnf,[status(esa)],[10707]) ).
thf(14832,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk608 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10711,4719]) ).
thf(14833,plain,
l1_struct_0 @ sk608,
inference(pattern_uni,[status(thm)],[14832:[bind(A,$thf( sk608 ))]]) ).
thf(1412,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(8475,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)],[1412]) ).
thf(1004,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(6566,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)],[1004]) ).
thf(1093,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(6954,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)],[1093]) ).
thf(624,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(4877,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)],[624]) ).
thf(1487,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_1) ).
thf(8828,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(993,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(6527,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)],[993]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_enumset1) ).
thf(5582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(1801,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(10387,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)],[1801]) ).
thf(1935,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(10832,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)],[1935]) ).
thf(71,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(2380,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)],[71]) ).
thf(2381,plain,
! [A: $i] :
( ~ ( m1_subset_1 @ A @ sk15 )
| ~ ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ A ) ) ) ),
inference(cnf,[status(esa)],[2380]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(7322,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(847,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(5873,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)],[847]) ).
thf(5878,plain,
v7_group_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(824,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_2) ).
thf(5793,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ B @ C )
= B )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(1729,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(10039,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)],[1729]) ).
thf(1512,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ 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 ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattices) ).
thf(8988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ 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 ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ 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 ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ 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 ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(1982,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(11008,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)],[1982]) ).
thf(898,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(6142,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)],[898]) ).
thf(381,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(3681,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)],[381]) ).
thf(1011,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(6587,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)],[1011]) ).
thf(1115,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(7040,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(460,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(4034,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)],[460]) ).
thf(4037,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk118 @ B @ A ) ),
inference(cnf,[status(esa)],[4034]) ).
thf(1302,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(7886,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)],[1302]) ).
thf(107,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( A
= ( k6_finseq_1 @ B ) )
<=> ( ( k3_finseq_1 @ A )
= np__0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finseq_1) ).
thf(2512,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( A
= ( k6_finseq_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= np__0 ) )
& ( ( ( k3_finseq_1 @ A )
= np__0 )
=> ( A
= ( k6_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1925,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(10794,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)],[1925]) ).
thf(10795,plain,
v4_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(527,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(4376,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)],[527]) ).
thf(1210,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(7477,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)],[1210]) ).
thf(1778,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(10299,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)],[1778]) ).
thf(1754,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(10149,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)],[1754]) ).
thf(2117,plain,
v4_group_1 @ sk1,
inference(cnf,[status(esa)],[2113]) ).
thf(1309,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
<=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattices) ).
thf(7940,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1124,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(7083,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)],[1124]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relset_1) ).
thf(3317,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1822,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(10446,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)],[1822]) ).
thf(1330,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( m3_vectsp_8 @ 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 @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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',d8_vectsp_8) ).
thf(8044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( ( m3_vectsp_8 @ 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 @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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 @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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 ) ) ) ) )
=> ( m3_vectsp_8 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(7358,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1087,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(6918,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)],[1087]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_lattice3) ).
thf(7517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(1817,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(10431,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)],[1817]) ).
thf(29,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(2231,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)],[29]) ).
thf(15122,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ k5_numbers @ k1_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3020,2203]) ).
thf(15123,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ k1_numbers ),
inference(pattern_uni,[status(thm)],[15122:[bind(A,$thf( k5_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(15128,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ k1_numbers ),
inference(simp,[status(thm)],[15123]) ).
thf(15321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ k1_numbers )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15128,2180]) ).
thf(15322,plain,
! [A: $i] : ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ k1_numbers ) ),
inference(pattern_uni,[status(thm)],[15321:[bind(A,$thf( A )),bind(B,$thf( k5_numbers )),bind(C,$thf( A )),bind(D,$thf( k1_numbers ))]]) ).
thf(15515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ k1_numbers ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15322,2203]) ).
thf(15516,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) ),
inference(pattern_uni,[status(thm)],[15515:[bind(A,$thf( E )),bind(B,$thf( k5_numbers )),bind(C,$thf( k2_xboole_0 @ E @ k1_numbers )),bind(D,$thf( D ))]]) ).
thf(15522,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) ),
inference(simp,[status(thm)],[15516]) ).
thf(31401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ C @ ( k2_xboole_0 @ D @ E ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) )
!= ( r1_tarski @ ( k4_xboole_0 @ C @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[15522,2180]) ).
thf(31402,plain,
! [B: $i,A: $i] : ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ k1_numbers ) ) ),
inference(pattern_uni,[status(thm)],[31401:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( k5_numbers )),bind(D,$thf( A )),bind(E,$thf( k2_xboole_0 @ F @ k1_numbers ))]]) ).
thf(31454,plain,
! [B: $i,A: $i] : ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ k1_numbers ) ) ),
inference(simp,[status(thm)],[31402]) ).
thf(41737,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ B @ k1_xboole_0 ) )
| ( ( k2_xboole_0 @ k1_xboole_0 @ A )
!= ( k2_xboole_0 @ C @ k1_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[41649,31454]) ).
thf(41738,plain,
! [A: $i] : ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[41737:[bind(A,$thf( k1_numbers )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(41771,plain,
! [A: $i] : ( r1_tarski @ k5_numbers @ ( k2_xboole_0 @ A @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[41738]) ).
thf(43633,plain,
! [A: $i] : ( r1_tarski @ k5_numbers @ A ),
inference(rewrite,[status(thm)],[41771,5082]) ).
thf(36,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(2258,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)],[36]) ).
thf(2260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
| ( r1_xboole_0 @ A @ C ) ),
inference(cnf,[status(esa)],[2258]) ).
thf(43647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ B @ D )
| ( ( r1_tarski @ k5_numbers @ A )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[43633,2260]) ).
thf(43648,plain,
! [A: $i] : ( r1_xboole_0 @ k5_numbers @ A ),
inference(pattern_uni,[status(thm)],[43647:[bind(A,$thf( k4_xboole_0 @ E @ F )),bind(B,$thf( k5_numbers )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(43656,plain,
! [A: $i] : ( r1_xboole_0 @ k5_numbers @ A ),
inference(simp,[status(thm)],[43648]) ).
thf(1993,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(11043,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)],[1993]) ).
thf(1708,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(9924,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)],[1708]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(552,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(4515,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(206,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(2908,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(839,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).
thf(5842,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(975,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(6463,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)],[975]) ).
thf(146,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(2657,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(2659,plain,
v1_funct_1 @ sk27,
inference(cnf,[status(esa)],[2657]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [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(5242,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)],[707]) ).
thf(2056,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(11277,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)],[2056]) ).
thf(1858,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(10567,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)],[1858]) ).
thf(243,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(3040,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)],[243]) ).
thf(1955,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(10912,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)],[1955]) ).
thf(32,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_finseq_3) ).
thf(2242,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) )
& ( ( r1_tarski @ ( k2_relat_1 @ A ) @ B )
=> ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(2243,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ! [B: $i] :
( ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) )
& ! [B: $i] :
( ( r1_tarski @ ( k2_relat_1 @ A ) @ B )
=> ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[2242]) ).
thf(2245,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ A ) @ B )
| ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2243]) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) ),
inference(lifteq,[status(thm)],[2245]) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( ( k1_finseq_3 @ A @ B )
= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) ),
inference(simp,[status(thm)],[2247]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(8447,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(259,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
thf(3108,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= A ) )
=> ( B
= ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(7198,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_filter_1) ).
thf(4711,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1358,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(8169,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)],[1358]) ).
thf(44,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( k2_relat_1 @ A )
!= k1_xboole_0 )
=> ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finseq_3) ).
thf(2282,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( k2_relat_1 @ A )
!= k1_xboole_0 )
=> ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(791,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(5669,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)],[791]) ).
thf(1553,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(9191,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)],[1553]) ).
thf(2053,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(11266,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)],[2053]) ).
thf(965,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k5_int_1 @ A @ np__0 )
= np__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_int_1) ).
thf(6426,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k5_int_1 @ A @ np__0 )
= np__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(2114,plain,
v3_group_1 @ sk1,
inference(cnf,[status(esa)],[2113]) ).
thf(518,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(4326,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)],[518]) ).
thf(1148,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(7182,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1948,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(10886,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)],[1948]) ).
thf(1630,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(9572,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)],[1630]) ).
thf(706,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(5237,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)],[706]) ).
thf(1667,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(9758,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(9759,plain,
v3_lattices @ sk545,
inference(cnf,[status(esa)],[9758]) ).
thf(1681,axiom,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(9818,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1050,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(6756,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(6757,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[6756]) ).
thf(6758,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[6757]) ).
thf(10709,plain,
~ ( v3_struct_0 @ sk608 ),
inference(cnf,[status(esa)],[10707]) ).
thf(16412,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk608 ) ),
inference(paramod_ordered,[status(thm)],[6758,10709]) ).
thf(16413,plain,
( ~ ( v1_xboole_0 @ sk608 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16412:[bind(A,$thf( sk608 ))]]) ).
thf(25446,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk608 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16413]) ).
thf(25459,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk608 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[25446]) ).
thf(980,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(6480,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1043,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(6732,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)],[1043]) ).
thf(1893,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(10685,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)],[1893]) ).
thf(10688,plain,
~ ( v3_struct_0 @ sk607 ),
inference(cnf,[status(esa)],[10685]) ).
thf(16237,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk607 ) ),
inference(paramod_ordered,[status(thm)],[6758,10688]) ).
thf(16238,plain,
( ~ ( v1_xboole_0 @ sk607 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16237:[bind(A,$thf( sk607 ))]]) ).
thf(24556,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk607 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16238]) ).
thf(24569,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk607 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[24556]) ).
thf(911,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(6214,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)],[911]) ).
thf(319,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(3382,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)],[319]) ).
thf(1288,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(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 @ 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)],[1288]) ).
thf(756,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(5501,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)],[756]) ).
thf(1097,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(6971,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)],[1097]) ).
thf(1090,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(6939,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)],[1090]) ).
thf(1027,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(6665,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)],[1027]) ).
thf(1751,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(10138,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(1560,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(9218,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)],[1560]) ).
thf(1904,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(10726,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)],[1904]) ).
thf(1571,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(9278,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)],[1571]) ).
thf(236,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(3017,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)],[236]) ).
thf(1641,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(9644,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)],[1641]) ).
thf(1340,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(8101,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)],[1340]) ).
thf(1833,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(10484,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)],[1833]) ).
thf(1467,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_1) ).
thf(8765,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(456,axiom,
r1_tarski @ k5_numbers @ k4_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_numbers) ).
thf(4002,plain,
r1_tarski @ k5_numbers @ k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(19248,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) )
| ( ( r1_tarski @ k5_numbers @ k4_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4002,2218]) ).
thf(19249,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) ),
inference(pattern_uni,[status(thm)],[19248:[bind(A,$thf( k5_numbers )),bind(B,$thf( k4_numbers ))]]) ).
thf(19272,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) ),
inference(simp,[status(thm)],[19249]) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
| ( r1_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[2258]) ).
thf(35594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ C )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19272,2259]) ).
thf(35595,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ A ),
inference(pattern_uni,[status(thm)],[35594:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ E @ k4_numbers )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(35664,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ A ),
inference(simp,[status(thm)],[35595]) ).
thf(36599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ A )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35664,2180]) ).
thf(36600,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k4_numbers @ A ) ),
inference(pattern_uni,[status(thm)],[36599:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k4_numbers )),bind(D,$thf( A ))]]) ).
thf(2008,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(11112,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)],[2008]) ).
thf(1379,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(8335,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)],[1379]) ).
thf(1818,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(10433,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)],[1818]) ).
thf(246,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(3048,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(3049,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(cnf,[status(esa)],[3048]) ).
thf(398,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(3745,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)],[398]) ).
thf(1760,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(10181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(1398,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(8430,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)],[1398]) ).
thf(1236,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(7573,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)],[1236]) ).
thf(1988,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(11029,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)],[1988]) ).
thf(305,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(3332,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)],[305]) ).
thf(917,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(6246,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)],[917]) ).
thf(313,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(3367,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)],[313]) ).
thf(375,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(3648,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)],[375]) ).
thf(468,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(4097,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)],[468]) ).
thf(1804,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(10395,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)],[1804]) ).
thf(1742,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_0) ).
thf(10093,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) )
& ( ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) )
=> ( D
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(1505,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(8915,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)],[1505]) ).
thf(896,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(6127,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)],[896]) ).
thf(1132,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(7115,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)],[1132]) ).
thf(4517,plain,
v1_xboole_0 @ sk167,
inference(cnf,[status(esa)],[4515]) ).
thf(16687,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk167 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4517,6758]) ).
thf(16688,plain,
sk167 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[16687:[bind(A,$thf( sk167 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_1) ).
thf(2181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2181]) ).
thf(1127,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 ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(7096,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 ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1385,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(8353,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)],[1385]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(2315,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(2316,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_relat_1 @ B )
| ( m1_filter_1 @ ( sk10 @ B @ A ) @ A @ B ) ),
inference(cnf,[status(esa)],[2315]) ).
thf(1443,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(8667,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(1627,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(9565,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)],[1627]) ).
thf(92,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(2448,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)],[92]) ).
thf(2118,plain,
~ ( v3_struct_0 @ sk1 ),
inference(cnf,[status(esa)],[2113]) ).
thf(16067,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,2118]) ).
thf(16068,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16067:[bind(A,$thf( sk1 ))]]) ).
thf(18437,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,16068]) ).
thf(18438,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[18437:[]]) ).
thf(890,axiom,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_1) ).
thf(6089,plain,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(307,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(3338,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)],[307]) ).
thf(2001,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(11075,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)],[2001]) ).
thf(709,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_0) ).
thf(5257,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(87,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k2_relat_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_finseq_3) ).
thf(2434,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k2_relat_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(962,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(6416,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)],[962]) ).
thf(1536,axiom,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(9109,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(9110,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9109]) ).
thf(1828,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(10469,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(10470,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[10469]) ).
thf(10471,plain,
! [A: $i] :
( ( k6_relat_1 @ A )
= ( k6_partfun1 @ A ) ),
inference(lifteq,[status(thm)],[10470]) ).
thf(14502,plain,
( ( k6_partfun1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[9110,10471]) ).
thf(5502,plain,
( ! [A: $i] : ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ! [A: $i] : ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
inference(miniscope,[status(thm)],[5501]) ).
thf(5504,plain,
! [A: $i] : ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(cnf,[status(esa)],[5502]) ).
thf(40562,plain,
! [A: $i] :
( ( v1_partfun1 @ k1_xboole_0 @ A @ A )
| ( ( k6_partfun1 @ k1_xboole_0 )
!= ( k6_partfun1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14502,5504]) ).
thf(40563,plain,
v1_partfun1 @ k1_xboole_0 @ k1_xboole_0 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[40562:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1381,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(8342,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)],[1381]) ).
thf(365,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(3616,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)],[365]) ).
thf(1609,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(9494,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)],[1609]) ).
thf(1840,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(10511,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)],[1840]) ).
thf(1142,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_0) ).
thf(7147,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
<=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_1) ).
thf(2167,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
| ( r5_binop_1 @ A @ C @ D ) ),
inference(cnf,[status(esa)],[2167]) ).
thf(793,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(5674,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)],[793]) ).
thf(1368,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(8210,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)],[1368]) ).
thf(1200,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(7422,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)],[1200]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_4) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1103,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(6996,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)],[1103]) ).
thf(10657,plain,
v3_realset2 @ sk605,
inference(cnf,[status(esa)],[10654]) ).
thf(19652,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_realset2 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[4339,10657]) ).
thf(19653,plain,
( ( v1_relat_1 @ ( sk150 @ sk605 ) )
| ( v3_realset2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19652:[bind(A,$thf( sk605 ))]]) ).
thf(1051,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(6759,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)],[1051]) ).
thf(1205,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice3) ).
thf(7452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(299,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(3313,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)],[299]) ).
thf(1490,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(8838,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)],[1490]) ).
thf(948,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(6370,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)],[948]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(5636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( k4_funct_2 @ A @ B @ C )
= ( k5_relat_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_4) ).
thf(2844,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1059,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(6804,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)],[1059]) ).
thf(1975,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(10991,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)],[1975]) ).
thf(7,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_1) ).
thf(2138,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2146,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
| ~ ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( l3_lattices @ ( k8_filter_1 @ A @ B ) )
| ( v16_lattices @ A ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(110,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(2530,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(2535,plain,
~ ( v1_xboole_0 @ sk19 ),
inference(cnf,[status(esa)],[2530]) ).
thf(11541,plain,
( ( v1_xboole_0 @ sk19 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,2535]) ).
thf(11549,plain,
sk19 != k1_xboole_0,
inference(simp,[status(thm)],[11541]) ).
thf(648,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(4980,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)],[648]) ).
thf(390,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(3717,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)],[390]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_partfun1) ).
thf(2359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(2360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v2_funct_1 @ C )
| ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ),
inference(cnf,[status(esa)],[2359]) ).
thf(1790,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(10341,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)],[1790]) ).
thf(15790,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,2114]) ).
thf(15791,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( v3_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15790:[bind(A,$thf( sk1 ))]]) ).
thf(1620,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 ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) )
& ( r2_hidden @ D @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsubgr) ).
thf(9540,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 ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) )
& ( r2_hidden @ D @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) )
=> ( r2_hidden @ ( k1_group_1 @ A @ C @ D ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1605,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(9481,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)],[1605]) ).
thf(745,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(5412,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)],[745]) ).
thf(15741,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk110 ) ),
inference(paramod_ordered,[status(thm)],[6758,3969]) ).
thf(15742,plain,
( ~ ( v1_xboole_0 @ sk110 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15741:[bind(A,$thf( sk110 ))]]) ).
thf(18417,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk110 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,15742]) ).
thf(18425,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk110 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[18417]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(4792,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(2073,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(11335,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)],[2073]) ).
thf(1120,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(7064,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)],[1120]) ).
thf(1268,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(7729,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)],[1268]) ).
thf(187,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(2817,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)],[187]) ).
thf(2818,plain,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2817]) ).
thf(2819,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ A ) ),
inference(lifteq,[status(thm)],[2818]) ).
thf(29365,plain,
! [A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ A ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6559,2819]) ).
thf(29366,plain,
( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[29365:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12,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(2171,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)],[12]) ).
thf(2172,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[2171]) ).
thf(2173,plain,
! [B: $i,A: $i] :
( ~ ( v1_finset_1 @ A )
| ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2172]) ).
thf(1172,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(7311,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)],[1172]) ).
thf(642,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_0) ).
thf(4941,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1243,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(7605,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)],[1243]) ).
thf(1602,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_1) ).
thf(9443,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(2047,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(11228,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)],[2047]) ).
thf(306,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(3335,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)],[306]) ).
thf(1504,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(8911,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)],[1504]) ).
thf(1597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattices) ).
thf(9424,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(2025,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(11171,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)],[2025]) ).
thf(286,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).
thf(3236,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(46,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(2287,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(2288,plain,
! [B: $i,A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(cnf,[status(esa)],[2287]) ).
thf(29400,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ ( k1_orders_1 @ A ) @ C )
| ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2819,2288]) ).
thf(29401,plain,
! [A: $i] : ( r1_xboole_0 @ ( k1_orders_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[29400:[bind(A,$thf( D )),bind(B,$thf( k1_zfmisc_1 @ D )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(29532,plain,
! [A: $i] : ( r1_xboole_0 @ ( k1_orders_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[29401]) ).
thf(703,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( v5_lattice3 @ A )
<=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice3) ).
thf(5227,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v5_lattice3 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) )
=> ( v5_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(976,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(6466,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)],[976]) ).
thf(811,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).
thf(5740,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(349,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(3545,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)],[349]) ).
thf(102,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
& ( B = np__0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finseq_3) ).
thf(2491,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
& ( B = np__0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(742,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(5393,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)],[742]) ).
thf(1338,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(8086,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)],[1338]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( m2_relset_1 @ B @ k5_numbers @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_finseq_1) ).
thf(2763,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( m2_relset_1 @ B @ k5_numbers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(435,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
thf(3915,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) )
& ( ( k5_relat_1 @ B @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(226,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(2985,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)],[226]) ).
thf(1953,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(10908,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)],[1953]) ).
thf(2087,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(11382,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)],[2087]) ).
thf(674,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(5123,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)],[674]) ).
thf(1830,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(10474,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)],[1830]) ).
thf(1076,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(6872,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)],[1076]) ).
thf(503,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(4266,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)],[503]) ).
thf(343,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(3513,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)],[343]) ).
thf(2055,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(11273,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)],[2055]) ).
thf(1517,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(9027,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)],[1517]) ).
thf(1590,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(9379,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)],[1590]) ).
thf(1532,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(9096,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)],[1532]) ).
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 ) )
=> ( ( 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(6009,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)],[870]) ).
thf(1724,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_filter_0) ).
thf(9994,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(677,axiom,
r1_tarski @ k4_numbers @ k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_numbers) ).
thf(5132,plain,
r1_tarski @ k4_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(19232,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) )
| ( ( r1_tarski @ k4_numbers @ k1_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5132,2218]) ).
thf(19233,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k4_numbers ) ),
inference(pattern_uni,[status(thm)],[19232:[bind(A,$thf( k4_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(19265,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k4_numbers ) ),
inference(simp,[status(thm)],[19233]) ).
thf(31701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ C )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k4_numbers ) )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19265,2259]) ).
thf(31702,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ A ),
inference(pattern_uni,[status(thm)],[31701:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ E @ k1_numbers )),bind(C,$thf( E )),bind(D,$thf( k4_numbers ))]]) ).
thf(31774,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ A ),
inference(simp,[status(thm)],[31702]) ).
thf(394,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
thf(3730,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
& ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
= ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1411,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(8472,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)],[1411]) ).
thf(1454,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(8705,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)],[1454]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice4) ).
thf(3898,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1086,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(6916,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(6917,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[6916]) ).
thf(13286,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6559,6917]) ).
thf(13287,plain,
m1_subset_1 @ k1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[13286:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1897,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(10698,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)],[1897]) ).
thf(1298,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(7856,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)],[1298]) ).
thf(1180,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(7343,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)],[1180]) ).
thf(5874,plain,
~ ( v3_struct_0 @ sk259 ),
inference(cnf,[status(esa)],[5873]) ).
thf(893,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(6102,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)],[893]) ).
thf(2075,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(11340,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)],[2075]) ).
thf(9760,plain,
~ ( v3_struct_0 @ sk545 ),
inference(cnf,[status(esa)],[9758]) ).
thf(16801,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk545 ) ),
inference(paramod_ordered,[status(thm)],[6758,9760]) ).
thf(16802,plain,
( ~ ( v1_xboole_0 @ sk545 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16801:[bind(A,$thf( sk545 ))]]) ).
thf(28830,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk545 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16802]) ).
thf(28843,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk545 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[28830]) ).
thf(1927,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(10807,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)],[1927]) ).
thf(1644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_filter_0) ).
thf(9657,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(522,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(4352,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)],[522]) ).
thf(4353,plain,
v1_xboole_0 @ sk152,
inference(cnf,[status(esa)],[4352]) ).
thf(15762,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,2117]) ).
thf(15763,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15762:[bind(A,$thf( sk1 ))]]) ).
thf(17407,plain,
( ( v4_group_1 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk152 )
!= ( v1_xboole_0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,15763]) ).
thf(17417,plain,
( ( v4_group_1 @ k1_xboole_0 )
| ( sk152 != sk1 ) ),
inference(simp,[status(thm)],[17407]) ).
thf(15923,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk152 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6758]) ).
thf(15924,plain,
sk152 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[15923:[bind(A,$thf( sk152 ))]]) ).
thf(19118,plain,
( ( v4_group_1 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[17417,15924]) ).
thf(19123,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,19118]) ).
thf(19124,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19123:[]]) ).
thf(32448,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ B )
| ( v4_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,19124]) ).
thf(32449,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[32448:[bind(A,$thf( sk1 ))]]) ).
thf(32456,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A ) ),
inference(simp,[status(thm)],[32449]) ).
thf(517,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(4322,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)],[517]) ).
thf(643,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(4948,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)],[643]) ).
thf(2531,plain,
v1_finseq_1 @ sk19,
inference(cnf,[status(esa)],[2530]) ).
thf(1241,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_int_1) ).
thf(7592,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ k4_numbers )
=> ( v1_int_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(544,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( C
= ( k3_lattice4 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4467,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( ( C
= ( k3_lattice4 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(453,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(3992,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(3993,plain,
~ ? [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ),
inference(miniscope,[status(thm)],[3992]) ).
thf(3994,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(cnf,[status(esa)],[3993]) ).
thf(3995,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3994]) ).
thf(16077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k2_xboole_0 @ ( k1_tarski @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6758,3995]) ).
thf(16078,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[16077:[bind(A,$thf( k2_xboole_0 @ ( k1_tarski @ F ) @ E )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(17337,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(simp,[status(thm)],[16078]) ).
thf(25415,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,17337]) ).
thf(25427,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25415]) ).
thf(2050,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(11250,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)],[2050]) ).
thf(1838,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(10501,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)],[1838]) ).
thf(19433,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk19 ) ),
inference(paramod_ordered,[status(thm)],[4339,11549]) ).
thf(19434,plain,
v1_relat_1 @ ( sk150 @ sk19 ),
inference(pattern_uni,[status(thm)],[19433:[bind(A,$thf( sk19 ))]]) ).
thf(825,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(5797,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)],[825]) ).
thf(765,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice4) ).
thf(5533,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1539,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(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] :
( ( ( 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)],[1539]) ).
thf(274,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(3195,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)],[274]) ).
thf(40,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(2269,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)],[40]) ).
thf(1588,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(9365,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(9366,plain,
v3_lattices @ sk510,
inference(cnf,[status(esa)],[9365]) ).
thf(20112,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_lattices @ k1_xboole_0 )
| ( A != sk510 ) ),
inference(paramod_ordered,[status(thm)],[4339,9366]) ).
thf(20113,plain,
( ( v1_relat_1 @ ( sk150 @ sk510 ) )
| ( v3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20112:[bind(A,$thf( sk510 ))]]) ).
thf(354,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(3574,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)],[354]) ).
thf(412,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(3821,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)],[412]) ).
thf(1441,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(8654,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)],[1441]) ).
thf(1540,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(9121,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(9122,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[9121]) ).
thf(9123,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9122]) ).
thf(430,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(3891,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)],[430]) ).
thf(581,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(4637,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)],[581]) ).
thf(145,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(2654,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)],[145]) ).
thf(290,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(3248,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)],[290]) ).
thf(1730,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(10042,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)],[1730]) ).
thf(1578,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(9300,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)],[1578]) ).
thf(1951,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(10903,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)],[1951]) ).
thf(9761,plain,
l3_lattices @ sk545,
inference(cnf,[status(esa)],[9758]) ).
thf(800,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(5692,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(5693,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( l1_lattices @ A ) ),
inference(cnf,[status(esa)],[5692]) ).
thf(15093,plain,
! [A: $i] :
( ( l1_lattices @ A )
| ( ( l3_lattices @ sk545 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9761,5693]) ).
thf(15094,plain,
l1_lattices @ sk545,
inference(pattern_uni,[status(thm)],[15093:[bind(A,$thf( sk545 ))]]) ).
thf(469,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(4102,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(4103,plain,
! [A: $i] :
( ~ ( l1_lattices @ A )
| ( l1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[4102]) ).
thf(15134,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_lattices @ sk545 )
!= ( l1_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15094,4103]) ).
thf(15135,plain,
l1_struct_0 @ sk545,
inference(pattern_uni,[status(thm)],[15134:[bind(A,$thf( sk545 ))]]) ).
thf(280,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_filter_0) ).
thf(3221,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1965,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(10955,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)],[1965]) ).
thf(1747,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(10121,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)],[1747]) ).
thf(130,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(2603,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)],[130]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_partfun1) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(784,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(5639,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(5640,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(miniscope,[status(thm)],[5639]) ).
thf(5641,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(cnf,[status(esa)],[5640]) ).
thf(13267,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,5641]) ).
thf(13280,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13267]) ).
thf(1820,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(10437,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)],[1820]) ).
thf(1080,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(6892,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)],[1080]) ).
thf(773,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(5585,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(328,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(3421,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)],[328]) ).
thf(3423,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3421]) ).
thf(3425,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3423]) ).
thf(999,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(6552,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)],[999]) ).
thf(1533,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(9099,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)],[1533]) ).
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 @ ( 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(7262,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)],[1164]) ).
thf(564,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
<=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_1) ).
thf(4563,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) )
& ( ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) )
=> ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1416,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(8494,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)],[1416]) ).
thf(1864,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(10587,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)],[1864]) ).
thf(5875,plain,
v6_vectsp_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(19625,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v6_vectsp_1 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[4339,5875]) ).
thf(19626,plain,
( ( v1_relat_1 @ ( sk150 @ sk259 ) )
| ( v6_vectsp_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19625:[bind(A,$thf( sk259 ))]]) ).
thf(19762,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,16068]) ).
thf(19763,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[19762:[]]) ).
thf(546,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(4488,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ k1_xboole_0 ) @ ( k2_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(4489,plain,
! [A: $i] : ( r2_hidden @ ( k1_card_1 @ k1_xboole_0 ) @ ( k2_card_1 @ A ) ),
inference(cnf,[status(esa)],[4488]) ).
thf(13524,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k2_card_1 @ A ) ),
inference(rewrite,[status(thm)],[4489,8072]) ).
thf(13525,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ k1_xboole_0 @ ( k2_card_1 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[13524,9072]) ).
thf(13526,plain,
! [B: $i,A: $i] :
( ( k1_xboole_0 != B )
| ( ( k2_card_1 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[13525]) ).
thf(13527,plain,
! [A: $i] :
( ( k2_card_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13526]) ).
thf(16215,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k2_card_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6758,13527]) ).
thf(16216,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k2_card_1 @ A ) ),
inference(pattern_uni,[status(thm)],[16215:[bind(A,$thf( k2_card_1 @ C )),bind(B,$thf( C ))]]) ).
thf(17366,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k2_card_1 @ A ) ),
inference(simp,[status(thm)],[16216]) ).
thf(138,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(2631,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(2636,plain,
v1_xboole_0 @ sk24,
inference(cnf,[status(esa)],[2631]) ).
thf(15977,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,14847]) ).
thf(15978,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15977:[bind(A,$thf( sk1 ))]]) ).
thf(17856,plain,
( ( l1_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk24 )
!= ( v1_xboole_0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2636,15978]) ).
thf(17858,plain,
( ( l1_struct_0 @ k1_xboole_0 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[17856]) ).
thf(16952,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk24 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2636,6758]) ).
thf(16953,plain,
sk24 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[16952:[bind(A,$thf( sk24 ))]]) ).
thf(21095,plain,
( ( l1_struct_0 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[17858,16953]) ).
thf(21100,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,21095]) ).
thf(21101,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21100:[]]) ).
thf(35616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19272,2180]) ).
thf(35617,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k4_numbers @ ( k4_xboole_0 @ A @ k5_numbers ) ) ),
inference(pattern_uni,[status(thm)],[35616:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k4_numbers )),bind(D,$thf( k4_xboole_0 @ E @ k5_numbers ))]]) ).
thf(35671,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k4_numbers @ ( k4_xboole_0 @ A @ k5_numbers ) ) ),
inference(simp,[status(thm)],[35617]) ).
thf(1339,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(8089,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)],[1339]) ).
thf(477,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(4151,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)],[477]) ).
thf(1370,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(8225,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)],[1370]) ).
thf(998,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(6547,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)],[998]) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( m1_orders_1 @ B @ A )
| ( v1_funct_1 @ B ) ),
inference(cnf,[status(esa)],[2336]) ).
thf(1600,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(9432,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)],[1600]) ).
thf(245,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(3046,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)],[245]) ).
thf(1559,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(9216,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)],[1559]) ).
thf(384,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finseq_1) ).
thf(3689,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ~ ( r1_xboole_0 @ A @ B )
| ( ( k4_xboole_0 @ A @ B )
= A ) ),
inference(cnf,[status(esa)],[2220]) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
= A )
| ~ ( r1_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[2222]) ).
thf(43666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ B @ C )
= B )
| ( ( r1_xboole_0 @ k5_numbers @ A )
!= ( r1_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43656,2225]) ).
thf(43667,plain,
! [A: $i] :
( ( k4_xboole_0 @ k5_numbers @ A )
= k5_numbers ),
inference(pattern_uni,[status(thm)],[43666:[bind(A,$thf( A )),bind(B,$thf( k5_numbers )),bind(C,$thf( A ))]]) ).
thf(1040,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(6723,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)],[1040]) ).
thf(606,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4761,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1983,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(11010,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)],[1983]) ).
thf(251,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v5_lattice3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattice3) ).
thf(3061,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v5_lattice3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(964,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(6423,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)],[964]) ).
thf(1048,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(6749,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)],[1048]) ).
thf(659,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(5064,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)],[659]) ).
thf(586,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_filter_0) ).
thf(4654,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) )
<=> ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_1) ).
thf(2444,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) )
=> ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1766,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(10221,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)],[1766]) ).
thf(1310,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(7945,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)],[1310]) ).
thf(1508,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_0) ).
thf(8951,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(377,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(3653,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)],[377]) ).
thf(919,axiom,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
thf(6252,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(6253,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[6252]) ).
thf(6254,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[6253]) ).
thf(24505,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_partfun1 @ A ) )
= ( k6_partfun1 @ A ) ),
inference(rewrite,[status(thm)],[6254,10471]) ).
thf(24510,plain,
! [A: $i] :
( ( ( k2_funct_1 @ k1_xboole_0 )
= ( k6_partfun1 @ A ) )
| ( ( k6_partfun1 @ k1_xboole_0 )
!= ( k6_partfun1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14502,24505]) ).
thf(24511,plain,
( ( k2_funct_1 @ k1_xboole_0 )
= ( k6_partfun1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[24510:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(24526,plain,
( ( k2_funct_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[24511,14502]) ).
thf(1475,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(8785,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)],[1475]) ).
thf(41,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [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 )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k1_nat_1 @ C @ np__1 ) )
& ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
& ( r1_xreal_0 @ B @ D )
& ( r1_xreal_0 @ D @ C ) )
=> ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ ( k1_nat_1 @ D @ np__1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_finseq_3) ).
thf(2272,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [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 )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k1_nat_1 @ C @ np__1 ) )
& ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
& ( r1_xreal_0 @ B @ D )
& ( r1_xreal_0 @ D @ C ) )
=> ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ ( k1_nat_1 @ D @ np__1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
| ( ( k3_finseq_1 @ A )
!= ( k1_nat_1 @ C @ np__1 ) )
| ~ ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
| ~ ( r1_xreal_0 @ B @ D )
| ~ ( r1_xreal_0 @ D @ C )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ ( k1_nat_1 @ D @ np__1 ) ) ) ),
inference(cnf,[status(esa)],[2272]) ).
thf(2274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ A )
!= ( k1_nat_1 @ C @ np__1 ) )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ ( k1_nat_1 @ D @ np__1 ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
| ~ ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
| ~ ( r1_xreal_0 @ B @ D )
| ~ ( r1_xreal_0 @ D @ C ) ),
inference(lifteq,[status(thm)],[2273]) ).
thf(2104,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(11448,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)],[2104]) ).
thf(2108,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(11458,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)],[2108]) ).
thf(1586,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(9360,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)],[1586]) ).
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 ) )
=> ! [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(8214,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)],[1369]) ).
thf(1096,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(6968,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( k2_enumset1 @ A @ B @ C @ D ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ E )
<=> ~ ( ( F != A )
& ( F != B )
& ( F != C )
& ( F != D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_enumset1) ).
thf(3125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( k2_enumset1 @ A @ B @ C @ D ) )
=> ! [F: $i] :
( ( ( r2_hidden @ F @ E )
=> ~ ( ( F != A )
& ( F != B )
& ( F != C )
& ( F != D ) ) )
& ( ~ ( ( F != A )
& ( F != B )
& ( F != C )
& ( F != D ) )
=> ( r2_hidden @ F @ E ) ) ) )
& ( ! [F: $i] :
( ( ( r2_hidden @ F @ E )
=> ~ ( ( F != A )
& ( F != B )
& ( F != C )
& ( F != D ) ) )
& ( ~ ( ( F != A )
& ( F != B )
& ( F != C )
& ( F != D ) )
=> ( r2_hidden @ F @ E ) ) )
=> ( E
= ( k2_enumset1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(2037,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(11200,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)],[2037]) ).
thf(1785,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(10328,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(10329,plain,
l3_lattices @ sk593,
inference(cnf,[status(esa)],[10328]) ).
thf(5694,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( l2_lattices @ A ) ),
inference(cnf,[status(esa)],[5692]) ).
thf(15145,plain,
! [A: $i] :
( ( l2_lattices @ A )
| ( ( l3_lattices @ sk593 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10329,5694]) ).
thf(15146,plain,
l2_lattices @ sk593,
inference(pattern_uni,[status(thm)],[15145:[bind(A,$thf( sk593 ))]]) ).
thf(17,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(2185,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)],[17]) ).
thf(1705,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(9909,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)],[1705]) ).
thf(1725,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(10001,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)],[1725]) ).
thf(10002,plain,
( ! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(miniscope,[status(thm)],[10001]) ).
thf(10007,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(cnf,[status(esa)],[10002]) ).
thf(10009,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(lifteq,[status(thm)],[10007]) ).
thf(10010,plain,
! [A: $i] : ( r2_hidden @ A @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[10009]) ).
thf(417,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(3843,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(3844,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[3843]) ).
thf(3845,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[3844]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) )
<=> ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_1) ).
thf(2562,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) )
=> ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1868,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(10606,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)],[1868]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_enumset1) ).
thf(3089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(101,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(2488,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)],[101]) ).
thf(1026,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(6662,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)],[1026]) ).
thf(869,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(6006,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)],[869]) ).
thf(804,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(5712,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)],[804]) ).
thf(717,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice4) ).
thf(5289,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(407,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(3803,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)],[407]) ).
thf(4,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(2123,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2126,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v11_lattices @ A ) ),
inference(cnf,[status(esa)],[2123]) ).
thf(1372,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(8242,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(536,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(4428,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)],[536]) ).
thf(909,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(6208,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)],[909]) ).
thf(244,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice4) ).
thf(3043,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(420,axiom,
~ ( v1_xboole_0 @ k1_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).
thf(3854,plain,
~ ( v1_xboole_0 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(3855,plain,
~ ( v1_xboole_0 @ k1_numbers ),
inference(polarity_switch,[status(thm)],[3854]) ).
thf(1024,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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) ) )
=> ( ( D
= ( k3_latsubgr @ A @ B @ C ) )
<=> ! [E: $i] :
( ( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( F
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k5_group_4 @ B @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_latsubgr) ).
thf(6643,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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) @ ( u1_struct_0 @ ( k11_group_4 @ B ) ) ) )
=> ( ( ( D
= ( k3_latsubgr @ A @ B @ C ) )
=> ! [E: $i] :
( ( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( F
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k5_group_4 @ B @ F ) ) ) ) ) )
& ( ! [E: $i] :
( ( ( v1_group_1 @ E )
& ( m1_group_2 @ E @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( F
= ( k2_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( u1_struct_0 @ E ) ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k5_group_4 @ B @ F ) ) ) ) )
=> ( D
= ( k3_latsubgr @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(389,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(3713,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)],[389]) ).
thf(1462,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattices) ).
thf(8753,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(63,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(2356,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)],[63]) ).
thf(1253,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(7665,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)],[1253]) ).
thf(713,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_relat_1) ).
thf(5279,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(10655,plain,
l1_group_1 @ sk605,
inference(cnf,[status(esa)],[10654]) ).
thf(1108,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(7011,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)],[1108]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) )
<=> ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_1) ).
thf(2703,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) )
=> ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(158,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r2_hidden @ B @ ( k2_relat_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ ( k1_tarski @ B ) ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ np__1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_finseq_3) ).
thf(2691,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r2_hidden @ B @ ( k2_relat_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ ( k1_tarski @ B ) ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ np__1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(472,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(4119,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)],[472]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_enumset1) ).
thf(4358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(338,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(3470,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)],[338]) ).
thf(1520,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(9039,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)],[1520]) ).
thf(646,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(4967,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)],[646]) ).
thf(1376,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(8257,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)],[1376]) ).
thf(704,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(5231,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)],[704]) ).
thf(1469,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(8770,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(2106,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(11453,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)],[2106]) ).
thf(416,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(3840,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)],[416]) ).
thf(733,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k15_lattice3 @ A @ B ) )
<=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
thf(5355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k15_lattice3 @ A @ B ) )
=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( C
= ( k15_lattice3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(320,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(3385,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)],[320]) ).
thf(1433,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(8590,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)],[1433]) ).
thf(1676,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m3_vectsp_8 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_vectsp_8) ).
thf(9800,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m3_vectsp_8 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(1264,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(7711,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)],[1264]) ).
thf(2110,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(11463,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)],[2110]) ).
thf(610,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(4788,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)],[610]) ).
thf(10687,plain,
v4_group_1 @ sk607,
inference(cnf,[status(esa)],[10685]) ).
thf(2169,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
| ( r5_binop_1 @ B @ E @ F ) ),
inference(cnf,[status(esa)],[2167]) ).
thf(1942,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(10850,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)],[1942]) ).
thf(17842,plain,
( ( v3_group_1 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk24 )
!= ( v1_xboole_0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2636,15791]) ).
thf(17845,plain,
( ( v3_group_1 @ k1_xboole_0 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[17842]) ).
thf(20924,plain,
( ( v3_group_1 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[17845,16953]) ).
thf(20929,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,20924]) ).
thf(20930,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20929:[]]) ).
thf(38785,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( v3_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,20930]) ).
thf(38786,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[38785:[bind(A,$thf( sk1 ))]]) ).
thf(38795,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A ) ),
inference(simp,[status(thm)],[38786]) ).
thf(697,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(5199,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)],[697]) ).
thf(1155,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(7209,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)],[1155]) ).
thf(827,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(5802,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)],[827]) ).
thf(1949,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(10891,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)],[1949]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r4_lattice3 @ B @ C @ A )
<=> ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
thf(5193,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r4_lattice3 @ B @ C @ A )
=> ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) )
& ( ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) )
=> ( r4_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(16518,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,2116]) ).
thf(16519,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16518:[bind(A,$thf( sk1 ))]]) ).
thf(18444,plain,
( ( l1_group_1 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16519]) ).
thf(18449,plain,
( ( l1_group_1 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[18444]) ).
thf(21512,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,18449]) ).
thf(21513,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21512:[]]) ).
thf(39938,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( l1_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,21513]) ).
thf(39939,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[39938:[bind(A,$thf( sk1 ))]]) ).
thf(39948,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A ) ),
inference(simp,[status(thm)],[39939]) ).
thf(930,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_0) ).
thf(6310,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(175,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) )
<=> ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_1) ).
thf(2767,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) )
=> ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1736,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(10074,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)],[1736]) ).
thf(1013,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(6599,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)],[1013]) ).
thf(68,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_orders_1) ).
thf(2373,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(2085,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(11378,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)],[2085]) ).
thf(860,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( C
= ( k2_latsubgr @ A @ B ) )
<=> ( ( u1_struct_0 @ C )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ ( k2_funct_2 @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsubgr) ).
thf(5925,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ! [C: $i] :
( ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) )
=> ( ( ( C
= ( k2_latsubgr @ A @ B ) )
=> ( ( u1_struct_0 @ C )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ ( k2_funct_2 @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_latsubgr @ A ) @ B ) ) ) )
& ( ( ( u1_struct_0 @ C )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ ( k2_funct_2 @ ( k1_group_3 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_latsubgr @ A ) @ B ) ) )
=> ( C
= ( k2_latsubgr @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(946,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(6365,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)],[946]) ).
thf(1089,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattices) ).
thf(6936,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1390,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(8367,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)],[1390]) ).
thf(19926,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk593 ) ),
inference(paramod_ordered,[status(thm)],[4339,10329]) ).
thf(19927,plain,
( ( v1_relat_1 @ ( sk150 @ sk593 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19926:[bind(A,$thf( sk593 ))]]) ).
thf(1554,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(9199,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)],[1554]) ).
thf(1157,axiom,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(7214,plain,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(7215,plain,
! [A: $i] : ( m2_finseq_1 @ ( sk348 @ A ) @ A ),
inference(cnf,[status(esa)],[7214]) ).
thf(1232,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(7560,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)],[1232]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_partfun1) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(813,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(5746,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)],[813]) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v10_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ( v10_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(simp,[status(thm)],[2149]) ).
thf(579,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(4632,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1066,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(6828,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)],[1066]) ).
thf(2299,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ~ ( r1_lattices @ A @ B @ ( sk9 @ B @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(2301,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ~ ( r1_lattices @ A @ B @ ( sk9 @ B @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[2299]) ).
thf(269,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(3180,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)],[269]) ).
thf(532,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(4390,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)],[532]) ).
thf(3009,plain,
v1_xboole_0 @ sk48,
inference(cnf,[status(esa)],[3008]) ).
thf(16639,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk48 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3009,6758]) ).
thf(16640,plain,
sk48 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[16639:[bind(A,$thf( sk48 ))]]) ).
thf(361,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(3602,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)],[361]) ).
thf(1246,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(7633,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)],[1246]) ).
thf(1460,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(8738,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)],[1460]) ).
thf(875,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(6025,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)],[875]) ).
thf(284,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(3231,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)],[284]) ).
thf(1892,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(10682,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)],[1892]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_enumset1) ).
thf(5077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(551,axiom,
k5_numbers != k4_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_numbers) ).
thf(4512,plain,
k5_numbers != k4_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(4513,plain,
k5_numbers != k4_numbers,
inference(polarity_switch,[status(thm)],[4512]) ).
thf(4514,plain,
k4_numbers != k5_numbers,
inference(lifteq,[status(thm)],[4513]) ).
thf(28,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2229,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2230,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[2229]) ).
thf(29640,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ A )
| ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29366,2230]) ).
thf(29641,plain,
r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[29640:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(425,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(3866,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( A
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(983,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(6487,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(2533,plain,
v1_relat_1 @ sk19,
inference(cnf,[status(esa)],[2530]) ).
thf(1356,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_filter_1) ).
thf(8161,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1218,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(7509,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)],[1218]) ).
thf(17854,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ sk1 )
| ( l1_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,15978]) ).
thf(17855,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ sk1 )
| ( l1_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[17854:[]]) ).
thf(590,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(4669,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)],[590]) ).
thf(1670,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(9768,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(1269,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice3) ).
thf(7733,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(192,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ ( k4_card_1 @ ( k3_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_finseq_3) ).
thf(2829,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ ( k4_card_1 @ ( k3_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(823,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(5790,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(5792,plain,
v1_relat_1 @ sk253,
inference(cnf,[status(esa)],[5790]) ).
thf(1944,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(10871,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)],[1944]) ).
thf(264,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(3163,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)],[264]) ).
thf(9367,plain,
l3_lattices @ sk510,
inference(cnf,[status(esa)],[9365]) ).
thf(15149,plain,
! [A: $i] :
( ( l2_lattices @ A )
| ( ( l3_lattices @ sk510 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9367,5694]) ).
thf(15150,plain,
l2_lattices @ sk510,
inference(pattern_uni,[status(thm)],[15149:[bind(A,$thf( sk510 ))]]) ).
thf(685,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(5156,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)],[685]) ).
thf(837,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(5834,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)],[837]) ).
thf(95,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(2456,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)],[95]) ).
thf(1593,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_lattice3) ).
thf(9401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_partfun1) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
| ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ),
inference(cnf,[status(esa)],[2177]) ).
thf(1342,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(8109,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)],[1342]) ).
thf(2022,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(11163,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)],[2022]) ).
thf(1752,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(10139,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)],[1752]) ).
thf(10140,plain,
( ! [A: $i] :
( ? [B: $i] : ( r2_wellord2 @ A @ ( k1_tarski @ B ) )
=> ? [B: $i] :
( A
= ( k1_tarski @ B ) ) )
& ! [A: $i] :
( ? [B: $i] :
( A
= ( k1_tarski @ B ) )
=> ! [B: $i] : ( r2_wellord2 @ A @ ( k1_tarski @ B ) ) ) ),
inference(miniscope,[status(thm)],[10139]) ).
thf(10141,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( r2_wellord2 @ A @ ( k1_tarski @ C ) ) ),
inference(cnf,[status(esa)],[10140]) ).
thf(10143,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( r2_wellord2 @ A @ ( k1_tarski @ C ) ) ),
inference(lifteq,[status(thm)],[10141]) ).
thf(10144,plain,
! [B: $i,A: $i] : ( r2_wellord2 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[10143]) ).
thf(6977,plain,
~ ? [A: $i] : ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[6976]) ).
thf(6978,plain,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[6977]) ).
thf(25190,plain,
! [C: $i,B: $i,A: $i] :
( ( r2_wellord2 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= ( r2_wellord2 @ C @ ( k1_zfmisc_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10144,6978]) ).
thf(25200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_tarski @ A )
!= C )
| ( ( k1_tarski @ B )
!= ( k1_zfmisc_1 @ C ) ) ),
inference(simp,[status(thm)],[25190]) ).
thf(25201,plain,
! [B: $i,A: $i] :
( ( k1_tarski @ B )
!= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[25200]) ).
thf(25938,plain,
! [B: $i,A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ B ) )
| ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[6559,25201]) ).
thf(25951,plain,
! [B: $i,A: $i] :
( ( k1_xboole_0 != B )
| ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(simp,[status(thm)],[25938]) ).
thf(25964,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[25951]) ).
thf(25965,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k1_tarski @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[25964,6559]) ).
thf(1842,axiom,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( l1_group_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(10519,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( l1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(592,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(4696,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)],[592]) ).
thf(651,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(4988,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)],[651]) ).
thf(1905,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(10729,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)],[1905]) ).
thf(301,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice4) ).
thf(3322,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(2067,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(11314,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)],[2067]) ).
thf(1509,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(8956,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)],[1509]) ).
thf(1963,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(10950,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)],[1963]) ).
thf(1283,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(7792,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)],[1283]) ).
thf(331,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(3431,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)],[331]) ).
thf(1929,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(10813,plain,
? [A: $i] :
( ( l1_group_1 @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(10816,plain,
l1_group_1 @ sk611,
inference(cnf,[status(esa)],[10813]) ).
thf(14836,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk611 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10816,4719]) ).
thf(14837,plain,
l1_struct_0 @ sk611,
inference(pattern_uni,[status(thm)],[14836:[bind(A,$thf( sk611 ))]]) ).
thf(1879,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(10641,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)],[1879]) ).
thf(172,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_finseq_1 @ B @ A )
& ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_finset_1 @ B )
& ( v1_finseq_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finseq_1) ).
thf(2753,plain,
! [A: $i] :
? [B: $i] :
( ( m1_finseq_1 @ B @ A )
& ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v2_funct_1 @ B )
& ( v1_finset_1 @ B )
& ( v1_finseq_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(2758,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk37 @ A ) ),
inference(cnf,[status(esa)],[2753]) ).
thf(16154,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( v1_xboole_0 @ ( sk37 @ A ) )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2758,6758]) ).
thf(16155,plain,
! [A: $i] :
( ( sk37 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16154:[bind(A,$thf( C )),bind(B,$thf( sk37 @ C ))]]) ).
thf(17354,plain,
! [A: $i] :
( ( sk37 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[16155]) ).
thf(1910,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(10746,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)],[1910]) ).
thf(1572,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
<=> ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice4) ).
thf(9283,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( ( v2_lattice4 @ C @ A @ B )
=> ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) ) )
& ( ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) )
=> ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(519,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(4329,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(55,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ k5_numbers @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finset_1 @ B )
& ( v1_finseq_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finseq_1) ).
thf(2320,plain,
! [A: $i] :
? [B: $i] :
( ( m1_relset_1 @ B @ k5_numbers @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finset_1 @ B )
& ( v1_finseq_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(2324,plain,
! [A: $i] : ( v1_finseq_1 @ ( sk11 @ A ) ),
inference(cnf,[status(esa)],[2320]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(3199,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1616,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(9520,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)],[1616]) ).
thf(35618,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ k4_numbers ) @ k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ A ) @ A )
!= ( k4_xboole_0 @ B @ k5_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[21283,19272]) ).
thf(35619,plain,
r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k4_numbers ) @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[35618:[bind(A,$thf( k5_numbers )),bind(B,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ))]]) ).
thf(35925,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k4_numbers ) @ k1_xboole_0 )
!= ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35619,2180]) ).
thf(35926,plain,
r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ ( k2_xboole_0 @ k4_numbers @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[35925:[bind(A,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers )),bind(B,$thf( k4_numbers )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(35999,plain,
r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k4_numbers,
inference(rewrite,[status(thm)],[35926,5082]) ).
thf(36014,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ k4_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35999,2203]) ).
thf(36015,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ A ) @ k4_numbers ),
inference(pattern_uni,[status(thm)],[36014:[bind(A,$thf( k2_xboole_0 @ k1_xboole_0 @ k5_numbers )),bind(B,$thf( k4_numbers )),bind(C,$thf( C ))]]) ).
thf(36056,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_xboole_0 @ k1_xboole_0 @ k5_numbers ) @ A ) @ k4_numbers ),
inference(simp,[status(thm)],[36015]) ).
thf(41656,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k1_xboole_0 @ A ) @ k4_numbers ),
inference(rewrite,[status(thm)],[36056,41649]) ).
thf(42944,plain,
r1_tarski @ k1_xboole_0 @ k4_numbers,
inference(rewrite,[status(thm)],[41656,2913]) ).
thf(764,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(5526,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)],[764]) ).
thf(537,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4443,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1608,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(9490,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)],[1608]) ).
thf(1872,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(10623,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)],[1872]) ).
thf(9521,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[9520]) ).
thf(9525,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk524 @ A ) ),
inference(cnf,[status(esa)],[9521]) ).
thf(14317,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk524 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[9525,9072]) ).
thf(14318,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk524 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[14317]) ).
thf(14319,plain,
! [A: $i] :
( ( sk524 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[14318]) ).
thf(16725,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( sk524 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6758,14319]) ).
thf(16726,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( sk524 @ A ) ),
inference(pattern_uni,[status(thm)],[16725:[bind(A,$thf( sk524 @ C )),bind(B,$thf( C ))]]) ).
thf(17171,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( sk524 @ A ) ),
inference(simp,[status(thm)],[16726]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_finset_1) ).
thf(3724,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(541,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m3_lattice4 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4454,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m3_lattice4 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) )
& ( ! [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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
=> ( m3_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(2060,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(11293,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)],[2060]) ).
thf(29947,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29641,2203]) ).
thf(29948,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) @ ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[29947:[bind(A,$thf( k1_orders_1 @ k1_xboole_0 )),bind(B,$thf( k1_tarski @ k1_xboole_0 )),bind(C,$thf( C ))]]) ).
thf(29990,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) @ ( k1_tarski @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[29948]) ).
thf(30315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ B @ C )
= B )
| ( ( r1_xboole_0 @ ( k1_orders_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( r1_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29532,2225]) ).
thf(30316,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_orders_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ A ) ),
inference(pattern_uni,[status(thm)],[30315:[bind(A,$thf( D )),bind(B,$thf( k1_orders_1 @ D )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(30346,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_orders_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ A ) ),
inference(simp,[status(thm)],[30316]) ).
thf(1081,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(6895,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)],[1081]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_0) ).
thf(6657,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(600,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(4733,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)],[600]) ).
thf(1355,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(8158,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)],[1355]) ).
thf(1188,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(7369,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)],[1188]) ).
thf(963,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(6419,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)],[963]) ).
thf(992,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(6523,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)],[992]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_partfun1) ).
thf(2451,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_funct_2) ).
thf(2236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1477,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(8791,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)],[1477]) ).
thf(450,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattices) ).
thf(3983,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(903,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(6189,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)],[903]) ).
thf(1506,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(8929,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)],[1506]) ).
thf(1190,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(7376,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)],[1190]) ).
thf(1046,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(6745,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_partfun1) ).
thf(2880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1227,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(7537,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)],[1227]) ).
thf(1295,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(7845,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)],[1295]) ).
thf(3,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice4) ).
thf(2120,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2122,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v3_filter_0 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_lattice4 @ C @ B @ A )
| ~ ( v3_lattice4 @ C @ B @ A )
| ( v3_filter_0 @ A ) ),
inference(cnf,[status(esa)],[2120]) ).
thf(1692,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_0) ).
thf(9860,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(1740,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(10085,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)],[1740]) ).
thf(856,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(5913,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(5914,plain,
l2_lattices @ sk261,
inference(cnf,[status(esa)],[5913]) ).
thf(1225,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(7532,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)],[1225]) ).
thf(1922,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(10786,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)],[1922]) ).
thf(1271,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(7739,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)],[1271]) ).
thf(1068,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(6841,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)],[1068]) ).
thf(311,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).
thf(3357,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( ( k5_relat_1 @ A @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(34,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(2252,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(2253,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[2252]) ).
thf(2254,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[2253]) ).
thf(352,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(3569,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)],[352]) ).
thf(721,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(5311,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)],[721]) ).
thf(1798,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(10378,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(1464,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(8759,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)],[1464]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
<=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_1) ).
thf(2332,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2335,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r4_binop_1 @ A @ C @ D )
| ~ ( r4_binop_1 @ B @ E @ F )
| ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ),
inference(cnf,[status(esa)],[2332]) ).
thf(355,axiom,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
thf(3578,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(3579,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[3578]) ).
thf(14500,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_partfun1 @ A ) ),
inference(rewrite,[status(thm)],[3579,10471]) ).
thf(969,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(6438,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)],[969]) ).
thf(1763,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(10201,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)],[1763]) ).
thf(561,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(4556,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)],[561]) ).
thf(710,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(5259,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)],[710]) ).
thf(1365,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k5_lattice4 @ A ) )
& ( v1_funct_2 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(8196,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k5_lattice4 @ A ) )
& ( v1_funct_2 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(1867,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( k3_lattices @ ( k11_group_4 @ A ) @ D @ E )
= ( k8_group_4 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_latsubgr) ).
thf(10602,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( k3_lattices @ ( k11_group_4 @ A ) @ D @ E )
= ( k8_group_4 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(419,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(3851,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)],[419]) ).
thf(451,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(3986,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)],[451]) ).
thf(21773,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,19540]) ).
thf(21774,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[21773:[]]) ).
thf(1249,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(7645,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)],[1249]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_partfun1) ).
thf(3226,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(2082,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(11367,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)],[2082]) ).
thf(164,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(2718,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)],[164]) ).
thf(1696,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(9875,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)],[1696]) ).
thf(221,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_tarski @ ( k4_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k4_finseq_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_finseq_3) ).
thf(2964,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_tarski @ ( k4_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k4_finseq_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1400,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattices) ).
thf(8438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(10799,plain,
v2_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(15095,plain,
! [A: $i] :
( ( l1_lattices @ A )
| ( ( l3_lattices @ sk593 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10329,5693]) ).
thf(15096,plain,
l1_lattices @ sk593,
inference(pattern_uni,[status(thm)],[15095:[bind(A,$thf( sk593 ))]]) ).
thf(15136,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_lattices @ sk593 )
!= ( l1_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15096,4103]) ).
thf(15137,plain,
l1_struct_0 @ sk593,
inference(pattern_uni,[status(thm)],[15136:[bind(A,$thf( sk593 ))]]) ).
thf(19674,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk593 ) ),
inference(paramod_ordered,[status(thm)],[4339,15137]) ).
thf(19675,plain,
( ( v1_relat_1 @ ( sk150 @ sk593 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19674:[bind(A,$thf( sk593 ))]]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_partfun1) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(2066,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(11312,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)],[2066]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_partfun1) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(347,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(3537,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)],[347]) ).
thf(1701,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(9897,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(971,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(6451,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)],[971]) ).
thf(2070,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(11325,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)],[2070]) ).
thf(1317,axiom,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(8001,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1434,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(8595,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)],[1434]) ).
thf(749,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(5448,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)],[749]) ).
thf(1635,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattices) ).
thf(9616,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(640,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(4935,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)],[640]) ).
thf(459,axiom,
! [A: $i,B: $i] : ( r2_setfam_1 @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_setfam_1) ).
thf(4032,plain,
! [A: $i] : ( r2_setfam_1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(4033,plain,
! [A: $i] : ( r2_setfam_1 @ A @ A ),
inference(cnf,[status(esa)],[4032]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( m1_finseq_1 @ B @ A )
<=> ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_finseq_1) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( m1_finseq_1 @ B @ A )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m1_finseq_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(193,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(2833,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)],[193]) ).
thf(272,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(3189,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)],[272]) ).
thf(43,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_partfun1) ).
thf(2279,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(2280,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(cnf,[status(esa)],[2279]) ).
thf(2281,plain,
! [A: $i] :
( ( ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
= A )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[2280]) ).
thf(1032,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(6685,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)],[1032]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_enumset1) ).
thf(5220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1407,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(8454,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)],[1407]) ).
thf(1431,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(8575,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)],[1431]) ).
thf(664,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(5096,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)],[664]) ).
thf(19,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(2189,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)],[19]) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( 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_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 )
| ~ ( r4_binop_1 @ A @ C @ B )
| ( r6_binop_1 @ A @ C @ B ) ),
inference(cnf,[status(esa)],[2189]) ).
thf(1044,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(6740,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)],[1044]) ).
thf(1191,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(7381,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)],[1191]) ).
thf(666,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(5101,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)],[666]) ).
thf(1694,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(9865,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)],[1694]) ).
thf(1486,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(8823,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)],[1486]) ).
thf(786,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(5648,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)],[786]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_finseq_1 @ B @ A ) )
=> ( ( k1_group_4 @ A @ B @ C )
= ( k1_finseq_3 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_group_4) ).
thf(7336,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_finseq_1 @ B @ A ) )
=> ( ( k1_group_4 @ A @ B @ C )
= ( k1_finseq_3 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(819,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(5772,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)],[819]) ).
thf(408,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k15_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice3) ).
thf(3808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k15_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1544,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(9140,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)],[1544]) ).
thf(2093,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(11413,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)],[2093]) ).
thf(67,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(2369,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)],[67]) ).
thf(2371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ),
inference(cnf,[status(esa)],[2369]) ).
thf(730,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) )
<=> ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_1) ).
thf(5343,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) )
=> ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(515,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(4307,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1383,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_0) ).
thf(8347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(379,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_0) ).
thf(3676,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(6,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v17_lattices @ A )
<=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_lattices) ).
thf(2133,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v17_lattices @ A )
=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) )
& ( ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) )
=> ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2137,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v11_lattices @ A )
| ( v17_lattices @ A ) ),
inference(cnf,[status(esa)],[2133]) ).
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 ) )
=> ! [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(8686,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)],[1448]) ).
thf(637,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice3) ).
thf(4924,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1968,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(10965,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)],[1968]) ).
thf(1551,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(9187,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)],[1551]) ).
thf(401,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r1_lattice4 @ A @ B @ C )
<=> ! [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 @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ 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',d6_lattice4) ).
thf(3756,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r1_lattice4 @ A @ B @ C )
=> ! [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 @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ 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 @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ 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 ) ) ) ) )
=> ( r1_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(6481,plain,
! [A: $i] : ( m1_subset_1 @ ( sk305 @ A ) @ A ),
inference(cnf,[status(esa)],[6480]) ).
thf(14621,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ B ) ) )
| ( ( m1_subset_1 @ ( sk305 @ A ) @ A )
!= ( m1_subset_1 @ B @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[6481,2381]) ).
thf(14622,plain,
~ ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(pattern_uni,[status(thm)],[14621:[bind(A,$thf( sk15 )),bind(B,$thf( sk305 @ sk15 ))]]) ).
thf(1802,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(10390,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)],[1802]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(6021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k10_relset_1 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(186,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(2809,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)],[186]) ).
thf(1359,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(8173,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)],[1359]) ).
thf(182,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) ) )
=> ( ( k3_finseq_1 @ A )
= np__1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_finseq_3) ).
thf(2799,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( ( k2_relat_1 @ A )
= ( k1_tarski @ B ) ) )
=> ( ( k3_finseq_1 @ A )
= np__1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(10801,plain,
v1_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(45,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_tarski @ ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_finseq_3) ).
thf(2285,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_tarski @ ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(2286,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k2_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[2285]) ).
thf(1589,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(9368,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)],[1589]) ).
thf(1566,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(9236,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)],[1566]) ).
thf(303,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(3327,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)],[303]) ).
thf(1938,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(10839,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)],[1938]) ).
thf(935,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(6327,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)],[935]) ).
thf(1402,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattices) ).
thf(8443,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(627,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k2_group_4 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_4) ).
thf(4892,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( k2_group_4 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(832,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(5819,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)],[832]) ).
thf(508,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_filter_0) ).
thf(4285,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(2148,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(2154,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) ) ),
inference(simp,[status(thm)],[2148]) ).
thf(1960,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(10933,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)],[1960]) ).
thf(834,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(5824,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)],[834]) ).
thf(572,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(4588,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)],[572]) ).
thf(21106,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_struct_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,21095]) ).
thf(21107,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_struct_0 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21106:[]]) ).
thf(1274,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(7758,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)],[1274]) ).
thf(1183,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(7354,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)],[1183]) ).
thf(1772,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(10256,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)],[1772]) ).
thf(21518,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,18449]) ).
thf(21519,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21518:[]]) ).
thf(33760,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ B )
| ( l1_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,21519]) ).
thf(33761,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[33760:[bind(A,$thf( sk1 ))]]) ).
thf(33768,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A ) ),
inference(simp,[status(thm)],[33761]) ).
thf(225,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(2982,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)],[225]) ).
thf(1633,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_0) ).
thf(9584,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
& ( ( ! [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 @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(3514,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ~ ? [C: $i] :
( ( r2_hidden @ C @ B )
& ~ ? [D: $i] :
( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[3513]) ).
thf(3516,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk81 @ A ) ),
inference(cnf,[status(esa)],[3514]) ).
thf(13946,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk81 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3516,9072]) ).
thf(13947,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk81 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[13946]) ).
thf(13948,plain,
! [A: $i] :
( ( sk81 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13947]) ).
thf(20211,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( sk81 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,13948]) ).
thf(20212,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( sk81 @ A ) ) ),
inference(pattern_uni,[status(thm)],[20211:[bind(A,$thf( sk81 @ C )),bind(B,$thf( C ))]]) ).
thf(20736,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( sk81 @ A ) ) ),
inference(simp,[status(thm)],[20212]) ).
thf(5879,plain,
l1_vectsp_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(19728,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_vectsp_1 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[4339,5879]) ).
thf(19729,plain,
( ( v1_relat_1 @ ( sk150 @ sk259 ) )
| ( l1_vectsp_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19728:[bind(A,$thf( sk259 ))]]) ).
thf(342,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(3510,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)],[342]) ).
thf(801,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(5695,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)],[801]) ).
thf(1894,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(10690,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)],[1894]) ).
thf(1395,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(8421,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)],[1395]) ).
thf(1421,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(8523,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)],[1421]) ).
thf(283,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(3229,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)],[283]) ).
thf(23,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(2204,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)],[23]) ).
thf(1006,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(6571,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)],[1006]) ).
thf(1591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(9384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ 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
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m1_filter_1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m1_filter_1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1920,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(10779,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)],[1920]) ).
thf(1497,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(8885,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(8886,plain,
( ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(miniscope,[status(thm)],[8885]) ).
thf(8887,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[8886]) ).
thf(8889,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[8887]) ).
thf(12958,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k1_tarski @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8889,2173]) ).
thf(12959,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[12958:[bind(A,$thf( D )),bind(B,$thf( k1_tarski @ D ))]]) ).
thf(12970,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(simp,[status(thm)],[12959]) ).
thf(29577,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k1_orders_1 @ k1_xboole_0 ) )
| ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29366,12970]) ).
thf(29578,plain,
v1_finset_1 @ ( k1_orders_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[29577:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(29750,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ ( k1_orders_1 @ k1_xboole_0 ) )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29578,2173]) ).
thf(29751,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) ),
inference(pattern_uni,[status(thm)],[29750:[bind(A,$thf( k1_orders_1 @ k1_xboole_0 )),bind(B,$thf( B ))]]) ).
thf(29765,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) ),
inference(simp,[status(thm)],[29751]) ).
thf(30363,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29765,2173]) ).
thf(30364,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[30363:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ E )),bind(C,$thf( C ))]]) ).
thf(30411,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ B ) @ A ) ),
inference(simp,[status(thm)],[30364]) ).
thf(1655,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(9703,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)],[1655]) ).
thf(1706,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(9917,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)],[1706]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_2) ).
thf(2922,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1162,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(7254,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)],[1162]) ).
thf(1226,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( r2_hidden @ ( k5_group_2 @ A ) @ B )
=> ( r1_group_2 @ A @ ( k2_latsubgr @ A @ B ) @ ( k5_group_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_latsubgr) ).
thf(7535,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( r2_hidden @ ( k5_group_2 @ A ) @ B )
=> ( r1_group_2 @ A @ ( k2_latsubgr @ A @ B ) @ ( k5_group_2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1649,axiom,
? [A: $i] : ( l2_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(9681,plain,
? [A: $i] : ( l2_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(9682,plain,
l2_struct_0 @ sk537,
inference(cnf,[status(esa)],[9681]) ).
thf(335,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(3459,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)],[335]) ).
thf(1002,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_0) ).
thf(6560,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(822,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattice3) ).
thf(5783,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(958,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(6406,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)],[958]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).
thf(4629,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
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 )
=> ( ( 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(10362,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)],[1795]) ).
thf(981,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(6482,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)],[981]) ).
thf(19460,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k1_funct_2 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,13280]) ).
thf(19461,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_funct_2 @ A @ A ) ) ),
inference(pattern_uni,[status(thm)],[19460:[bind(A,$thf( k1_funct_2 @ D @ D )),bind(B,$thf( D ))]]) ).
thf(20528,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_funct_2 @ A @ A ) ) ),
inference(simp,[status(thm)],[19461]) ).
thf(1579,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(9308,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)],[1579]) ).
thf(872,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k15_lattice3 @ A @ ( k3_tarski @ B ) )
= ( k15_lattice3 @ A @ ( a_2_7_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattice3) ).
thf(6015,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k15_lattice3 @ A @ ( k3_tarski @ B ) )
= ( k15_lattice3 @ A @ ( a_2_7_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(5839,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1856,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(10561,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)],[1856]) ).
thf(1932,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(10823,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(10825,plain,
l2_struct_0 @ sk612,
inference(cnf,[status(esa)],[10823]) ).
thf(20024,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l2_struct_0 @ k1_xboole_0 )
| ( A != sk612 ) ),
inference(paramod_ordered,[status(thm)],[4339,10825]) ).
thf(20025,plain,
( ( v1_relat_1 @ ( sk150 @ sk612 ) )
| ( l2_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20024:[bind(A,$thf( sk612 ))]]) ).
thf(1561,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(9221,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)],[1561]) ).
thf(265,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_1) ).
thf(3169,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(545,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_partfun1 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k2_xboole_0 @ A @ B )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_partfun1) ).
thf(4480,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)],[545]) ).
thf(1229,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(7550,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)],[1229]) ).
thf(142,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k3_finseq_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_finseq_3) ).
thf(2646,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k3_finseq_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(11537,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
!= ( v1_xboole_0 @ k1_numbers ) ),
inference(paramod_ordered,[status(thm)],[5730,3855]) ).
thf(11550,plain,
k1_xboole_0 != k1_numbers,
inference(simp,[status(thm)],[11537]) ).
thf(19613,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,2118]) ).
thf(19614,plain,
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19613:[bind(A,$thf( sk1 ))]]) ).
thf(21783,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v3_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,19614]) ).
thf(21784,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v3_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[21783:[]]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_2) ).
thf(3635,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k2_relat_1 @ B )
= A )
& ( ( k2_relat_1 @ C )
= A ) )
=> ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(65,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(2361,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)],[65]) ).
thf(2364,plain,
! [B: $i,A: $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 )
| ( m1_subset_1 @ ( sk14 @ B @ A ) @ A )
| ( v3_binop_1 @ B @ A ) ),
inference(cnf,[status(esa)],[2361]) ).
thf(9,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [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 )
=> ( ( ( k3_finseq_1 @ A )
= ( k1_nat_1 @ C @ np__1 ) )
=> ( ( r1_xreal_0 @ B @ D )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_finseq_3) ).
thf(2162,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [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 )
=> ( ( ( k3_finseq_1 @ A )
= ( k1_nat_1 @ C @ np__1 ) )
=> ( ( r1_xreal_0 @ B @ D )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
| ( ( k3_finseq_1 @ A )
!= ( k1_nat_1 @ C @ np__1 ) )
| ( r1_xreal_0 @ B @ D )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ D ) ) ),
inference(cnf,[status(esa)],[2162]) ).
thf(2164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_finseq_1 @ A )
!= ( k1_nat_1 @ C @ np__1 ) )
| ( ( k1_funct_1 @ ( k2_finseq_3 @ B @ A ) @ D )
= ( k1_funct_1 @ A @ D ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
| ~ ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
| ( r1_xreal_0 @ B @ D ) ),
inference(lifteq,[status(thm)],[2163]) ).
thf(802,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(5697,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)],[802]) ).
thf(271,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(3186,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)],[271]) ).
thf(1989,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(11032,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)],[1989]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(5167,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1299,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(7859,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)],[1299]) ).
thf(681,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(5142,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)],[681]) ).
thf(1308,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(7937,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)],[1308]) ).
thf(718,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(5291,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)],[718]) ).
thf(1510,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(8959,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)],[1510]) ).
thf(887,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(6069,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(6071,plain,
v1_xboole_0 @ sk272,
inference(cnf,[status(esa)],[6069]) ).
thf(15919,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk272 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6071,6758]) ).
thf(15920,plain,
sk272 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[15919:[bind(A,$thf( sk272 ))]]) ).
thf(954,axiom,
k4_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_numbers) ).
thf(6386,plain,
k4_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(6387,plain,
k4_numbers != k1_numbers,
inference(polarity_switch,[status(thm)],[6386]) ).
thf(6388,plain,
k4_numbers != k1_numbers,
inference(lifteq,[status(thm)],[6387]) ).
thf(1513,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(9009,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)],[1513]) ).
thf(1248,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(7642,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)],[1248]) ).
thf(747,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(5416,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)],[747]) ).
thf(526,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(4370,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)],[526]) ).
thf(7005,plain,
l1_group_1 @ sk335,
inference(cnf,[status(esa)],[7003]) ).
thf(844,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r2_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_lattice4) ).
thf(5862,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r2_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) )
=> ( r2_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(2534,plain,
v1_finset_1 @ sk19,
inference(cnf,[status(esa)],[2530]) ).
thf(12954,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk19 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2534,2173]) ).
thf(12955,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) ),
inference(pattern_uni,[status(thm)],[12954:[bind(A,$thf( sk19 ))]]) ).
thf(12968,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) ),
inference(simp,[status(thm)],[12955]) ).
thf(13513,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12968,2173]) ).
thf(13514,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[13513:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk19 @ E )),bind(C,$thf( C ))]]) ).
thf(13519,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(simp,[status(thm)],[13514]) ).
thf(2307,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v15_lattices @ A )
| ( v14_lattices @ A ) ),
inference(cnf,[status(esa)],[2306]) ).
thf(2296,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ( r4_lattice3 @ A @ ( sk7 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(568,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(4576,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k4_card_1 @ A )
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(140,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ A )
= ( k1_card_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_finseq_1) ).
thf(2641,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k3_finseq_1 @ A )
= ( k1_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(10710,plain,
v1_group_1 @ sk608,
inference(cnf,[status(esa)],[10707]) ).
thf(19726,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_group_1 @ k1_xboole_0 )
| ( A != sk608 ) ),
inference(paramod_ordered,[status(thm)],[4339,10710]) ).
thf(19727,plain,
( ( v1_relat_1 @ ( sk150 @ sk608 ) )
| ( v1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19726:[bind(A,$thf( sk608 ))]]) ).
thf(6940,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk330 @ A ) ),
inference(cnf,[status(esa)],[6939]) ).
thf(16198,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( v1_xboole_0 @ ( sk330 @ A ) )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6940,6758]) ).
thf(16199,plain,
! [A: $i] :
( ( sk330 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16198:[bind(A,$thf( C )),bind(B,$thf( sk330 @ C ))]]) ).
thf(17363,plain,
! [A: $i] :
( ( sk330 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[16199]) ).
thf(1675,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(9785,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)],[1675]) ).
thf(103,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(2496,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)],[103]) ).
thf(136,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(2621,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)],[136]) ).
thf(2660,plain,
v1_relat_1 @ sk27,
inference(cnf,[status(esa)],[2657]) ).
thf(1831,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(10477,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)],[1831]) ).
thf(726,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_0) ).
thf(5334,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(2382,plain,
~ ( v1_xboole_0 @ sk15 ),
inference(cnf,[status(esa)],[2380]) ).
thf(350,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(3550,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)],[350]) ).
thf(483,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice4) ).
thf(4172,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(177,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(2773,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)],[177]) ).
thf(2038,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(11202,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)],[2038]) ).
thf(1697,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(9881,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)],[1697]) ).
thf(1791,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(10345,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)],[1791]) ).
thf(11538,plain,
( ( v1_xboole_0 @ sk15 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,2382]) ).
thf(11545,plain,
sk15 != k1_xboole_0,
inference(simp,[status(thm)],[11538]) ).
thf(38,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(2264,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)],[38]) ).
thf(4881,plain,
~ ( v1_xboole_0 @ sk196 ),
inference(cnf,[status(esa)],[4877]) ).
thf(11543,plain,
( ( v1_xboole_0 @ sk196 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,4881]) ).
thf(11548,plain,
sk196 != k1_xboole_0,
inference(simp,[status(thm)],[11543]) ).
thf(20415,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk196 ) ),
inference(paramod_ordered,[status(thm)],[4339,11548]) ).
thf(20416,plain,
v1_relat_1 @ ( sk150 @ sk196 ),
inference(pattern_uni,[status(thm)],[20415:[bind(A,$thf( sk196 ))]]) ).
thf(939,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(6343,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)],[939]) ).
thf(113,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(2541,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)],[113]) ).
thf(1595,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(9412,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)],[1595]) ).
thf(429,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(3889,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)],[429]) ).
thf(1749,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(10133,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)],[1749]) ).
thf(1343,axiom,
~ ( v1_xboole_0 @ k4_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_numbers) ).
thf(8112,plain,
~ ( v1_xboole_0 @ k4_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(8113,plain,
~ ( v1_xboole_0 @ k4_numbers ),
inference(polarity_switch,[status(thm)],[8112]) ).
thf(1419,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(8513,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)],[1419]) ).
thf(127,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(2589,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)],[127]) ).
thf(395,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(3735,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)],[395]) ).
thf(1607,axiom,
? [A: $i] : ( v1_card_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_1) ).
thf(9488,plain,
? [A: $i] : ( v1_card_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(543,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4465,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(4466,plain,
! [A: $i] :
( ~ ( l2_lattices @ A )
| ( l1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[4465]) ).
thf(778,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(5611,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)],[778]) ).
thf(809,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(5734,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1116,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(7042,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)],[1116]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_partfun1) ).
thf(2601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1472,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(8778,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(1082,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice4) ).
thf(6897,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(85,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(2428,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)],[85]) ).
thf(168,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(2733,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)],[168]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(2805,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(388,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(3711,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1314,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(7989,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)],[1314]) ).
thf(312,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(3360,plain,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(3361,plain,
( ! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
inference(miniscope,[status(thm)],[3360]) ).
thf(3363,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[3361]) ).
thf(3366,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[3363]) ).
thf(14501,plain,
! [A: $i] :
( ( k1_relat_1 @ ( k6_partfun1 @ A ) )
= A ),
inference(rewrite,[status(thm)],[3366,10471]) ).
thf(33,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_finseq_3) ).
thf(2249,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(876,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(6032,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)],[876]) ).
thf(42,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(2275,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)],[42]) ).
thf(2277,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ),
inference(cnf,[status(esa)],[2275]) ).
thf(4375,plain,
l1_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ),
inference(cnf,[status(esa)],[4370]) ).
thf(1463,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(8756,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)],[1463]) ).
thf(8888,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[8886]) ).
thf(4878,plain,
v1_finset_1 @ sk196,
inference(cnf,[status(esa)],[4877]) ).
thf(1159,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(7229,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)],[1159]) ).
thf(2045,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(11223,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)],[2045]) ).
thf(1145,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(7160,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(7161,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(cnf,[status(esa)],[7160]) ).
thf(1292,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(7834,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)],[1292]) ).
thf(1493,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(8856,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)],[1493]) ).
thf(1815,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(10426,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)],[1815]) ).
thf(1557,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(9207,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)],[1557]) ).
thf(14658,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ sk48 ) ),
inference(paramod_ordered,[status(thm)],[3009,14622]) ).
thf(14668,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk48 ),
inference(simp,[status(thm)],[14658]) ).
thf(14930,plain,
! [A: $i] :
( ( A != sk48 )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2254,14668]) ).
thf(14933,plain,
( ( k4_xboole_0 @ sk48 @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[14930]) ).
thf(21646,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk48 ),
inference(rewrite,[status(thm)],[14933,2254]) ).
thf(1809,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(10409,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)],[1809]) ).
thf(452,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(3989,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)],[452]) ).
thf(254,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(3069,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)],[254]) ).
thf(1690,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(9849,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)],[1690]) ).
thf(287,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(3239,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)],[287]) ).
thf(15116,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ k4_numbers @ k1_numbers )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5132,2203]) ).
thf(15117,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ k1_numbers ),
inference(pattern_uni,[status(thm)],[15116:[bind(A,$thf( k4_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(15133,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ k1_numbers ),
inference(simp,[status(thm)],[15117]) ).
thf(15507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ k1_numbers )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15133,2180]) ).
thf(15508,plain,
! [A: $i] : ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ k1_numbers ) ),
inference(pattern_uni,[status(thm)],[15507:[bind(A,$thf( A )),bind(B,$thf( k4_numbers )),bind(C,$thf( A )),bind(D,$thf( k1_numbers ))]]) ).
thf(15533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ k1_numbers ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15508,2203]) ).
thf(15534,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) ),
inference(pattern_uni,[status(thm)],[15533:[bind(A,$thf( E )),bind(B,$thf( k4_numbers )),bind(C,$thf( k2_xboole_0 @ E @ k1_numbers )),bind(D,$thf( D ))]]) ).
thf(15541,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) ),
inference(simp,[status(thm)],[15534]) ).
thf(31623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ C @ ( k2_xboole_0 @ D @ E ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ k4_numbers @ A ) @ ( k2_xboole_0 @ B @ k1_numbers ) )
!= ( r1_tarski @ ( k4_xboole_0 @ C @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[15541,2180]) ).
thf(31624,plain,
! [B: $i,A: $i] : ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ k1_numbers ) ) ),
inference(pattern_uni,[status(thm)],[31623:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( k4_numbers )),bind(D,$thf( A )),bind(E,$thf( k2_xboole_0 @ F @ k1_numbers ))]]) ).
thf(31663,plain,
! [B: $i,A: $i] : ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ k1_numbers ) ) ),
inference(simp,[status(thm)],[31624]) ).
thf(41718,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ B @ k1_xboole_0 ) )
| ( ( k2_xboole_0 @ k1_xboole_0 @ A )
!= ( k2_xboole_0 @ C @ k1_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[41649,31663]) ).
thf(41719,plain,
! [A: $i] : ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[41718:[bind(A,$thf( k1_numbers )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(41796,plain,
! [A: $i] : ( r1_tarski @ k4_numbers @ ( k2_xboole_0 @ A @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[41719]) ).
thf(45505,plain,
! [A: $i] : ( r1_tarski @ k4_numbers @ A ),
inference(rewrite,[status(thm)],[41796,5082]) ).
thf(45517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ B @ D )
| ( ( r1_tarski @ k4_numbers @ A )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[45505,2260]) ).
thf(45518,plain,
! [A: $i] : ( r1_xboole_0 @ k4_numbers @ A ),
inference(pattern_uni,[status(thm)],[45517:[bind(A,$thf( k4_xboole_0 @ E @ F )),bind(B,$thf( k4_numbers )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(45536,plain,
! [A: $i] : ( r1_xboole_0 @ k4_numbers @ A ),
inference(simp,[status(thm)],[45518]) ).
thf(45542,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ B @ C )
= B )
| ( ( r1_xboole_0 @ k4_numbers @ A )
!= ( r1_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[45536,2225]) ).
thf(45543,plain,
! [A: $i] :
( ( k4_xboole_0 @ k4_numbers @ A )
= k4_numbers ),
inference(pattern_uni,[status(thm)],[45542:[bind(A,$thf( A )),bind(B,$thf( k4_numbers )),bind(C,$thf( A ))]]) ).
thf(315,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(3371,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)],[315]) ).
thf(1542,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(9126,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)],[1542]) ).
thf(131,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(2606,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)],[131]) ).
thf(1980,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(11003,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)],[1980]) ).
thf(539,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(4449,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)],[539]) ).
thf(10660,plain,
~ ( v3_struct_0 @ sk605 ),
inference(cnf,[status(esa)],[10654]) ).
thf(16596,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[6758,10660]) ).
thf(16597,plain,
( ~ ( v1_xboole_0 @ sk605 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16596:[bind(A,$thf( sk605 ))]]) ).
thf(1336,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(8081,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)],[1336]) ).
thf(663,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(5085,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)],[663]) ).
thf(1260,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m4_vectsp_8 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m4_vectsp_8) ).
thf(7692,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m4_vectsp_8 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(411,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(3816,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)],[411]) ).
thf(1851,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(10548,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)],[1851]) ).
thf(410,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_filter_0) ).
thf(3814,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(743,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_0) ).
thf(5396,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(2132,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_lattice4 @ C @ B @ A )
| ~ ( v2_lattice4 @ C @ B @ A )
| ( v17_lattices @ A ) ),
inference(cnf,[status(esa)],[2130]) ).
thf(79,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_xreal_0 @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) )
<=> ( r1_tarski @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finseq_3) ).
thf(2414,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( r1_xreal_0 @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) )
=> ( r1_tarski @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ B ) ) )
& ( ( r1_tarski @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ B ) )
=> ( r1_xreal_0 @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(5594,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(480,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(4160,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)],[480]) ).
thf(2033,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(11191,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)],[2033]) ).
thf(278,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(3207,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)],[278]) ).
thf(1660,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(9734,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)],[1660]) ).
thf(1168,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_1) ).
thf(7301,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1549,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(9177,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)],[1549]) ).
thf(1438,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(8623,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)],[1438]) ).
thf(575,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(4608,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)],[575]) ).
thf(1440,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(8651,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)],[1440]) ).
thf(2198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 )
| ~ ( m1_subset_1 @ D @ A )
| ( ( k1_binop_1 @ C @ B @ D )
= D ) ),
inference(cnf,[status(esa)],[2195]) ).
thf(2200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ C @ B @ D )
= D )
| ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 )
| ~ ( m1_subset_1 @ D @ A ) ),
inference(lifteq,[status(thm)],[2198]) ).
thf(219,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(2958,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)],[219]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(8683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(297,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_0) ).
thf(3307,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(818,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(5769,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)],[818]) ).
thf(1171,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(7308,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)],[1171]) ).
thf(1774,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice3) ).
thf(10263,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(1538,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(9113,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)],[1538]) ).
thf(1482,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(8810,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)],[1482]) ).
thf(273,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(3191,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)],[273]) ).
thf(6919,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[6918]) ).
thf(6921,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[6919]) ).
thf(6925,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(lifteq,[status(thm)],[6921]) ).
thf(6926,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(simp,[status(thm)],[6925]) ).
thf(98,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_0) ).
thf(2464,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1176,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(7325,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)],[1176]) ).
thf(203,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(2873,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)],[203]) ).
thf(3980,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk111 @ B @ A ) ),
inference(cnf,[status(esa)],[3979]) ).
thf(1877,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(10634,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)],[1877]) ).
thf(1962,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(10939,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)],[1962]) ).
thf(1786,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(10330,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)],[1786]) ).
thf(754,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(5492,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)],[754]) ).
thf(967,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(6432,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)],[967]) ).
thf(1423,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(8540,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)],[1423]) ).
thf(1476,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(8788,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)],[1476]) ).
thf(137,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(2628,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)],[137]) ).
thf(150,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(2670,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)],[150]) ).
thf(1294,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(7842,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)],[1294]) ).
thf(13281,plain,
! [A: $i] :
( ~ ( r2_wellord2 @ A @ ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6559,6978]) ).
thf(13282,plain,
~ ( r2_wellord2 @ k1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13281:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1326,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(8026,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)],[1326]) ).
thf(571,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(4585,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)],[571]) ).
thf(1149,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(7185,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1933,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(10826,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)],[1933]) ).
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_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(7762,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)],[1275]) ).
thf(1646,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattices) ).
thf(9671,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(879,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(6043,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)],[879]) ).
thf(479,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r3_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice4) ).
thf(4155,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r3_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) )
=> ( r3_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1204,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_0) ).
thf(7449,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_partfun1) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(400,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(3750,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)],[400]) ).
thf(308,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattices) ).
thf(3349,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(799,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(5690,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)],[799]) ).
thf(9274,plain,
~ ? [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(miniscope,[status(thm)],[9273]) ).
thf(9275,plain,
! [B: $i,A: $i] :
( ~ ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[9274]) ).
thf(9276,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(lifteq,[status(thm)],[9275]) ).
thf(9277,plain,
! [A: $i] :
~ ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[9276]) ).
thf(1863,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(10583,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)],[1863]) ).
thf(1306,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(7902,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)],[1306]) ).
thf(1915,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(10765,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)],[1915]) ).
thf(865,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ 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 ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_1) ).
thf(5988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ 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 ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(431,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( v6_lattice3 @ A )
<=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice3) ).
thf(3894,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v6_lattice3 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) )
=> ( v6_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(2026,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(11174,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)],[2026]) ).
thf(729,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(5341,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)],[729]) ).
thf(1361,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(8181,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)],[1361]) ).
thf(19368,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_lattices @ k1_xboole_0 )
| ( A != sk545 ) ),
inference(paramod_ordered,[status(thm)],[4339,9759]) ).
thf(19369,plain,
( ( v1_relat_1 @ ( sk150 @ sk545 ) )
| ( v3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19368:[bind(A,$thf( sk545 ))]]) ).
thf(956,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(6392,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)],[956]) ).
thf(1307,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(7934,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)],[1307]) ).
thf(2209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( 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 ) ) ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(2213,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ ( 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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( m1_subset_1 @ F @ A ) ),
inference(lifteq,[status(thm)],[2209]) ).
thf(602,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(4740,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)],[602]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ ( k1_funct_1 @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_4) ).
thf(5658,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ ( k1_funct_1 @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(247,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(3050,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)],[247]) ).
thf(1966,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(10958,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)],[1966]) ).
thf(2210,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( 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 ) ) ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(2211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ ( 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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( m1_subset_1 @ F @ A ) ),
inference(lifteq,[status(thm)],[2210]) ).
thf(1767,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_0) ).
thf(10235,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(52,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(2313,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)],[52]) ).
thf(402,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_filter_1) ).
thf(3763,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(470,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 )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_2) ).
thf(4104,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 )
& ( ( k2_relat_1 @ B )
= A ) )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( v3_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(115,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(2547,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)],[115]) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r4_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
thf(2344,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r4_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) )
=> ( r4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1297,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(7853,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)],[1297]) ).
thf(1328,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(8031,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)],[1328]) ).
thf(1634,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(9613,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)],[1634]) ).
thf(378,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_1) ).
thf(3667,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(27,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relat_1) ).
thf(2226,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_relat_1 @ B )
| ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ),
inference(cnf,[status(esa)],[2226]) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ( ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) )
= ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_relat_1 @ B ) ),
inference(lifteq,[status(thm)],[2227]) ).
thf(2006,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(11101,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)],[2006]) ).
thf(1341,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(8104,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)],[1341]) ).
thf(241,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(3033,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)],[241]) ).
thf(1685,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(9829,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)],[1685]) ).
thf(4670,plain,
~ ? [A: $i,B: $i] :
( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[4669]) ).
thf(4675,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk180 @ B @ A ) ) ),
inference(cnf,[status(esa)],[4670]) ).
thf(4679,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk180 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[4675]) ).
thf(4680,plain,
! [A: $i] : ( v1_relat_1 @ ( sk180 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[4679]) ).
thf(760,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(5515,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(360,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_0) ).
thf(3595,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1258,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(7686,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)],[1258]) ).
thf(715,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(5285,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)],[715]) ).
thf(1335,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(8073,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)],[1335]) ).
thf(6090,plain,
! [A: $i] : ( v1_card_1 @ ( k2_card_1 @ A ) ),
inference(cnf,[status(esa)],[6089]) ).
thf(1079,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(6888,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)],[1079]) ).
thf(1658,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(9730,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)],[1658]) ).
thf(1845,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(10529,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)],[1845]) ).
thf(231,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_0) ).
thf(3001,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(267,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(3176,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)],[267]) ).
thf(12371,plain,
! [A: $i] :
( ( v2_funct_1 @ k1_xboole_0 )
| ( ( k6_relat_1 @ k1_xboole_0 )
!= ( k6_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9110,3579]) ).
thf(12372,plain,
v2_funct_1 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[12371:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(5735,plain,
! [A: $i] :
( ~ ( l2_struct_0 @ A )
| ( l1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[5734]) ).
thf(15558,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l2_struct_0 @ sk612 )
!= ( l2_struct_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10825,5735]) ).
thf(15559,plain,
l1_struct_0 @ sk612,
inference(pattern_uni,[status(thm)],[15558:[bind(A,$thf( sk612 ))]]) ).
thf(722,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_0) ).
thf(5313,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(473,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(4123,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)],[473]) ).
thf(1181,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(7346,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)],[1181]) ).
thf(386,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_0) ).
thf(3699,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(2300,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ C @ B )
| ( r1_lattices @ A @ ( sk7 @ B @ A ) @ C ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(337,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
thf(3467,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) ) )
& ( ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_setfam_1) ).
thf(5626,plain,
! [A: $i,B: $i] :
( ( ( r2_setfam_1 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( r1_tarski @ D @ C ) ) )
=> ( r2_setfam_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_partfun1) ).
thf(2498,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(961,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(6413,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)],[961]) ).
thf(854,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_0) ).
thf(5904,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(2078,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(11356,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)],[2078]) ).
thf(1140,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(7142,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)],[1140]) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v16_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ( v16_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(simp,[status(thm)],[2150]) ).
thf(195,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(2840,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2016,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(11133,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)],[2016]) ).
thf(340,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(3482,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)],[340]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(5145,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(20183,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,19118]) ).
thf(20184,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20183:[]]) ).
thf(292,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(3254,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)],[292]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_partfun1) ).
thf(2377,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1678,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(9804,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)],[1678]) ).
thf(589,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4667,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(4668,plain,
l1_struct_0 @ sk179,
inference(cnf,[status(esa)],[4667]) ).
thf(1058,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(6801,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)],[1058]) ).
thf(894,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(6118,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(6120,plain,
~ ( v1_xboole_0 @ sk280 ),
inference(cnf,[status(esa)],[6118]) ).
thf(11542,plain,
( ( v1_xboole_0 @ sk280 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,6120]) ).
thf(11544,plain,
sk280 != k1_xboole_0,
inference(simp,[status(thm)],[11542]) ).
thf(19863,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk280 ) ),
inference(paramod_ordered,[status(thm)],[4339,11544]) ).
thf(19864,plain,
v1_relat_1 @ ( sk150 @ sk280 ),
inference(pattern_uni,[status(thm)],[19863:[bind(A,$thf( sk280 ))]]) ).
thf(1777,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattice3) ).
thf(10295,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(1584,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(9355,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)],[1584]) ).
thf(1973,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(10986,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)],[1973]) ).
thf(1527,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(9073,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)],[1527]) ).
thf(423,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(3862,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)],[423]) ).
thf(1320,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(8009,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)],[1320]) ).
thf(1924,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(10791,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)],[1924]) ).
thf(950,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(6375,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)],[950]) ).
thf(906,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(6195,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)],[906]) ).
thf(979,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(6477,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)],[979]) ).
thf(1380,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(8339,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)],[1380]) ).
thf(1394,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(8414,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)],[1394]) ).
thf(1711,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(9945,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)],[1711]) ).
thf(1581,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(9328,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)],[1581]) ).
thf(974,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(6459,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)],[974]) ).
thf(1672,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(9773,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)],[1672]) ).
thf(32656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ A )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[31774,2180]) ).
thf(32657,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k1_numbers @ A ) ),
inference(pattern_uni,[status(thm)],[32656:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_numbers )),bind(D,$thf( A ))]]) ).
thf(1192,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(7389,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)],[1192]) ).
thf(770,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(5577,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)],[770]) ).
thf(7183,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[7182]) ).
thf(7184,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[7183]) ).
thf(12005,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,7184]) ).
thf(12016,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[12005]) ).
thf(559,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(4544,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)],[559]) ).
thf(2044,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(11221,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)],[2044]) ).
thf(1880,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(10644,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)],[1880]) ).
thf(1399,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice3) ).
thf(8435,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(159,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(2694,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)],[159]) ).
thf(1881,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(10646,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)],[1881]) ).
thf(14657,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,14622]) ).
thf(14666,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[14657]) ).
thf(1788,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(10335,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)],[1788]) ).
thf(1996,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(11057,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)],[1996]) ).
thf(106,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(2509,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)],[106]) ).
thf(2100,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(11435,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)],[2100]) ).
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] :
( ( 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(9977,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)],[1720]) ).
thf(1755,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(10152,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(29428,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k1_orders_1 @ A ) @ B )
| ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2819,2230]) ).
thf(29429,plain,
! [A: $i] : ( r1_tarski @ ( k1_orders_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(pattern_uni,[status(thm)],[29428:[bind(A,$thf( D )),bind(B,$thf( k1_zfmisc_1 @ D )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(29541,plain,
! [A: $i] : ( r1_tarski @ ( k1_orders_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(simp,[status(thm)],[29429]) ).
thf(166,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(2724,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)],[166]) ).
thf(1885,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(10661,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)],[1885]) ).
thf(2014,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(11128,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)],[2014]) ).
thf(371,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(3632,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)],[371]) ).
thf(1262,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(7698,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)],[1262]) ).
thf(1220,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_0) ).
thf(7513,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(735,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(5373,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(829,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice4) ).
thf(5811,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1805,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(10398,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)],[1805]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_subset_1) ).
thf(6360,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(619,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r4_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice4) ).
thf(4840,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r4_lattice4 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) )
=> ( r4_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1726,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( m1_lattice4 @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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 ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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',d1_lattice4) ).
thf(10021,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( ( m1_lattice4 @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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 ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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 ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ 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 ) ) ) ) ) )
=> ( m1_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(2032,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(11189,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)],[2032]) ).
thf(376,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(3650,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)],[376]) ).
thf(1430,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(8567,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)],[1430]) ).
thf(1154,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(7204,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)],[1154]) ).
thf(19477,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l2_lattices @ k1_xboole_0 )
| ( A != sk593 ) ),
inference(paramod_ordered,[status(thm)],[4339,15146]) ).
thf(19478,plain,
( ( v1_relat_1 @ ( sk150 @ sk593 ) )
| ( l2_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19477:[bind(A,$thf( sk593 ))]]) ).
thf(1582,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(9333,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)],[1582]) ).
thf(1947,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(10882,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)],[1947]) ).
thf(139,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(2638,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)],[139]) ).
thf(705,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(5233,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)],[705]) ).
thf(798,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(5687,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)],[798]) ).
thf(2112,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(11467,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)],[2112]) ).
thf(39,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(2267,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)],[39]) ).
thf(2268,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[2267]) ).
thf(1484,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(8815,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)],[1484]) ).
thf(277,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(3205,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)],[277]) ).
thf(1890,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(10678,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)],[1890]) ).
thf(585,axiom,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_card_1) ).
thf(4651,plain,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(4652,plain,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
inference(cnf,[status(esa)],[4651]) ).
thf(4653,plain,
! [A: $i] :
( ( k4_card_1 @ ( k1_tarski @ A ) )
= np__1 ),
inference(lifteq,[status(thm)],[4652]) ).
thf(1771,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(10252,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)],[1771]) ).
thf(10255,plain,
r1_tarski @ sk581 @ ( k1_group_3 @ f1_s2_group_4 ),
inference(cnf,[status(esa)],[10252]) ).
thf(15120,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ sk581 @ ( k1_group_3 @ f1_s2_group_4 ) )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10255,2203]) ).
thf(15121,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ sk581 @ A ) @ ( k1_group_3 @ f1_s2_group_4 ) ),
inference(pattern_uni,[status(thm)],[15120:[bind(A,$thf( sk581 )),bind(B,$thf( k1_group_3 @ f1_s2_group_4 )),bind(C,$thf( C ))]]) ).
thf(15126,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ sk581 @ A ) @ ( k1_group_3 @ f1_s2_group_4 ) ),
inference(simp,[status(thm)],[15121]) ).
thf(15547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ sk581 @ A ) @ ( k1_group_3 @ f1_s2_group_4 ) )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15126,2180]) ).
thf(15548,plain,
! [A: $i] : ( r1_tarski @ sk581 @ ( k2_xboole_0 @ A @ ( k1_group_3 @ f1_s2_group_4 ) ) ),
inference(pattern_uni,[status(thm)],[15547:[bind(A,$thf( A )),bind(B,$thf( sk581 )),bind(C,$thf( A )),bind(D,$thf( k1_group_3 @ f1_s2_group_4 ))]]) ).
thf(41733,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ sk581 @ k1_xboole_0 )
| ( ( k2_xboole_0 @ k1_xboole_0 @ A )
!= ( k2_xboole_0 @ B @ ( k1_group_3 @ f1_s2_group_4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[41649,15548]) ).
thf(41734,plain,
r1_tarski @ sk581 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[41733:[bind(A,$thf( k1_group_3 @ f1_s2_group_4 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(438,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(3922,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)],[438]) ).
thf(510,axiom,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(4291,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(926,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ A @ B @ C @ D )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_filter_0) ).
thf(6299,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_filter_0 @ A @ B @ C @ D )
=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
=> ( r1_filter_0 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1129,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(7101,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)],[1129]) ).
thf(1360,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(8176,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)],[1360]) ).
thf(1695,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(9872,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)],[1695]) ).
thf(1125,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(7091,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)],[1125]) ).
thf(553,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(4518,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)],[553]) ).
thf(14840,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4375,4719]) ).
thf(14841,plain,
l1_struct_0 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ),
inference(pattern_uni,[status(thm)],[14840:[bind(A,$thf( g1_group_1 @ k1_numbers @ k33_binop_2 ))]]) ).
thf(991,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(6518,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)],[991]) ).
thf(10708,plain,
v4_group_1 @ sk608,
inference(cnf,[status(esa)],[10707]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(4582,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1495,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(8864,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)],[1495]) ).
thf(2323,plain,
! [A: $i] : ( v1_funct_1 @ ( sk11 @ A ) ),
inference(cnf,[status(esa)],[2320]) ).
thf(1323,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(8017,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)],[1323]) ).
thf(1245,axiom,
! [A: $i] :
? [B: $i] : ( m1_finseq_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_1) ).
thf(7631,plain,
! [A: $i] :
? [B: $i] : ( m1_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(649,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(4983,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)],[649]) ).
thf(1613,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(9508,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)],[1613]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( v5_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k4_lattices @ B @ C @ ( k15_lattice3 @ B @ A ) )
= ( k15_lattice3 @ B @ ( a_3_7_lattice3 @ A @ B @ C ) ) )
& ( ( k4_lattices @ B @ ( k15_lattice3 @ B @ A ) @ C )
= ( k15_lattice3 @ B @ ( a_3_8_lattice3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_lattice3) ).
thf(5915,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( v5_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k4_lattices @ B @ C @ ( k15_lattice3 @ B @ A ) )
= ( k15_lattice3 @ B @ ( a_3_7_lattice3 @ A @ B @ C ) ) )
& ( ( k4_lattices @ B @ ( k15_lattice3 @ B @ A ) @ C )
= ( k15_lattice3 @ B @ ( a_3_8_lattice3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(418,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(3846,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)],[418]) ).
thf(691,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 ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5181,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 ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(367,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(3622,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)],[367]) ).
thf(9769,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[9768]) ).
thf(1270,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(7736,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(7737,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(cnf,[status(esa)],[7736]) ).
thf(7738,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(lifteq,[status(thm)],[7737]) ).
thf(25133,plain,
! [A: $i] : ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(rewrite,[status(thm)],[9769,7738]) ).
thf(1645,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(9662,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1069,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(6844,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)],[1069]) ).
thf(787,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(5651,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)],[787]) ).
thf(1244,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(7629,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)],[1244]) ).
thf(1012,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(6593,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)],[1012]) ).
thf(1374,axiom,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(8251,plain,
! [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
= ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(2091,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(11403,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)],[2091]) ).
thf(1837,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(10498,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)],[1837]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(5791,plain,
v1_funct_1 @ sk253,
inference(cnf,[status(esa)],[5790]) ).
thf(945,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(6363,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)],[945]) ).
thf(1799,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(10381,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)],[1799]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(2868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(7318,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(812,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(5743,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relset_1) ).
thf(2419,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(19372,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk610 ) ),
inference(paramod_ordered,[status(thm)],[4339,10795]) ).
thf(19373,plain,
( ( v1_relat_1 @ ( sk150 @ sk610 ) )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19372:[bind(A,$thf( sk610 ))]]) ).
thf(51,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_finseq_3) ).
thf(2310,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(2311,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[2310]) ).
thf(2312,plain,
! [B: $i,A: $i] :
( ( ( k2_relat_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ B ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A ) ),
inference(lifteq,[status(thm)],[2311]) ).
thf(1919,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(10776,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)],[1919]) ).
thf(727,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(5337,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)],[727]) ).
thf(641,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(4938,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)],[641]) ).
thf(20032,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_lattices @ k1_xboole_0 )
| ( A != sk545 ) ),
inference(paramod_ordered,[status(thm)],[4339,15094]) ).
thf(20033,plain,
( ( v1_relat_1 @ ( sk150 @ sk545 ) )
| ( l1_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20032:[bind(A,$thf( sk545 ))]]) ).
thf(10798,plain,
l1_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(2196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk2 @ C @ B @ A ) @ A )
| ( r1_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2195]) ).
thf(2237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( A != k1_xboole_0 )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(cnf,[status(esa)],[2236]) ).
thf(2239,plain,
! [C: $i,B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(lifteq,[status(thm)],[2237]) ).
thf(2240,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ k1_xboole_0 @ A )
| ~ ( m2_relset_1 @ B @ k1_xboole_0 @ A )
| ( v1_partfun1 @ ( k3_partfun1 @ B @ k1_xboole_0 @ A ) @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[2239]) ).
thf(19734,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk179 ) ),
inference(paramod_ordered,[status(thm)],[4339,4668]) ).
thf(19735,plain,
( ( v1_relat_1 @ ( sk150 @ sk179 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19734:[bind(A,$thf( sk179 ))]]) ).
thf(1961,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(10936,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)],[1961]) ).
thf(488,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(4191,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)],[488]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_relat_1) ).
thf(5588,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
& ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1348,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_0) ).
thf(8132,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1994,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(11046,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)],[1994]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).
thf(4648,plain,
! [A: $i,B: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(330,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_filter_1) ).
thf(3428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1573,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(9288,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)],[1573]) ).
thf(2102,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(11442,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)],[2102]) ).
thf(1211,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(7480,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)],[1211]) ).
thf(2345,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( r4_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) )
=> ( r4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[2344]) ).
thf(2349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ C )
| ~ ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
| ~ ( r2_hidden @ D @ C )
| ( r1_lattices @ A @ D @ B ) ),
inference(cnf,[status(esa)],[2345]) ).
thf(1987,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(11026,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)],[1987]) ).
thf(117,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(2551,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)],[117]) ).
thf(1848,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(10539,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)],[1848]) ).
thf(1198,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(7417,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)],[1198]) ).
thf(1237,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(7577,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( m1_subset_1 @ ( k2_group_4 @ A ) @ k4_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(995,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(6539,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)],[995]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(6946,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(149,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)],[149]) ).
thf(1020,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(6625,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)],[1020]) ).
thf(1312,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(7976,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)],[1312]) ).
thf(1912,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(10752,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)],[1912]) ).
thf(1304,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(7895,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)],[1304]) ).
thf(224,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(2978,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)],[224]) ).
thf(143,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
=> ( m2_subset_1 @ B @ k1_numbers @ k5_numbers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finseq_3) ).
thf(2649,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
=> ( m2_subset_1 @ B @ k1_numbers @ k5_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1409,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(8467,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)],[1409]) ).
thf(1256,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(7682,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)],[1256]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(740,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(5387,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)],[740]) ).
thf(601,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
<=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_1) ).
thf(4736,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) )
=> ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(2049,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(11248,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)],[2049]) ).
thf(886,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(6065,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)],[886]) ).
thf(7749,plain,
v1_finset_1 @ sk385,
inference(cnf,[status(esa)],[7748]) ).
thf(43724,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ k5_numbers )
| ( ( k4_xboole_0 @ k5_numbers @ A )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[43667,14622]) ).
thf(43847,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ k5_numbers )
| ( sk15 != k5_numbers )
| ( A
!= ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[43724]) ).
thf(43903,plain,
( ~ ( v1_xboole_0 @ k5_numbers )
| ( sk15 != k5_numbers ) ),
inference(simp,[status(thm)],[43847]) ).
thf(261,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_filter_0) ).
thf(3115,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1702,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(9900,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)],[1702]) ).
thf(1902,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(10720,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)],[1902]) ).
thf(288,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(3242,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)],[288]) ).
thf(1254,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_0) ).
thf(7668,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1861,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(10575,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)],[1861]) ).
thf(4372,plain,
~ ( v3_struct_0 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ),
inference(cnf,[status(esa)],[4370]) ).
thf(16888,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A
!= ( g1_group_1 @ k1_numbers @ k33_binop_2 ) ) ),
inference(paramod_ordered,[status(thm)],[6758,4372]) ).
thf(16889,plain,
( ~ ( v1_xboole_0 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ) )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16888:[bind(A,$thf( g1_group_1 @ k1_numbers @ k33_binop_2 ))]]) ).
thf(2099,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(11432,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)],[2099]) ).
thf(1445,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( m4_vectsp_8 @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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',d9_vectsp_8) ).
thf(8673,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( ( m4_vectsp_8 @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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 @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ 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 ) ) ) ) )
=> ( m4_vectsp_8 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(19789,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk610 ) ),
inference(paramod_ordered,[status(thm)],[4339,10798]) ).
thf(19790,plain,
( ( v1_relat_1 @ ( sk150 @ sk610 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19789:[bind(A,$thf( sk610 ))]]) ).
thf(1986,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(11023,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)],[1986]) ).
thf(620,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice4) ).
thf(4846,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1321,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(8013,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)],[1321]) ).
thf(16723,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( sk81 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6758,13948]) ).
thf(16724,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( sk81 @ A ) ),
inference(pattern_uni,[status(thm)],[16723:[bind(A,$thf( sk81 @ C )),bind(B,$thf( C ))]]) ).
thf(17170,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( sk81 @ A ) ),
inference(simp,[status(thm)],[16724]) ).
thf(1179,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
thf(7340,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1814,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(10423,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)],[1814]) ).
thf(1250,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(7651,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)],[1250]) ).
thf(1301,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(7878,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)],[1301]) ).
thf(530,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(4384,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)],[530]) ).
thf(10800,plain,
~ ( v3_struct_0 @ sk610 ),
inference(cnf,[status(esa)],[10794]) ).
thf(17053,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk610 ) ),
inference(paramod_ordered,[status(thm)],[6758,10800]) ).
thf(17054,plain,
( ~ ( v1_xboole_0 @ sk610 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[17053:[bind(A,$thf( sk610 ))]]) ).
thf(111,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(2536,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)],[111]) ).
thf(43772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ B @ k5_numbers )
= C )
| ( ( k4_xboole_0 @ k5_numbers @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43667,2343]) ).
thf(43773,plain,
! [A: $i] :
( ( sk12 @ A @ k5_numbers )
= k5_numbers ),
inference(pattern_uni,[status(thm)],[43772:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k5_numbers ))]]) ).
thf(39908,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( l1_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,21513]) ).
thf(39909,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[39908:[bind(A,$thf( sk1 ))]]) ).
thf(39949,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ A ) ),
inference(simp,[status(thm)],[39909]) ).
thf(1887,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(10666,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)],[1887]) ).
thf(154,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(2681,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)],[154]) ).
thf(1936,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(10834,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)],[1936]) ).
thf(683,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(5149,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)],[683]) ).
thf(49,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(2304,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)],[49]) ).
thf(194,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
<=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_1) ).
thf(2836,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v15_lattices @ A )
& ( v15_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(550,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(4508,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)],[550]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
<=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(7014,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(250,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(3059,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)],[250]) ).
thf(936,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(6331,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)],[936]) ).
thf(1104,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(6999,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( v6_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ B @ C @ ( k16_lattice3 @ B @ A ) )
= ( k16_lattice3 @ B @ ( a_3_9_lattice3 @ A @ B @ C ) ) )
& ( ( k3_lattices @ B @ ( k16_lattice3 @ B @ A ) @ C )
= ( k16_lattice3 @ B @ ( a_3_10_lattice3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_lattice3) ).
thf(5380,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( v6_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ B @ C @ ( k16_lattice3 @ B @ A ) )
= ( k16_lattice3 @ B @ ( a_3_9_lattice3 @ A @ B @ C ) ) )
& ( ( k3_lattices @ B @ ( k16_lattice3 @ B @ A ) @ C )
= ( k16_lattice3 @ B @ ( a_3_10_lattice3 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1217,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(7507,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(7508,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[7507]) ).
thf(1056,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(6788,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)],[1056]) ).
thf(397,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(3743,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1906,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(10735,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)],[1906]) ).
thf(403,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(3770,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)],[403]) ).
thf(1699,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_0) ).
thf(9893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(198,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(2851,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)],[198]) ).
thf(62,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(2353,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)],[62]) ).
thf(2354,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[2353]) ).
thf(2355,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[2354]) ).
thf(1212,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(7485,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)],[1212]) ).
thf(1449,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(8690,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)],[1449]) ).
thf(910,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(6211,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)],[910]) ).
thf(1603,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(9448,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)],[1603]) ).
thf(19561,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v2_group_1 @ k1_xboole_0 )
| ( A != sk610 ) ),
inference(paramod_ordered,[status(thm)],[4339,10799]) ).
thf(19562,plain,
( ( v1_relat_1 @ ( sk150 @ sk610 ) )
| ( v2_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19561:[bind(A,$thf( sk610 ))]]) ).
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 @ C )
<=> ( r5_group_3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_group_3) ).
thf(9630,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)],[1638]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_finseq_3 @ A @ B ) )
& ( v1_funct_1 @ ( k1_finseq_3 @ A @ B ) )
& ( v1_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finseq_3) ).
thf(2566,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_finseq_3 @ A @ B ) )
& ( v1_funct_1 @ ( k1_finseq_3 @ A @ B ) )
& ( v1_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1537,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_card_1) ).
thf(9111,plain,
np__0 = k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(9112,plain,
np__0 = k1_xboole_0,
inference(lifteq,[status(thm)],[9111]) ).
thf(1764,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(10207,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)],[1764]) ).
thf(7481,plain,
( ! [A: $i] : ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
& ! [A: $i] : ( m2_finseq_1 @ ( k6_finseq_1 @ A ) @ A ) ),
inference(miniscope,[status(thm)],[7480]) ).
thf(7483,plain,
! [A: $i] : ( v1_xboole_0 @ ( k6_finseq_1 @ A ) ),
inference(cnf,[status(esa)],[7481]) ).
thf(12468,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7483,7184]) ).
thf(12473,plain,
! [B: $i,A: $i] :
( ( k6_finseq_1 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[12468]) ).
thf(1626,axiom,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_finseq_1) ).
thf(9562,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(9563,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[9562]) ).
thf(9564,plain,
! [A: $i] :
( ( k6_finseq_1 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[9563]) ).
thf(13718,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[12473,9564]) ).
thf(1282,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(7789,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)],[1282]) ).
thf(2030,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(11184,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)],[2030]) ).
thf(940,axiom,
! [A: $i,B: $i] :
( ( ( v1_int_1 @ A )
& ( v1_int_1 @ B ) )
=> ( v1_int_1 @ ( k5_int_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_int_1) ).
thf(6346,plain,
! [A: $i,B: $i] :
( ( ( v1_int_1 @ A )
& ( v1_int_1 @ B ) )
=> ( v1_int_1 @ ( k5_int_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(1085,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(6908,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)],[1085]) ).
thf(1779,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(10302,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(325,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(3409,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)],[325]) ).
thf(1875,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(10629,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)],[1875]) ).
thf(630,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(4902,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)],[630]) ).
thf(644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_0) ).
thf(4953,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(2052,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(11261,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)],[2052]) ).
thf(1852,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(10550,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)],[1852]) ).
thf(252,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(3064,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)],[252]) ).
thf(500,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(4259,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)],[500]) ).
thf(1943,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(10866,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)],[1943]) ).
thf(437,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(3920,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)],[437]) ).
thf(2140,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
| ~ ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( l3_lattices @ ( k8_filter_1 @ A @ B ) )
| ( v15_lattices @ B ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(465,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(4086,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)],[465]) ).
thf(1511,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(8980,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)],[1511]) ).
thf(914,axiom,
! [A: $i] :
( ( k1_finseq_3 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_3) ).
thf(6222,plain,
! [A: $i] :
( ( k1_finseq_3 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(6223,plain,
! [A: $i] :
( ( k1_finseq_3 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[6222]) ).
thf(6224,plain,
! [A: $i] :
( ( k1_finseq_3 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[6223]) ).
thf(1710,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(9942,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)],[1710]) ).
thf(256,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(3083,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)],[256]) ).
thf(3200,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(cnf,[status(esa)],[3199]) ).
thf(3201,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[3200]) ).
thf(496,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(4223,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)],[496]) ).
thf(2370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ),
inference(cnf,[status(esa)],[2369]) ).
thf(19594,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != k1_numbers )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,11550]) ).
thf(19595,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != k1_numbers ) ),
inference(pattern_uni,[status(thm)],[19594:[]]) ).
thf(20574,plain,
v1_relat_1 @ ( sk150 @ k1_numbers ),
inference(simp,[status(thm)],[19595]) ).
thf(12944,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk196 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4878,2173]) ).
thf(12945,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk196 @ A ) ),
inference(pattern_uni,[status(thm)],[12944:[bind(A,$thf( sk196 ))]]) ).
thf(12962,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk196 @ A ) ),
inference(simp,[status(thm)],[12945]) ).
thf(524,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(4361,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)],[524]) ).
thf(1808,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(10406,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)],[1808]) ).
thf(1883,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(10651,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)],[1883]) ).
thf(720,axiom,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(5310,plain,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1391,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(8393,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)],[1391]) ).
thf(850,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(5887,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)],[850]) ).
thf(1286,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(7802,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)],[1286]) ).
thf(19738,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,12016]) ).
thf(19739,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[19738:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(20614,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[19739]) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( m1_orders_1 @ B @ A )
| ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[2336]) ).
thf(689,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( r1_xreal_0 @ np__1 @ C )
& ( r1_xreal_0 @ C @ ( k3_finseq_1 @ A ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finseq_1) ).
thf(5170,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
& ! [C: $i] :
( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
=> ( ( ( r1_xreal_0 @ np__1 @ C )
& ( r1_xreal_0 @ C @ ( k3_finseq_1 @ A ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(19497,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk607 ) ),
inference(paramod_ordered,[status(thm)],[4339,10687]) ).
thf(19498,plain,
( ( v1_relat_1 @ ( sk150 @ sk607 ) )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19497:[bind(A,$thf( sk607 ))]]) ).
thf(19458,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk545 ) ),
inference(paramod_ordered,[status(thm)],[4339,15135]) ).
thf(19459,plain,
( ( v1_relat_1 @ ( sk150 @ sk545 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19458:[bind(A,$thf( sk545 ))]]) ).
thf(1478,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(8796,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)],[1478]) ).
thf(670,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(5112,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)],[670]) ).
thf(1143,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(7150,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)],[1143]) ).
thf(414,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(3834,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)],[414]) ).
thf(1926,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(10802,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)],[1926]) ).
thf(2043,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(11216,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)],[2043]) ).
thf(1866,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(10597,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)],[1866]) ).
thf(10815,plain,
~ ( v3_struct_0 @ sk611 ),
inference(cnf,[status(esa)],[10813]) ).
thf(1959,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(10929,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)],[1959]) ).
thf(2003,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E )
<=> ( m1_group_6 @ B @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_latsubgr) ).
thf(11084,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E )
=> ( m1_group_6 @ B @ A @ C ) )
& ( ( m1_group_6 @ B @ A @ C )
=> ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).
thf(583,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(4644,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)],[583]) ).
thf(2019,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(11153,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)],[2019]) ).
thf(509,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(4288,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)],[509]) ).
thf(1789,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(10338,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(173,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relat_1) ).
thf(2761,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1414,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(8482,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)],[1414]) ).
thf(576,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(4625,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)],[576]) ).
thf(1118,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice3) ).
thf(7052,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(565,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(4567,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)],[565]) ).
thf(2208,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk5 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(2013,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(11125,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)],[2013]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(3183,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(626,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(4889,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)],[626]) ).
thf(1871,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(10614,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)],[1871]) ).
thf(1908,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(10740,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)],[1908]) ).
thf(1674,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(9782,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)],[1674]) ).
thf(1388,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(8361,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)],[1388]) ).
thf(266,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(3173,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)],[266]) ).
thf(1521,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(9044,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)],[1521]) ).
thf(10689,plain,
l1_group_1 @ sk607,
inference(cnf,[status(esa)],[10685]) ).
thf(11539,plain,
( ( v1_xboole_0 @ k4_numbers )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,8113]) ).
thf(11546,plain,
k4_numbers != k1_xboole_0,
inference(simp,[status(thm)],[11539]) ).
thf(421,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_filter_0) ).
thf(3856,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(10656,plain,
v3_group_1 @ sk605,
inference(cnf,[status(esa)],[10654]) ).
thf(1039,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(6716,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)],[1039]) ).
thf(1427,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(8559,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)],[1427]) ).
thf(1061,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(6812,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)],[1061]) ).
thf(4355,plain,
v1_finset_1 @ sk152,
inference(cnf,[status(esa)],[4352]) ).
thf(12950,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk152 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4355,2173]) ).
thf(12951,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk152 @ A ) ),
inference(pattern_uni,[status(thm)],[12950:[bind(A,$thf( sk152 ))]]) ).
thf(12966,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk152 @ A ) ),
inference(simp,[status(thm)],[12951]) ).
thf(13507,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ k1_xboole_0 )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ sk152 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2913,12966]) ).
thf(13509,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ k1_xboole_0 )
| ( sk152 != k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[13507]) ).
thf(13512,plain,
( ( v1_finset_1 @ k1_xboole_0 )
| ( sk152 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[13509]) ).
thf(17766,plain,
( ( v1_finset_1 @ k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[13512,15924]) ).
thf(17767,plain,
v1_finset_1 @ k1_xboole_0,
inference(simp,[status(thm)],[17766]) ).
thf(10824,plain,
~ ( v3_struct_0 @ sk612 ),
inference(cnf,[status(esa)],[10823]) ).
thf(16643,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk612 ) ),
inference(paramod_ordered,[status(thm)],[6758,10824]) ).
thf(16644,plain,
( ~ ( v1_xboole_0 @ sk612 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16643:[bind(A,$thf( sk612 ))]]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_enumset1) ).
thf(3999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(2368,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[2367]) ).
thf(1558,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(9213,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)],[1558]) ).
thf(951,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(6378,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)],[951]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) )
<=> ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_1) ).
thf(2402,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) )
=> ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(2035,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(11196,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)],[2035]) ).
thf(1318,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(8004,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)],[1318]) ).
thf(373,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(3639,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)],[373]) ).
thf(89,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(2440,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)],[89]) ).
thf(1033,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(6688,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)],[1033]) ).
thf(78,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(2408,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)],[78]) ).
thf(9898,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[9897]) ).
thf(9899,plain,
~ ( v1_xboole_0 @ sk555 ),
inference(cnf,[status(esa)],[9898]) ).
thf(11553,plain,
( ( v1_xboole_0 @ sk555 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,9899]) ).
thf(11559,plain,
sk555 != k1_xboole_0,
inference(simp,[status(thm)],[11553]) ).
thf(1999,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(11065,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)],[1999]) ).
thf(1015,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(6610,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)],[1015]) ).
thf(19877,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != k4_numbers ) ),
inference(paramod_ordered,[status(thm)],[4339,11546]) ).
thf(19878,plain,
v1_relat_1 @ ( sk150 @ k4_numbers ),
inference(pattern_uni,[status(thm)],[19877:[bind(A,$thf( k4_numbers ))]]) ).
thf(4036,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk118 @ B @ A ) ),
inference(cnf,[status(esa)],[4034]) ).
thf(1794,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(10359,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)],[1794]) ).
thf(1663,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(9744,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)],[1663]) ).
thf(957,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(6400,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)],[957]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_partfun1) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1563,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(9226,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(567,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(4572,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)],[567]) ).
thf(987,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(6497,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)],[987]) ).
thf(2011,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(11120,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)],[2011]) ).
thf(560,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(4550,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)],[560]) ).
thf(1622,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(9545,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)],[1622]) ).
thf(1854,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(10556,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)],[1854]) ).
thf(1647,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(9677,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)],[1647]) ).
thf(1727,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(10030,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)],[1727]) ).
thf(215,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(2941,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v3_filter_0 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_lattice4 @ C @ B @ A )
| ~ ( v3_lattice4 @ C @ B @ A )
| ( r1_lattice4 @ B @ A @ C ) ),
inference(cnf,[status(esa)],[2120]) ).
thf(30,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_finseq_1) ).
thf(2234,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2235,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ),
inference(cnf,[status(esa)],[2234]) ).
thf(1970,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(10978,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)],[1970]) ).
thf(795,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(5679,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)],[795]) ).
thf(947,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(6368,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1606,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(9484,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)],[1606]) ).
thf(1657,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_0) ).
thf(9726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_enumset1) ).
thf(4919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(882,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(6053,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(805,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(5722,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)],[805]) ).
thf(2007,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(11110,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)],[2007]) ).
thf(989,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(6507,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)],[989]) ).
thf(2028,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(11179,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)],[2028]) ).
thf(1501,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(8903,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)],[1501]) ).
thf(596,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(4708,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(4673,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk180 @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[4670]) ).
thf(4684,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk180 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[4673]) ).
thf(4685,plain,
! [A: $i] : ( r1_tarski @ ( k2_relat_1 @ ( sk180 @ k1_xboole_0 @ A ) ) @ A ),
inference(simp,[status(thm)],[4684]) ).
thf(21799,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v3_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,19614]) ).
thf(21800,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v3_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[21799:[]]) ).
thf(47,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(2289,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)],[47]) ).
thf(2292,plain,
! [B: $i,A: $i] :
( ~ ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
| ~ ( v1_int_1 @ B )
| ( r1_xreal_0 @ B @ A )
| ( r1_xreal_0 @ np__1 @ ( sk6 @ B @ A ) ) ),
inference(cnf,[status(esa)],[2289]) ).
thf(1669,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).
thf(9765,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( k9_domain_1 @ A @ B @ C @ D @ E )
= ( k2_enumset1 @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(3362,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[3361]) ).
thf(3364,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[3362]) ).
thf(3365,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ),
inference(simp,[status(thm)],[3364]) ).
thf(14497,plain,
! [A: $i] :
( ( k2_relat_1 @ ( k6_partfun1 @ A ) )
= A ),
inference(rewrite,[status(thm)],[3365,10471]) ).
thf(1239,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(7582,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)],[1239]) ).
thf(41076,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ B @ A )
= C )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2254,2343]) ).
thf(41077,plain,
! [A: $i] :
( ( sk12 @ k1_xboole_0 @ A )
= A ),
inference(pattern_uni,[status(thm)],[41076:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(1137,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(7128,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)],[1137]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(6615,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(125,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(2585,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)],[125]) ).
thf(1219,axiom,
? [A: $i] : ( l1_vectsp_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(7511,plain,
? [A: $i] : ( l1_vectsp_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(7512,plain,
l1_vectsp_1 @ sk370,
inference(cnf,[status(esa)],[7511]) ).
thf(1612,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(9502,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)],[1612]) ).
thf(163,axiom,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(2714,plain,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2717,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2714]) ).
thf(750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( C
= ( k8_filter_0 @ A @ B ) )
<=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).
thf(5451,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( C
= ( k8_filter_0 @ A @ B ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) ) )
& ( ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) )
=> ( C
= ( k8_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(363,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(3607,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)],[363]) ).
thf(1107,axiom,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_1) ).
thf(7009,plain,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(7010,plain,
! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
inference(cnf,[status(esa)],[7009]) ).
thf(758,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(5508,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)],[758]) ).
thf(1738,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(10079,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)],[1738]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(8906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(587,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(4657,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(2018,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(11148,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)],[2018]) ).
thf(1515,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(9021,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)],[1515]) ).
thf(1985,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(11016,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)],[1985]) ).
thf(1656,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(9721,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)],[1656]) ).
thf(1976,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(10993,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)],[1976]) ).
thf(19364,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v7_group_1 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[4339,5878]) ).
thf(19365,plain,
( ( v1_relat_1 @ ( sk150 @ sk259 ) )
| ( v7_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19364:[bind(A,$thf( sk259 ))]]) ).
thf(867,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(6001,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)],[867]) ).
thf(533,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( m1_filter_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_1) ).
thf(4393,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( m1_filter_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) )
=> ( m1_filter_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(977,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(6469,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)],[977]) ).
thf(614,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(4797,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)],[614]) ).
thf(1813,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(10420,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)],[1813]) ).
thf(344,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(3523,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1147,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( B
= ( k16_lattice3 @ A @ C ) )
<=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
thf(7165,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( B
= ( k16_lattice3 @ A @ C ) )
=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) )
& ( ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) )
=> ( B
= ( k16_lattice3 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(657,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(5016,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)],[657]) ).
thf(35610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ B @ D )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k4_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19272,2260]) ).
thf(35611,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k4_numbers ) @ k5_numbers ),
inference(pattern_uni,[status(thm)],[35610:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ E @ k4_numbers )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(35670,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k4_numbers ) @ k5_numbers ),
inference(simp,[status(thm)],[35611]) ).
thf(1998,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(11063,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)],[1998]) ).
thf(260,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(3111,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)],[260]) ).
thf(1456,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(8718,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)],[1456]) ).
thf(1281,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(7785,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m1_relset_1 @ B @ A @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m1_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
& ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1133,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(7118,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(383,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(3686,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)],[383]) ).
thf(1643,axiom,
! [A: $i] :
( ( r2_wellord2 @ A @ k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_card_1) ).
thf(9650,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)],[1643]) ).
thf(385,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(3696,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)],[385]) ).
thf(12777,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6559,12016]) ).
thf(12778,plain,
( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12777:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1873,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(10625,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)],[1873]) ).
thf(1523,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(9049,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)],[1523]) ).
thf(985,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(6492,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)],[985]) ).
thf(12099,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5730,8888]) ).
thf(12107,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[12099]) ).
thf(20149,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,12107]) ).
thf(20150,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[20149:[bind(A,$thf( k1_tarski @ C )),bind(B,$thf( C ))]]) ).
thf(20720,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[20150]) ).
thf(815,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(5758,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)],[815]) ).
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] :
( ( ( 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(9974,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)],[1719]) ).
thf(1156,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(7212,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)],[1156]) ).
thf(525,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(4365,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)],[525]) ).
thf(1481,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(8807,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(1503,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(8909,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)],[1503]) ).
thf(2069,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(11323,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)],[2069]) ).
thf(1546,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(9157,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)],[1546]) ).
thf(863,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(5984,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
thf(5535,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1888,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(10668,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)],[1888]) ).
thf(897,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(6140,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)],[897]) ).
thf(1981,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(11006,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)],[1981]) ).
thf(461,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(4039,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(4040,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(cnf,[status(esa)],[4039]) ).
thf(4041,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(lifteq,[status(thm)],[4040]) ).
thf(1146,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(7162,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)],[1146]) ).
thf(1322,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(8015,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)],[1322]) ).
thf(652,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).
thf(4998,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1756,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(10155,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)],[1756]) ).
thf(396,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(3741,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)],[396]) ).
thf(588,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(4662,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)],[588]) ).
thf(2090,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(11396,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)],[2090]) ).
thf(1265,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(7714,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)],[1265]) ).
thf(504,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(4268,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)],[504]) ).
thf(285,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(3234,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)],[285]) ).
thf(2107,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(11455,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)],[2107]) ).
thf(439,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(3925,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)],[439]) ).
thf(200,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( k3_finseq_1 @ A )
= np__0 )
<=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finseq_1) ).
thf(2859,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( ( k3_finseq_1 @ A )
= np__0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( k3_finseq_1 @ A )
= np__0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(214,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(2938,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)],[214]) ).
thf(1247,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattices) ).
thf(7639,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(1018,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_0) ).
thf(6617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(507,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(4283,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)],[507]) ).
thf(752,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(5488,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)],[752]) ).
thf(464,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(4077,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)],[464]) ).
thf(1215,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(7497,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)],[1215]) ).
thf(33764,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ B )
| ( l1_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,21519]) ).
thf(33765,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[33764:[bind(A,$thf( sk1 ))]]) ).
thf(33769,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( l1_group_1 @ A ) ),
inference(simp,[status(thm)],[33765]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v6_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_3_9_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_9_lattice3) ).
thf(6510,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v6_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_9_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ A @ ( a_3_9_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(409,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(3811,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)],[409]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_partfun1) ).
thf(2789,plain,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(2790,plain,
! [B: $i,A: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2789]) ).
thf(2791,plain,
! [B: $i,A: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2790]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_relat_1) ).
thf(6312,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( ( k5_relat_1 @ C @ B )
= ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
& ( ( k5_relat_1 @ B @ D )
= ( k6_relat_1 @ A ) ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1160,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(7233,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)],[1160]) ).
thf(1967,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(10963,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)],[1967]) ).
thf(516,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(4309,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)],[516]) ).
thf(1410,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(8470,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)],[1410]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(2187,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2188,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_filter_0 @ B @ A )
| ~ ( m1_filter_0 @ C @ A )
| ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
inference(cnf,[status(esa)],[2187]) ).
thf(673,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(5121,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)],[673]) ).
thf(2489,plain,
v3_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ),
inference(cnf,[status(esa)],[2488]) ).
thf(1123,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(7073,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)],[1123]) ).
thf(1138,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(7134,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)],[1138]) ).
thf(1516,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(9025,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)],[1516]) ).
thf(1273,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(7751,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)],[1273]) ).
thf(1202,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(7440,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)],[1202]) ).
thf(862,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(5940,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)],[862]) ).
thf(31713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ B @ D )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k4_numbers ) )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19265,2260]) ).
thf(31714,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k1_numbers ) @ k4_numbers ),
inference(pattern_uni,[status(thm)],[31713:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ E @ k1_numbers )),bind(C,$thf( E )),bind(D,$thf( k4_numbers ))]]) ).
thf(31778,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k1_numbers ) @ k4_numbers ),
inference(simp,[status(thm)],[31714]) ).
thf(1499,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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_lattice4 @ C @ A @ B )
<=> ( v2_funct_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice4) ).
thf(8894,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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_lattice4 @ C @ A @ B )
=> ( v2_funct_1 @ C ) )
& ( ( v2_funct_1 @ C )
=> ( v1_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(1346,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(8124,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)],[1346]) ).
thf(1618,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(9531,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)],[1618]) ).
thf(836,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(5831,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)],[836]) ).
thf(916,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(6229,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)],[916]) ).
thf(1576,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(9295,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)],[1576]) ).
thf(574,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(4605,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)],[574]) ).
thf(665,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(5099,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)],[665]) ).
thf(1552,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(9189,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)],[1552]) ).
thf(5876,plain,
v8_vectsp_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(227,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_filter_0) ).
thf(2991,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(359,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice3) ).
thf(3590,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(75,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(2398,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1819,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(10435,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)],[1819]) ).
thf(2716,plain,
v1_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2714]) ).
thf(529,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(4381,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)],[529]) ).
thf(732,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(5350,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)],[732]) ).
thf(1945,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(10874,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)],[1945]) ).
thf(826,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(5799,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)],[826]) ).
thf(1682,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(9820,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)],[1682]) ).
thf(1713,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(9952,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)],[1713]) ).
thf(19813,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk545 ) ),
inference(paramod_ordered,[status(thm)],[4339,9761]) ).
thf(19814,plain,
( ( v1_relat_1 @ ( sk150 @ sk545 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19813:[bind(A,$thf( sk545 ))]]) ).
thf(191,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(2827,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)],[191]) ).
thf(12946,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk385 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7749,2173]) ).
thf(12947,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk385 @ A ) ),
inference(pattern_uni,[status(thm)],[12946:[bind(A,$thf( sk385 ))]]) ).
thf(12964,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk385 @ A ) ),
inference(simp,[status(thm)],[12947]) ).
thf(549,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(4505,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1637,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(9627,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)],[1637]) ).
thf(1114,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(7038,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)],[1114]) ).
thf(1284,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_1) ).
thf(7795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(555,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(4526,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)],[555]) ).
thf(19053,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk37 @ A ) )
!= ( v1_xboole_0 @ ( sk81 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2758,17170]) ).
thf(19058,plain,
! [B: $i,A: $i] :
( ( sk37 @ A )
!= ( sk81 @ B ) ),
inference(simp,[status(thm)],[19053]) ).
thf(22113,plain,
! [A: $i] :
( ( sk81 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[19058,17354]) ).
thf(2083,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(11370,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)],[2083]) ).
thf(374,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_0) ).
thf(3641,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
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 @ ( 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(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 @ ( 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)],[1238]) ).
thf(1373,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(8244,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)],[1373]) ).
thf(20935,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,20924]) ).
thf(20936,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20935:[]]) ).
thf(32780,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ B )
| ( v3_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,20936]) ).
thf(32781,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[32780:[bind(A,$thf( sk1 ))]]) ).
thf(32785,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A ) ),
inference(simp,[status(thm)],[32781]) ).
thf(1468,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(8767,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)],[1468]) ).
thf(20,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(2192,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2193,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v13_lattices @ A )
| ~ ( v14_lattices @ A )
| ( v15_lattices @ A ) ),
inference(cnf,[status(esa)],[2192]) ).
thf(26168,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ ( k1_card_1 @ A ) @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[8704,9072]) ).
thf(26183,plain,
! [B: $i,A: $i] :
( ( ( k1_card_1 @ A )
!= B )
| ( ( k1_card_1 @ ( k1_zfmisc_1 @ A ) )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[26168]) ).
thf(26188,plain,
! [A: $i] :
( ( k1_card_1 @ ( k1_zfmisc_1 @ A ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26183]) ).
thf(26492,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k1_card_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4339,26188]) ).
thf(26493,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[26492:[bind(A,$thf( k1_card_1 @ ( k1_zfmisc_1 @ D ) )),bind(B,$thf( D ))]]) ).
thf(26512,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(simp,[status(thm)],[26493]) ).
thf(262,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(3118,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)],[262]) ).
thf(475,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(4127,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)],[475]) ).
thf(486,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(4186,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)],[486]) ).
thf(56,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(2326,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)],[56]) ).
thf(1425,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(8549,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)],[1425]) ).
thf(2291,plain,
! [B: $i,A: $i] :
( ~ ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
| ~ ( v1_int_1 @ B )
| ( r1_xreal_0 @ B @ A )
| ( ( sk6 @ B @ A )
= ( k6_xcmplx_0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[2289]) ).
thf(2293,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ B @ A )
= ( k6_xcmplx_0 @ B @ A ) )
| ~ ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
| ~ ( v1_int_1 @ B )
| ( r1_xreal_0 @ B @ A ) ),
inference(lifteq,[status(thm)],[2291]) ).
thf(2308,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v15_lattices @ A )
| ( v13_lattices @ A ) ),
inference(cnf,[status(esa)],[2306]) ).
thf(655,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(5011,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)],[655]) ).
thf(393,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
<=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_1) ).
thf(3726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v14_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v14_lattices @ A )
& ( v14_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(618,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(4837,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)],[618]) ).
thf(5880,plain,
v4_group_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(20004,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[4339,5880]) ).
thf(20005,plain,
( ( v1_relat_1 @ ( sk150 @ sk259 ) )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20004:[bind(A,$thf( sk259 ))]]) ).
thf(1491,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(8841,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)],[1491]) ).
thf(1917,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(10770,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)],[1917]) ).
thf(1259,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 ) )
=> ( ( k1_funct_1 @ ( k1_latsubgr @ A ) @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).
thf(7689,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 ) )
=> ( ( k1_funct_1 @ ( k1_latsubgr @ A ) @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(843,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(5859,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)],[843]) ).
thf(1494,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(8862,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)],[1494]) ).
thf(476,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(4149,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)],[476]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
thf(5331,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
=> ( ( k1_funct_1 @ C @ B )
= ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(714,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(5282,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)],[714]) ).
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 @ ( 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(8359,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)],[1387]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice3) ).
thf(6091,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1732,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(10051,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)],[1732]) ).
thf(927,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(6302,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)],[927]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ C @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_enumset1) ).
thf(4764,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ C @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1673,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(9776,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)],[1673]) ).
thf(1126,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(7094,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)],[1126]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_partfun1) ).
thf(2442,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(694,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(5190,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)],[694]) ).
thf(1382,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(8344,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)],[1382]) ).
thf(1285,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(7800,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1023,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(6638,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)],[1023]) ).
thf(1624,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(9555,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)],[1624]) ).
thf(41070,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ A @ ( k1_orders_1 @ k1_xboole_0 ) )
= B )
| ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29366,2343]) ).
thf(41071,plain,
( ( sk12 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_orders_1 @ k1_xboole_0 ) )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[41070:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(1610,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(9496,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)],[1610]) ).
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 @ ( 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(7671,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)],[1255]) ).
thf(1208,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice4) ).
thf(7465,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1141,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(7145,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)],[1141]) ).
thf(413,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(3832,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)],[413]) ).
thf(10,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice4) ).
thf(2165,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v3_filter_0 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_lattice4 @ C @ B @ A )
| ~ ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
| ~ ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
| ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ),
inference(cnf,[status(esa)],[2165]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(6636,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1206,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(7455,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)],[1206]) ).
thf(15886,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[6758,5874]) ).
thf(15887,plain,
( ~ ( v1_xboole_0 @ sk259 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15886:[bind(A,$thf( sk259 ))]]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(3619,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1106,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(7006,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)],[1106]) ).
thf(84,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relat_1) ).
thf(2425,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1574,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(9290,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)],[1574]) ).
thf(937,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [H: $i] :
( ( ( v1_funct_1 @ H )
& ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
= ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_1) ).
thf(6334,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [H: $i] :
( ( ( v1_funct_1 @ H )
& ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
= ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(5993,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[5992]) ).
thf(5996,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[5993]) ).
thf(5997,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[5996]) ).
thf(949,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6372,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(14834,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk605 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10655,4719]) ).
thf(14835,plain,
l1_struct_0 @ sk605,
inference(pattern_uni,[status(thm)],[14834:[bind(A,$thf( sk605 ))]]) ).
thf(310,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(3355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1964,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(10953,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)],[1964]) ).
thf(121,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( m2_finseq_1 @ A @ B )
=> ( m2_finseq_1 @ ( k1_finseq_3 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_finseq_3) ).
thf(2573,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( m2_finseq_1 @ A @ B )
=> ( m2_finseq_1 @ ( k1_finseq_3 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l1_struct_0 @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(cnf,[status(esa)],[2317]) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) )
| ( v3_struct_0 @ A )
| ~ ( l1_struct_0 @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ),
inference(lifteq,[status(thm)],[2318]) ).
thf(1991,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(11038,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)],[1991]) ).
thf(2357,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[2356]) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[2357]) ).
thf(782,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(5634,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)],[782]) ).
thf(771,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(5580,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(19740,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4339,14666]) ).
thf(19741,plain,
v1_relat_1 @ ( sk150 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(pattern_uni,[status(thm)],[19740:[bind(A,$thf( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ))]]) ).
thf(881,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(6048,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)],[881]) ).
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 )
& ( 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(7837,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)],[1293]) ).
thf(1403,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(8445,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)],[1403]) ).
thf(19559,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l2_lattices @ k1_xboole_0 )
| ( A != sk261 ) ),
inference(paramod_ordered,[status(thm)],[4339,5914]) ).
thf(19560,plain,
( ( v1_relat_1 @ ( sk150 @ sk261 ) )
| ( l2_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19559:[bind(A,$thf( sk261 ))]]) ).
thf(216,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(2945,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)],[216]) ).
thf(7632,plain,
! [A: $i] : ( m1_finseq_1 @ ( sk378 @ A ) @ A ),
inference(cnf,[status(esa)],[7631]) ).
thf(2024,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(11169,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)],[2024]) ).
thf(1316,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(7995,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)],[1316]) ).
thf(18432,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16068]) ).
thf(18439,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[18432]) ).
thf(21387,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6758,18439]) ).
thf(21388,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21387:[]]) ).
thf(1144,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7158,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(899,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(6144,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)],[899]) ).
thf(380,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(3678,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)],[380]) ).
thf(1224,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattices) ).
thf(7529,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(1939,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(10842,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)],[1939]) ).
thf(846,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(5870,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)],[846]) ).
thf(611,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(4790,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(165,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(2721,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)],[165]) ).
thf(2115,plain,
( ( k3_latsubgr @ sk1 @ sk1 @ ( k6_partfun1 @ ( u1_struct_0 @ sk1 ) ) )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[2113]) ).
thf(2119,plain,
( ( k3_latsubgr @ sk1 @ sk1 @ ( k6_partfun1 @ ( u1_struct_0 @ sk1 ) ) )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) ),
inference(lifteq,[status(thm)],[2115]) ).
thf(1406,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(8452,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(884,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(6059,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)],[884]) ).
thf(7801,plain,
v1_xboole_0 @ sk388,
inference(cnf,[status(esa)],[7800]) ).
thf(14660,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ sk388 ) ),
inference(paramod_ordered,[status(thm)],[7801,14622]) ).
thf(14671,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk388 ),
inference(simp,[status(thm)],[14660]) ).
thf(15069,plain,
! [A: $i] :
( ( A != sk388 )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2254,14671]) ).
thf(15072,plain,
( ( k4_xboole_0 @ sk388 @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[15069]) ).
thf(21714,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk388 ),
inference(rewrite,[status(thm)],[15072,2254]) ).
thf(1631,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(9575,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)],[1631]) ).
thf(1958,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(10921,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)],[1958]) ).
thf(700,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(5212,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)],[700]) ).
thf(638,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(4929,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)],[638]) ).
thf(1091,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(6942,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)],[1091]) ).
thf(1816,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(10429,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)],[1816]) ).
thf(1823,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(10448,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)],[1823]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(4228,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1782,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(10317,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)],[1782]) ).
thf(1242,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(7594,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)],[1242]) ).
thf(454,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_0) ).
thf(3996,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(112,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(2538,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)],[112]) ).
thf(1280,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(7783,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(929,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(6308,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)],[929]) ).
thf(792,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(5671,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)],[792]) ).
thf(1954,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(10910,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)],[1954]) ).
thf(1016,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(6613,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(99,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(2478,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)],[99]) ).
thf(291,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(3251,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)],[291]) ).
thf(45539,plain,
! [B: $i,A: $i] :
( ( r1_xboole_0 @ k4_numbers @ A )
!= ( r1_xboole_0 @ ( k1_tarski @ B ) @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45536,9277]) ).
thf(45554,plain,
! [B: $i,A: $i] :
( ( ( k1_tarski @ B )
!= k4_numbers )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(simp,[status(thm)],[45539]) ).
thf(45557,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k4_numbers ),
inference(simp,[status(thm)],[45554]) ).
thf(2010,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(11117,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)],[2010]) ).
thf(757,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(5506,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)],[757]) ).
thf(24,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(2214,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)],[24]) ).
thf(1455,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattices) ).
thf(8715,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(72,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k1_finseq_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_finseq_3) ).
thf(2383,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k1_finseq_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(901,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(6179,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)],[901]) ).
thf(1479,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(8799,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)],[1479]) ).
thf(13337,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk385 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12964,2173]) ).
thf(13338,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk385 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[13337:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk385 @ E )),bind(C,$thf( C ))]]) ).
thf(13343,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk385 @ B ) @ A ) ),
inference(simp,[status(thm)],[13338]) ).
thf(762,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(5520,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)],[762]) ).
thf(1349,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(8135,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)],[1349]) ).
thf(1703,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattices) ).
thf(9903,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(514,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(4303,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(4305,plain,
v1_funct_1 @ sk145,
inference(cnf,[status(esa)],[4303]) ).
thf(900,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(6147,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)],[900]) ).
thf(445,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(3957,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)],[445]) ).
thf(1889,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(10675,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)],[1889]) ).
thf(296,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(3287,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)],[296]) ).
thf(1062,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(6815,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)],[1062]) ).
thf(19944,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[4339,14835]) ).
thf(19945,plain,
( ( v1_relat_1 @ ( sk150 @ sk605 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19944:[bind(A,$thf( sk605 ))]]) ).
thf(327,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(3419,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)],[327]) ).
thf(19869,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk555 ) ),
inference(paramod_ordered,[status(thm)],[4339,11559]) ).
thf(19870,plain,
v1_relat_1 @ ( sk150 @ sk555 ),
inference(pattern_uni,[status(thm)],[19869:[bind(A,$thf( sk555 ))]]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_enumset1) ).
thf(4914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ B @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(593,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(4699,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)],[593]) ).
thf(1345,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(8120,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)],[1345]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_lattice3) ).
thf(7328,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) )
=> ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(295,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_1) ).
thf(3270,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(2283,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 )
| ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ),
inference(cnf,[status(esa)],[2282]) ).
thf(2284,plain,
! [A: $i] :
( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ),
inference(lifteq,[status(thm)],[2283]) ).
thf(35,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(2255,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)],[35]) ).
thf(2256,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(cnf,[status(esa)],[2255]) ).
thf(2257,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(lifteq,[status(thm)],[2256]) ).
thf(1522,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(9047,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)],[1522]) ).
thf(2244,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( ( k1_finseq_3 @ A @ B )
!= k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) ),
inference(cnf,[status(esa)],[2243]) ).
thf(2246,plain,
! [B: $i,A: $i] :
( ( ( k1_finseq_3 @ A @ B )
!= k1_xboole_0 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) ),
inference(lifteq,[status(thm)],[2244]) ).
thf(1450,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(8693,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(1857,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(10564,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)],[1857]) ).
thf(1375,axiom,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_setfam_1) ).
thf(8254,plain,
! [A: $i,B: $i] :
( ( r2_setfam_1 @ B @ A )
=> ( ( A = k1_xboole_0 )
| ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1707,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(9920,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)],[1707]) ).
thf(1629,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice4) ).
thf(9570,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(495,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).
thf(4213,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(13326,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk196 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12962,2173]) ).
thf(13327,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk196 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[13326:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk196 @ E )),bind(C,$thf( C ))]]) ).
thf(13334,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk196 @ B ) @ A ) ),
inference(simp,[status(thm)],[13327]) ).
thf(2081,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(11365,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)],[2081]) ).
thf(1428,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_0) ).
thf(8561,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(253,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(3066,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)],[253]) ).
thf(358,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(3586,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)],[358]) ).
thf(1186,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(7362,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)],[1186]) ).
thf(1745,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(10115,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(2101,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(11438,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)],[2101]) ).
thf(912,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(6216,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)],[912]) ).
thf(531,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(4388,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)],[531]) ).
thf(558,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(4541,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)],[558]) ).
thf(233,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(3006,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)],[233]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_4) ).
thf(2928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1969,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(10970,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)],[1969]) ).
thf(1775,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(10265,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)],[1775]) ).
thf(190,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(2824,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)],[190]) ).
thf(492,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_0) ).
thf(4203,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(2182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) ) ),
inference(cnf,[status(esa)],[2181]) ).
thf(1216,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(7504,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)],[1216]) ).
thf(759,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(5511,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)],[759]) ).
thf(580,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(4635,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(5114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
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] :
( ( ( 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(8735,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)],[1459]) ).
thf(831,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(5816,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)],[831]) ).
thf(1543,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v2_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_0) ).
thf(9129,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v2_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( v2_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(698,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(5202,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)],[698]) ).
thf(1691,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_0) ).
thf(9857,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(1277,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(7768,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)],[1277]) ).
thf(1363,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(8192,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)],[1363]) ).
thf(858,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(5920,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)],[858]) ).
thf(14838,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk335 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7005,4719]) ).
thf(14839,plain,
l1_struct_0 @ sk335,
inference(pattern_uni,[status(thm)],[14838:[bind(A,$thf( sk335 ))]]) ).
thf(239,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( m1_lattice4 @ C @ A @ B )
<=> ( ( m4_vectsp_8 @ C @ A @ B )
& ( m3_vectsp_8 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_vectsp_8) ).
thf(3027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ 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 ) ) )
=> ( ( ( m1_lattice4 @ C @ A @ B )
=> ( ( m4_vectsp_8 @ C @ A @ B )
& ( m3_vectsp_8 @ C @ A @ B ) ) )
& ( ( ( m4_vectsp_8 @ C @ A @ B )
& ( m3_vectsp_8 @ C @ A @ B ) )
=> ( m1_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1797,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(10375,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)],[1797]) ).
thf(625,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(4882,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)],[625]) ).
thf(2314,plain,
! [B: $i,A: $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(cnf,[status(esa)],[2313]) ).
thf(2129,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v15_lattices @ A ) ),
inference(cnf,[status(esa)],[2123]) ).
thf(1131,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(7113,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)],[1131]) ).
thf(1928,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(10810,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)],[1928]) ).
thf(851,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(5894,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)],[851]) ).
thf(9651,plain,
( ! [A: $i] :
( ( r2_wellord2 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( r2_wellord2 @ A @ k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[9650]) ).
thf(9652,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( r2_wellord2 @ A @ k1_xboole_0 ) ),
inference(cnf,[status(esa)],[9651]) ).
thf(9654,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( r2_wellord2 @ A @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[9652]) ).
thf(9655,plain,
r2_wellord2 @ k1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[9654]) ).
thf(1529,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(9079,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)],[1529]) ).
thf(542,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(4462,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)],[542]) ).
thf(255,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(3073,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)],[255]) ).
thf(1442,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(8661,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)],[1442]) ).
thf(20000,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ sk1 )
| ( l1_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,15978]) ).
thf(20001,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ sk1 )
| ( l1_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[20000:[]]) ).
thf(2095,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(11419,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)],[2095]) ).
thf(2039,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(11205,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)],[2039]) ).
thf(1234,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 ) )
=> ( ( u1_struct_0 @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsubgr) ).
thf(7566,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 ) )
=> ( ( u1_struct_0 @ ( k9_group_2 @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1640,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(9642,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)],[1640]) ).
thf(2000,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(11073,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)],[2000]) ).
thf(406,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(3800,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)],[406]) ).
thf(502,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(4264,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)],[502]) ).
thf(29608,plain,
! [B: $i,A: $i] :
( ( r1_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ B )
| ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29366,2288]) ).
thf(29609,plain,
r1_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[29608:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(29891,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A )
| ( ( r1_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( r1_xboole_0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29609,2176]) ).
thf(29892,plain,
( ( k4_xboole_0 @ ( k2_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_orders_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[29891:[bind(A,$thf( k1_orders_1 @ k1_xboole_0 )),bind(B,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(41092,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ A @ ( k1_orders_1 @ k1_xboole_0 ) )
= B )
| ( ( k4_xboole_0 @ ( k2_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( k4_xboole_0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29892,2343]) ).
thf(41093,plain,
( ( sk12 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_orders_1 @ k1_xboole_0 ) )
= ( k2_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[41092:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k2_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ))]]) ).
thf(41235,plain,
( ( k2_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[41093,41071]) ).
thf(353,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(3572,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)],[353]) ).
thf(441,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(3932,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)],[441]) ).
thf(1461,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice3) ).
thf(8750,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) )
& ( ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1113,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_0) ).
thf(7033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) )
& ( ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(2020,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(11156,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)],[2020]) ).
thf(2021,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(11158,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)],[2021]) ).
thf(1313,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(7978,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)],[1313]) ).
thf(1666,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(9756,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)],[1666]) ).
thf(1941,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(10847,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)],[1941]) ).
thf(1750,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(10136,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)],[1750]) ).
thf(1047,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(6747,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)],[1047]) ).
thf(788,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(5656,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)],[788]) ).
thf(933,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(6319,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)],[933]) ).
thf(966,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(6429,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(512,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(4296,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)],[512]) ).
thf(1474,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(8782,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)],[1474]) ).
thf(1300,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(7869,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)],[1300]) ).
thf(1834,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(10489,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)],[1834]) ).
thf(447,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(3971,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)],[447]) ).
thf(357,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(3583,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)],[357]) ).
thf(1693,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(9862,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)],[1693]) ).
thf(1810,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(10412,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)],[1810]) ).
thf(1759,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(10172,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)],[1759]) ).
thf(1070,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(6847,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)],[1070]) ).
thf(1617,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(9528,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)],[1617]) ).
thf(1614,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(9511,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)],[1614]) ).
thf(434,axiom,
( ( k4_card_1 @ k1_xboole_0 )
= np__0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_card_1) ).
thf(3913,plain,
( ( k4_card_1 @ k1_xboole_0 )
= np__0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(3914,plain,
( ( k4_card_1 @ k1_xboole_0 )
= np__0 ),
inference(lifteq,[status(thm)],[3913]) ).
thf(11814,plain,
( ( k4_card_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[3914,9112]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(2664,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(30925,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk610 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,17054]) ).
thf(30938,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk610 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[30925]) ).
thf(2278,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( v1_funct_1 @ ( k1_realset1 @ B @ C ) ) ),
inference(cnf,[status(esa)],[2275]) ).
thf(1564,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(9228,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)],[1564]) ).
thf(2327,plain,
~ ? [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(miniscope,[status(thm)],[2326]) ).
thf(2328,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(cnf,[status(esa)],[2327]) ).
thf(2329,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(lifteq,[status(thm)],[2328]) ).
thf(2084,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(11375,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)],[2084]) ).
thf(1827,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(10467,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)],[1827]) ).
thf(861,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(5931,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)],[861]) ).
thf(2048,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(11245,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)],[2048]) ).
thf(988,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(6504,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)],[988]) ).
thf(444,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_1) ).
thf(3953,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1535,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).
thf(9106,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(2076,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(11342,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)],[2076]) ).
thf(2297,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ( m1_subset_1 @ ( sk9 @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(2303,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ( m1_subset_1 @ ( sk9 @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[2297]) ).
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 )
=> ! [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(9762,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)],[1668]) ).
thf(1807,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(10402,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)],[1807]) ).
thf(1319,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(8007,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)],[1319]) ).
thf(339,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3480,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(2065,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(11310,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)],[2065]) ).
thf(348,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(3539,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)],[348]) ).
thf(920,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(6255,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)],[920]) ).
thf(616,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(4832,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)],[616]) ).
thf(599,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(4720,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)],[599]) ).
thf(1007,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(6574,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)],[1007]) ).
thf(2362,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_subset_1 @ C @ A )
| ( ( k1_binop_1 @ B @ C @ C )
= C ) ),
inference(cnf,[status(esa)],[2361]) ).
thf(2365,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ C @ C )
= C )
| ~ ( 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 )
| ~ ( m1_subset_1 @ C @ A ) ),
inference(lifteq,[status(thm)],[2362]) ).
thf(32452,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ B )
| ( v4_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,19124]) ).
thf(32453,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[32452:[bind(A,$thf( sk1 ))]]) ).
thf(32457,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ A )
| ( v4_group_1 @ A ) ),
inference(simp,[status(thm)],[32453]) ).
thf(1664,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(9751,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)],[1664]) ).
thf(2346,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( m1_subset_1 @ ( sk13 @ C @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2345]) ).
thf(2350,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( m1_subset_1 @ ( sk13 @ C @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[2346]) ).
thf(1636,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(9619,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)],[1636]) ).
thf(1821,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(10444,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)],[1821]) ).
thf(2205,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( k1_binop_1 @ C @ ( sk4 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk4 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) ) )
| ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ ( sk3 @ C @ B @ A ) @ ( sk4 @ C @ B @ A ) ) @ ( sk5 @ C @ B @ A ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk4 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) ) )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(2212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( k1_binop_1 @ C @ ( sk4 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk4 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) ) )
| ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ ( sk3 @ C @ B @ A ) @ ( sk4 @ C @ B @ A ) ) @ ( sk5 @ C @ B @ A ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk3 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk4 @ C @ B @ A ) @ ( sk5 @ C @ B @ A ) ) ) )
| ~ ( 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_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 ) ),
inference(lifteq,[status(thm)],[2205]) ).
thf(1408,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(8456,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)],[1408]) ).
thf(369,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_1) ).
thf(3627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1432,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(8588,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)],[1432]) ).
thf(1471,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(8776,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(1992,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(11041,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)],[1992]) ).
thf(1841,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(10514,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)],[1841]) ).
thf(1662,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattices) ).
thf(9741,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(751,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(5482,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)],[751]) ).
thf(1849,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(10544,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)],[1849]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattice3 @ B @ C @ A )
<=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice3) ).
thf(4502,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattice3 @ B @ C @ A )
=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r3_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(4373,plain,
v7_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ),
inference(cnf,[status(esa)],[4370]) ).
thf(1737,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(10076,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)],[1737]) ).
thf(1209,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(7469,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)],[1209]) ).
thf(2086,axiom,
? [A: $i] : ( l1_group_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(11380,plain,
? [A: $i] : ( l1_group_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).
thf(1287,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(7805,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)],[1287]) ).
thf(38695,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( v4_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,20184]) ).
thf(38696,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[38695:[bind(A,$thf( sk1 ))]]) ).
thf(38738,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A ) ),
inference(simp,[status(thm)],[38696]) ).
thf(1972,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(10984,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)],[1972]) ).
thf(213,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k1_finseq_3 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_finseq_3) ).
thf(2931,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( ( k1_finseq_3 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ ( k2_relat_1 @ A ) ) )
& ( ~ ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ ( k1_tarski @ B ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1734,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(10063,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)],[1734]) ).
thf(298,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_filter_0) ).
thf(3310,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(2015,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(11130,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)],[2015]) ).
thf(1152,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(7200,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)],[1152]) ).
thf(806,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(5725,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)],[806]) ).
thf(1401,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(8441,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)],[1401]) ).
thf(4304,plain,
v2_funct_1 @ sk145,
inference(cnf,[status(esa)],[4303]) ).
thf(19879,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[4339,10656]) ).
thf(19880,plain,
( ( v1_relat_1 @ ( sk150 @ sk605 ) )
| ( v3_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19879:[bind(A,$thf( sk605 ))]]) ).
thf(924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
thf(6293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(268,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(3178,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(230,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(2999,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)],[230]) ).
thf(2147,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(2156,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(simp,[status(thm)],[2147]) ).
thf(2034,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(11193,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)],[2034]) ).
thf(2207,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk4 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_enumset1) ).
thf(5139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(26499,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k1_card_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6758,26188]) ).
thf(26500,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26499:[bind(A,$thf( k1_card_1 @ ( k1_zfmisc_1 @ D ) )),bind(B,$thf( D ))]]) ).
thf(26508,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_card_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[26500]) ).
thf(1184,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k15_lattice3 @ A @ ( a_3_2_lattice3 @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattice3) ).
thf(7356,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k15_lattice3 @ A @ ( a_3_2_lattice3 @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1466,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(8763,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)],[1466]) ).
thf(433,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(3908,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)],[433]) ).
thf(982,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(6485,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)],[982]) ).
thf(2079,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(11359,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)],[2079]) ).
thf(1914,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(10762,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)],[1914]) ).
thf(1895,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(10692,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)],[1895]) ).
thf(1715,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(9958,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)],[1715]) ).
thf(332,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(3444,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)],[332]) ).
thf(4879,plain,
v1_funct_1 @ sk196,
inference(cnf,[status(esa)],[4877]) ).
thf(1825,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(10456,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)],[1825]) ).
thf(1525,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(9054,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)],[1525]) ).
thf(1812,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(10417,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)],[1812]) ).
thf(2068,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(11316,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)],[2068]) ).
thf(4674,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk180 @ B @ A ) ) ),
inference(cnf,[status(esa)],[4670]) ).
thf(4689,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk180 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[4674]) ).
thf(4690,plain,
! [A: $i] : ( v1_funct_1 @ ( sk180 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[4689]) ).
thf(767,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ 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 )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k15_lattice3 @ A @ ( a_3_6_lattice3 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattice3) ).
thf(5538,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ 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 )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k15_lattice3 @ A @ ( a_3_6_lattice3 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(5586,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[5585]) ).
thf(5587,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[5586]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_funct_2) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(240,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(3031,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)],[240]) ).
thf(134,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(2614,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)],[134]) ).
thf(19541,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l2_lattices @ k1_xboole_0 )
| ( A != sk510 ) ),
inference(paramod_ordered,[status(thm)],[4339,15150]) ).
thf(19542,plain,
( ( v1_relat_1 @ ( sk150 @ sk510 ) )
| ( l2_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19541:[bind(A,$thf( sk510 ))]]) ).
thf(458,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(4013,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)],[458]) ).
thf(1911,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(10749,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)],[1911]) ).
thf(1876,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(10632,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)],[1876]) ).
thf(996,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(6542,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)],[996]) ).
thf(1166,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(7296,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)],[1166]) ).
thf(848,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(5881,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)],[848]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_1) ).
thf(6225,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
& ( v2_funct_1 @ B )
& ( ( k5_relat_1 @ C @ B )
= B ) )
=> ( C
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1195,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(7403,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)],[1195]) ).
thf(228,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(2994,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)],[228]) ).
thf(322,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(3395,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)],[322]) ).
thf(1913,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(10759,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)],[1913]) ).
thf(2270,plain,
! [C: $i,B: $i,A: $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(cnf,[status(esa)],[2269]) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(lifteq,[status(thm)],[2270]) ).
thf(1615,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(9514,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)],[1615]) ).
thf(1793,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(10354,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)],[1793]) ).
thf(1567,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_0) ).
thf(9259,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1599,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(9430,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)],[1599]) ).
thf(1167,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(7298,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)],[1167]) ).
thf(16341,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk611 ) ),
inference(paramod_ordered,[status(thm)],[6758,10815]) ).
thf(16342,plain,
( ~ ( v1_xboole_0 @ sk611 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[16341:[bind(A,$thf( sk611 ))]]) ).
thf(1770,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(10249,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)],[1770]) ).
thf(1741,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(10091,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)],[1741]) ).
thf(556,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m2_filter_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_1) ).
thf(4529,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m2_filter_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) )
=> ( m2_filter_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1684,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(9826,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)],[1684]) ).
thf(3981,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk111 @ B @ A ) ),
inference(cnf,[status(esa)],[3979]) ).
thf(2002,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 @ ( k11_group_4 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( B = C )
=> ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_latsubgr) ).
thf(11077,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 @ ( k11_group_4 @ A ) ) )
=> ! [C: $i] :
( ( m1_group_2 @ C @ A )
=> ( ( B = C )
=> ( ( v1_group_1 @ C )
& ( m1_group_2 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(1049,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(6751,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)],[1049]) ).
thf(2124,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v13_lattices @ A ) ),
inference(cnf,[status(esa)],[2123]) ).
thf(904,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(6191,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)],[904]) ).
thf(4292,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(cnf,[status(esa)],[4291]) ).
thf(1800,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(10384,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)],[1800]) ).
thf(1315,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(7992,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)],[1315]) ).
thf(10814,plain,
v1_group_1 @ sk611,
inference(cnf,[status(esa)],[10813]) ).
thf(19366,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,2114]) ).
thf(19367,plain,
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v3_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19366:[bind(A,$thf( sk1 ))]]) ).
thf(883,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(6056,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)],[883]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_partfun1) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(19343,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk608 ) ),
inference(paramod_ordered,[status(thm)],[4339,14833]) ).
thf(19344,plain,
( ( v1_relat_1 @ ( sk150 @ sk608 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19343:[bind(A,$thf( sk608 ))]]) ).
thf(1934,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(10829,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)],[1934]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(6853,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
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 @ ( 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(7420,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)],[1199]) ).
thf(1135,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(7122,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)],[1135]) ).
thf(334,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(3455,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)],[334]) ).
thf(4678,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( B
= ( k1_relat_1 @ ( sk180 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[4670]) ).
thf(4687,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k1_relat_1 @ ( sk180 @ B @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[4678]) ).
thf(4688,plain,
! [A: $i] :
( ( k1_relat_1 @ ( sk180 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[4687]) ).
thf(2333,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
| ( r4_binop_1 @ A @ C @ D ) ),
inference(cnf,[status(esa)],[2332]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m2_filter_1 @ 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_filter_1) ).
thf(2597,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m2_filter_1 @ 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)],[128]) ).
thf(1139,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(7137,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)],[1139]) ).
thf(828,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(5807,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)],[828]) ).
thf(970,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v4_lattice3 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r3_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_vectsp_8) ).
thf(6440,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v4_lattice3 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r3_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ D @ C ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r3_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ D @ C ) ) ) ) )
=> ( v4_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1413,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(8477,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)],[1413]) ).
thf(1324,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(8020,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)],[1324]) ).
thf(1364,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(8194,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)],[1364]) ).
thf(678,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(5133,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)],[678]) ).
thf(1098,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(6973,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(650,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_1) ).
thf(4986,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(19756,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk612 ) ),
inference(paramod_ordered,[status(thm)],[4339,15559]) ).
thf(19757,plain,
( ( v1_relat_1 @ ( sk150 @ sk612 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19756:[bind(A,$thf( sk612 ))]]) ).
thf(1555,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(9202,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)],[1555]) ).
thf(481,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(4168,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)],[481]) ).
thf(124,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ k1_xboole_0 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_3) ).
thf(2582,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ k1_xboole_0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1077,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(6875,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)],[1077]) ).
thf(746,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(5414,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)],[746]) ).
thf(871,axiom,
! [A: $i] :
( ( k2_enumset1 @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_enumset1) ).
thf(6012,plain,
! [A: $i] :
( ( k2_enumset1 @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( v3_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( ( k2_funct_2 @ A @ A @ C @ ( k3_funct_2 @ A @ A @ C @ B ) )
= B )
& ( ( k3_funct_2 @ A @ A @ C @ ( k2_funct_2 @ A @ A @ C @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_funct_2) ).
thf(4749,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( v3_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( ( k2_funct_2 @ A @ A @ C @ ( k3_funct_2 @ A @ A @ C @ B ) )
= B )
& ( ( k3_funct_2 @ A @ A @ C @ ( k2_funct_2 @ A @ A @ C @ B ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1008,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(6577,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)],[1008]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
thf(3376,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1689,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(9847,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)],[1689]) ).
thf(69,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(2375,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)],[69]) ).
thf(744,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(5399,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)],[744]) ).
thf(1435,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(8598,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)],[1435]) ).
thf(636,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(4922,plain,
! [A: $i] :
( ( v1_card_1 @ A )
=> ( r2_hidden @ A @ ( k2_card_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1230,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(7554,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)],[1230]) ).
thf(10797,plain,
v3_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(1111,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(7026,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)],[1111]) ).
thf(8002,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(cnf,[status(esa)],[8001]) ).
thf(8003,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(lifteq,[status(thm)],[8002]) ).
thf(1458,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(8725,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)],[1458]) ).
thf(2715,plain,
v1_finseq_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2714]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).
thf(6249,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
= ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(2071,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(11327,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)],[2071]) ).
thf(2109,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(11461,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)],[2109]) ).
thf(978,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(6472,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)],[978]) ).
thf(972,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v3_lattice4 @ C @ A @ B )
<=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6453,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( v3_lattice4 @ C @ A @ B )
=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) )
& ( ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) )
=> ( v3_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(19861,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk607 ) ),
inference(paramod_ordered,[status(thm)],[4339,10689]) ).
thf(19862,plain,
( ( v1_relat_1 @ ( sk150 @ sk607 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19861:[bind(A,$thf( sk607 ))]]) ).
thf(1351,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(8143,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)],[1351]) ).
thf(547,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(4490,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)],[547]) ).
thf(147,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(2661,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)],[147]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(5125,plain,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(2005,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(11098,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)],[2005]) ).
thf(1744,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(10112,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)],[1744]) ).
thf(1019,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(6621,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)],[1019]) ).
thf(2321,plain,
! [A: $i] : ( v1_finset_1 @ ( sk11 @ A ) ),
inference(cnf,[status(esa)],[2320]) ).
thf(12960,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( sk11 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2321,2173]) ).
thf(12961,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( sk11 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[12960:[bind(A,$thf( D )),bind(B,$thf( sk11 @ D ))]]) ).
thf(12963,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( sk11 @ B ) @ A ) ),
inference(simp,[status(thm)],[12961]) ).
thf(279,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(3214,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)],[279]) ).
thf(1498,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m3_vectsp_8 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_vectsp_8) ).
thf(8890,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m3_vectsp_8 @ C @ A @ B )
=> ( ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(2143,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
| ~ ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( l3_lattices @ ( k8_filter_1 @ A @ B ) )
| ( v16_lattices @ B ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(1084,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(6902,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)],[1084]) ).
thf(1860,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(10572,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)],[1860]) ).
thf(491,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(4200,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)],[491]) ).
thf(763,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( k8_filter_1 @ A @ B )
= ( g3_lattices @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u2_lattices @ A ) @ ( u2_lattices @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_lattices @ A ) @ ( u1_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_1) ).
thf(5523,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( k8_filter_1 @ A @ B )
= ( g3_lattices @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u2_lattices @ A ) @ ( u2_lattices @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_lattices @ A ) @ ( u1_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(153,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(2678,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1117,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(7045,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)],[1117]) ).
thf(1853,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(10553,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)],[1853]) ).
thf(1207,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(7462,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)],[1207]) ).
thf(1632,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(9578,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)],[1632]) ).
thf(604,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(4754,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)],[604]) ).
thf(1843,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(10521,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)],[1843]) ).
thf(43663,plain,
! [B: $i,A: $i] :
( ( r1_xboole_0 @ k5_numbers @ A )
!= ( r1_xboole_0 @ ( k1_tarski @ B ) @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43656,9277]) ).
thf(43676,plain,
! [B: $i,A: $i] :
( ( ( k1_tarski @ B )
!= k5_numbers )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(simp,[status(thm)],[43663]) ).
thf(43680,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k5_numbers ),
inference(simp,[status(thm)],[43676]) ).
thf(73,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ ( k4_card_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_finseq_3) ).
thf(2386,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( v1_finset_1 @ B )
=> ( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k2_relat_1 @ A ) ) )
=> ( ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k6_xcmplx_0 @ ( k3_finseq_1 @ A ) @ ( k4_card_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(15101,plain,
! [A: $i] :
( ( l1_lattices @ A )
| ( ( l3_lattices @ sk510 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9367,5693]) ).
thf(15102,plain,
l1_lattices @ sk510,
inference(pattern_uni,[status(thm)],[15101:[bind(A,$thf( sk510 ))]]) ).
thf(1611,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(9499,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)],[1611]) ).
thf(33601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19271,2180]) ).
thf(33602,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k1_numbers @ ( k4_xboole_0 @ A @ k5_numbers ) ) ),
inference(pattern_uni,[status(thm)],[33601:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k1_numbers )),bind(D,$thf( k4_xboole_0 @ E @ k5_numbers ))]]) ).
thf(33638,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k1_numbers @ ( k4_xboole_0 @ A @ k5_numbers ) ) ),
inference(simp,[status(thm)],[33602]) ).
thf(14651,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ sk272 ) ),
inference(paramod_ordered,[status(thm)],[6071,14622]) ).
thf(14674,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk272 ),
inference(simp,[status(thm)],[14651]) ).
thf(15080,plain,
! [A: $i] :
( ( A != sk272 )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2254,14674]) ).
thf(15083,plain,
( ( k4_xboole_0 @ sk272 @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[15080]) ).
thf(21941,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk272 ),
inference(rewrite,[status(thm)],[15083,2254]) ).
thf(1389,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(8364,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)],[1389]) ).
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 @ ( 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(8350,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)],[1384]) ).
thf(2051,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(11252,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)],[2051]) ).
thf(1712,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_group_3 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( C
= ( k18_group_2 @ ( k1_group_3 @ A ) @ B ) )
=> ( ( k2_latsubgr @ A @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_latsubgr) ).
thf(9948,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_group_3 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) )
=> ( ( C
= ( k18_group_2 @ ( k1_group_3 @ A ) @ B ) )
=> ( ( k2_latsubgr @ A @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(1769,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(10246,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)],[1769]) ).
thf(1483,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_0) ).
thf(8813,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(1569,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(9270,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)],[1569]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_lattice3) ).
thf(7055,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1803,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(10392,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)],[1803]) ).
thf(205,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(2882,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)],[205]) ).
thf(1291,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) @ ( k16_lattice3 @ A @ ( a_3_4_lattice3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice3) ).
thf(7832,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) @ ( k16_lattice3 @ A @ ( a_3_4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(19583,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_group_1 @ k1_xboole_0 )
| ( A != sk610 ) ),
inference(paramod_ordered,[status(thm)],[4339,10801]) ).
thf(19584,plain,
( ( v1_relat_1 @ ( sk150 @ sk610 ) )
| ( v1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19583:[bind(A,$thf( sk610 ))]]) ).
thf(2046,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(11225,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)],[2046]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_partfun1) ).
thf(2689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(457,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice4) ).
thf(4003,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) )
=> ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1439,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(8625,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)],[1439]) ).
thf(1252,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(7662,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)],[1252]) ).
thf(623,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ 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',t7_lattice4) ).
thf(4875,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ 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)],[623]) ).
thf(171,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(2747,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(797,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice4) ).
thf(5684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1931,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(10820,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)],[1931]) ).
thf(1956,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(10915,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)],[1956]) ).
thf(955,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(6389,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)],[955]) ).
thf(19889,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_vectsp_1 @ k1_xboole_0 )
| ( A != sk370 ) ),
inference(paramod_ordered,[status(thm)],[4339,7512]) ).
thf(19890,plain,
( ( v1_relat_1 @ ( sk150 @ sk370 ) )
| ( l1_vectsp_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19889:[bind(A,$thf( sk370 ))]]) ).
thf(711,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(5262,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)],[711]) ).
thf(1776,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(10288,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)],[1776]) ).
thf(1392,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(8396,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)],[1392]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(5767,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1052,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(6762,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)],[1052]) ).
thf(1417,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(8498,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)],[1417]) ).
thf(563,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(4561,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(521,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(4346,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)],[521]) ).
thf(1723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
thf(9991,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(631,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(4905,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)],[631]) ).
thf(1101,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 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
& ( v3_funct_2 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
& ( m2_relset_1 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) ) )
=> ( ( C
= ( k5_relat_1 @ D @ B ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_4 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_group_4) ).
thf(6981,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 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
& ( v3_funct_2 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
& ( m2_relset_1 @ D @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) ) )
=> ( ( C
= ( k5_relat_1 @ D @ B ) )
=> ( ( k3_group_4 @ A @ B )
= ( k3_group_4 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1721,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(9980,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)],[1721]) ).
thf(808,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(5731,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)],[808]) ).
thf(428,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(3885,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)],[428]) ).
thf(19348,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,2117]) ).
thf(19349,plain,
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19348:[bind(A,$thf( sk1 ))]]) ).
thf(20022,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk335 ) ),
inference(paramod_ordered,[status(thm)],[4339,14839]) ).
thf(20023,plain,
( ( v1_relat_1 @ ( sk150 @ sk335 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[20022:[bind(A,$thf( sk335 ))]]) ).
thf(19773,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ k1_xboole_0 )
| ( A != sk608 ) ),
inference(paramod_ordered,[status(thm)],[4339,10708]) ).
thf(19774,plain,
( ( v1_relat_1 @ ( sk150 @ sk608 ) )
| ( v4_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19773:[bind(A,$thf( sk608 ))]]) ).
thf(1397,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(8428,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)],[1397]) ).
thf(1371,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_0) ).
thf(8231,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ! [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 @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(2061,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(11295,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)],[2061]) ).
thf(1203,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(7443,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)],[1203]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_enumset1) ).
thf(3202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1901,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(10717,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)],[1901]) ).
thf(2023,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(11166,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)],[2023]) ).
thf(16891,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ ( g1_group_1 @ k1_numbers @ k1_xboole_0 ) )
| ( A != k33_binop_2 ) ),
inference(paramod_ordered,[status(thm)],[6758,4372]) ).
thf(16892,plain,
( ~ ( v1_xboole_0 @ k33_binop_2 )
| ~ ( v3_struct_0 @ ( g1_group_1 @ k1_numbers @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[16891:[bind(A,$thf( k33_binop_2 ))]]) ).
thf(1585,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(9358,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)],[1585]) ).
thf(1680,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(9815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(2337,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( m1_orders_1 @ B @ A )
| ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[2336]) ).
thf(2276,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ),
inference(cnf,[status(esa)],[2275]) ).
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 )
=> ( ( ( 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(9082,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)],[1530]) ).
thf(2128,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v14_lattices @ A ) ),
inference(cnf,[status(esa)],[2123]) ).
thf(1650,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(9683,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)],[1650]) ).
thf(2322,plain,
! [A: $i] : ( v1_relat_1 @ ( sk11 @ A ) ),
inference(cnf,[status(esa)],[2320]) ).
thf(1352,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(8148,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)],[1352]) ).
thf(1182,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(7351,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)],[1182]) ).
thf(653,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(5001,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)],[653]) ).
thf(160,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(2701,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)],[160]) ).
thf(2036,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(11198,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)],[2036]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_setfam_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(4800,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_setfam_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k3_xboole_0 @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_setfam_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(26770,plain,
! [B: $i,A: $i] :
( ( ( k1_card_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
| ( ( k1_card_1 @ ( k1_tarski @ B ) )
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9891,26243]) ).
thf(26771,plain,
! [A: $i] :
( ( k1_card_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[26770:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(16709,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk388 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7801,6758]) ).
thf(16710,plain,
sk388 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[16709:[bind(A,$thf( sk388 ))]]) ).
thf(3712,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[3711]) ).
thf(14498,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_partfun1 @ A ) ),
inference(rewrite,[status(thm)],[3712,10471]) ).
thf(304,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(3329,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)],[304]) ).
thf(1995,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(11049,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)],[1995]) ).
thf(471,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_lattice4) ).
thf(4117,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1296,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(7847,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)],[1296]) ).
thf(1652,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(9690,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)],[1652]) ).
thf(668,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
thf(5106,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(19062,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk37 @ A ) )
!= ( v1_xboole_0 @ ( sk524 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2758,17171]) ).
thf(19067,plain,
! [B: $i,A: $i] :
( ( sk37 @ A )
!= ( sk524 @ B ) ),
inference(simp,[status(thm)],[19062]) ).
thf(24239,plain,
! [A: $i] :
( ( sk524 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[19067,17354]) ).
thf(1869,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(10608,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)],[1869]) ).
thf(853,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(5902,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)],[853]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
thf(5223,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
=> ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1846,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(10531,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)],[1846]) ).
thf(123,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(2579,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)],[123]) ).
thf(467,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(4093,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)],[467]) ).
thf(1891,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(10680,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)],[1891]) ).
thf(973,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6457,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_2) ).
thf(2675,plain,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(14659,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ sk167 ) ),
inference(paramod_ordered,[status(thm)],[4517,14622]) ).
thf(14667,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk167 ),
inference(simp,[status(thm)],[14659]) ).
thf(14803,plain,
! [A: $i] :
( ( A != sk167 )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2254,14667]) ).
thf(14806,plain,
( ( k4_xboole_0 @ sk167 @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[14803]) ).
thf(19295,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk167 ),
inference(rewrite,[status(thm)],[14806,2254]) ).
thf(1035,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(6701,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)],[1035]) ).
thf(15556,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l2_struct_0 @ sk537 )
!= ( l2_struct_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9682,5735]) ).
thf(15557,plain,
l1_struct_0 @ sk537,
inference(pattern_uni,[status(thm)],[15556:[bind(A,$thf( sk537 ))]]) ).
thf(31719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k4_numbers ) )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19265,2180]) ).
thf(31720,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k1_numbers @ ( k4_xboole_0 @ A @ k4_numbers ) ) ),
inference(pattern_uni,[status(thm)],[31719:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( k1_numbers )),bind(D,$thf( k4_xboole_0 @ E @ k4_numbers ))]]) ).
thf(31779,plain,
! [A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ k1_numbers @ ( k4_xboole_0 @ A @ k4_numbers ) ) ),
inference(simp,[status(thm)],[31720]) ).
thf(217,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( k4_finseq_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finseq_1) ).
thf(2948,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( k4_finseq_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k4_finseq_1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(6746,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[6745]) ).
thf(1451,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(8696,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)],[1451]) ).
thf(105,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
thf(2500,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r3_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) )
=> ( r3_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(938,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(6337,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)],[938]) ).
thf(1065,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_funct_1 @ ( k1_latsubgr @ A ) @ B )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
thf(6825,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)],[1065]) ).
thf(1847,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(10536,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)],[1847]) ).
thf(1021,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(6633,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)],[1021]) ).
thf(1083,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(6899,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)],[1083]) ).
thf(1855,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(10558,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)],[1855]) ).
thf(3970,plain,
l1_struct_0 @ sk110,
inference(cnf,[status(esa)],[3968]) ).
thf(888,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6073,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(810,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(5736,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)],[810]) ).
thf(1221,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(7515,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)],[1221]) ).
thf(1429,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
<=> ( r3_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_0) ).
thf(8564,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
=> ( r3_lattices @ A @ C @ B ) )
& ( ( r3_lattices @ A @ C @ B )
=> ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_1) ).
thf(5347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1014,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(6601,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)],[1014]) ).
thf(1545,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(9151,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)],[1545]) ).
thf(647,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(4976,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)],[647]) ).
thf(26254,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6758,26243]) ).
thf(26255,plain,
~ ( v1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[26254:[bind(A,$thf( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ))]]) ).
thf(26788,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ A ) ) )
| ( ( k1_card_1 @ ( k1_tarski @ B ) )
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9891,26255]) ).
thf(26789,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[26788:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1161,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(7251,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)],[1161]) ).
thf(2088,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(11386,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)],[2088]) ).
thf(1811,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(10415,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)],[1811]) ).
thf(1121,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(7067,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)],[1121]) ).
thf(6369,plain,
! [A: $i] : ( m1_eqrel_1 @ ( sk297 @ A ) @ A ),
inference(cnf,[status(esa)],[6368]) ).
thf(1583,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(9353,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)],[1583]) ).
thf(19928,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v8_vectsp_1 @ k1_xboole_0 )
| ( A != sk259 ) ),
inference(paramod_ordered,[status(thm)],[4339,5876]) ).
thf(19929,plain,
( ( v1_relat_1 @ ( sk150 @ sk259 ) )
| ( v8_vectsp_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19928:[bind(A,$thf( sk259 ))]]) ).
thf(1587,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(9363,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)],[1587]) ).
thf(1240,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(7585,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)],[1240]) ).
thf(2145,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
| ~ ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
| ~ ( l3_lattices @ ( k8_filter_1 @ A @ B ) )
| ( v15_lattices @ A ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(905,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(6193,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)],[905]) ).
thf(639,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(4932,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)],[639]) ).
thf(281,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(3224,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)],[281]) ).
thf(557,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(4538,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)],[557]) ).
thf(321,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( k15_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_5_lattice3 @ A @ B ) ) )
& ( ( k16_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_6_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattice3) ).
thf(3388,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( k15_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_5_lattice3 @ A @ B ) ) )
& ( ( k16_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_6_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1886,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(10663,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)],[1886]) ).
thf(1492,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(8850,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)],[1492]) ).
thf(2077,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(11351,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)],[2077]) ).
thf(889,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(6086,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)],[889]) ).
thf(2637,plain,
v1_finset_1 @ sk24,
inference(cnf,[status(esa)],[2631]) ).
thf(12948,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk24 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2637,2173]) ).
thf(12949,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk24 @ A ) ),
inference(pattern_uni,[status(thm)],[12948:[bind(A,$thf( sk24 ))]]) ).
thf(12965,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk24 @ A ) ),
inference(simp,[status(thm)],[12949]) ).
thf(13495,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk24 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12965,2173]) ).
thf(13496,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk24 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[13495:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk24 @ E )),bind(C,$thf( C ))]]) ).
thf(13501,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk24 @ B ) @ A ) ),
inference(simp,[status(thm)],[13496]) ).
thf(27911,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ k1_xboole_0 @ B ) @ A ) ),
inference(rewrite,[status(thm)],[13501,16953]) ).
thf(1514,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(9019,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)],[1514]) ).
thf(1405,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(8449,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)],[1405]) ).
thf(1153,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(7202,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)],[1153]) ).
thf(497,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(4225,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)],[497]) ).
thf(1783,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(10320,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)],[1783]) ).
thf(19362,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk608 ) ),
inference(paramod_ordered,[status(thm)],[4339,10711]) ).
thf(19363,plain,
( ( v1_relat_1 @ ( sk150 @ sk608 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19362:[bind(A,$thf( sk608 ))]]) ).
thf(293,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(3256,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)],[293]) ).
thf(662,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(5083,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)],[662]) ).
thf(943,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(6358,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)],[943]) ).
thf(185,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(2807,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(613,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(4795,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)],[613]) ).
thf(1353,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(8151,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)],[1353]) ).
thf(2057,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(11280,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)],[2057]) ).
thf(777,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(5596,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)],[777]) ).
thf(994,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(6531,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)],[994]) ).
thf(1659,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(9732,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)],[1659]) ).
thf(1266,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(7720,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)],[1266]) ).
thf(2265,plain,
~ ? [A: $i,B: $i] :
( ~ ( r1_xboole_0 @ A @ B )
& ? [C: $i] :
( ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[2264]) ).
thf(2266,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ A @ B )
| ~ ( r1_xboole_0 @ A @ C )
| ~ ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[2265]) ).
thf(1213,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(7488,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)],[1213]) ).
thf(2111,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v4_lattice3 @ ( k11_group_4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_latsubgr) ).
thf(11465,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( v4_lattice3 @ ( k11_group_4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(1997,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(11059,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)],[1997]) ).
thf(1350,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( A != np__0 )
=> ( ( k5_int_1 @ A @ A )
= np__1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_int_1) ).
thf(8140,plain,
! [A: $i] :
( ( v1_int_1 @ A )
=> ( ( A != np__0 )
=> ( ( k5_int_1 @ A @ A )
= np__1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(323,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
thf(3398,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(382,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_0) ).
thf(3684,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(6220,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(8914,plain,
m1_subset_1 @ sk464 @ ( k1_zfmisc_1 @ k4_numbers ),
inference(cnf,[status(esa)],[8911]) ).
thf(2063,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(11302,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)],[2063]) ).
thf(1671,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(9770,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)],[1671]) ).
thf(1900,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(10714,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)],[1900]) ).
thf(1251,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(7659,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1592,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(9395,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)],[1592]) ).
thf(1170,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(7306,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)],[1170]) ).
thf(368,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(3625,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)],[368]) ).
thf(201,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(2865,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)],[201]) ).
thf(654,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(5009,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(5010,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[5009]) ).
thf(19183,plain,
! [A: $i] :
( ( r1_tarski @ ( k1_setfam_1 @ A ) @ k1_xboole_0 )
| ( ( k3_tarski @ k1_xboole_0 )
!= ( k3_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5010,4292]) ).
thf(19184,plain,
r1_tarski @ ( k1_setfam_1 @ k1_xboole_0 ) @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[19183:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7903,plain,
( ! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ! [B: $i] :
( ( B
= ( k1_setfam_1 @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( ! [B: $i] :
( ( B
= ( k1_setfam_1 @ A ) )
=> ( B = k1_xboole_0 ) )
& ! [B: $i] :
( ( B = k1_xboole_0 )
=> ( B
= ( k1_setfam_1 @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[7902]) ).
thf(7905,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( B != k1_xboole_0 )
| ( B
= ( k1_setfam_1 @ A ) ) ),
inference(cnf,[status(esa)],[7903]) ).
thf(7914,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( B != k1_xboole_0 )
| ( B
= ( k1_setfam_1 @ A ) ) ),
inference(lifteq,[status(thm)],[7905]) ).
thf(7915,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[7914]) ).
thf(19275,plain,
r1_tarski @ k1_xboole_0 @ k1_xboole_0,
inference(rewrite,[status(thm)],[19184,7915]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_enumset1) ).
thf(6284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1787,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k6_eqrel_1 @ A @ ( k6_partfun1 @ A ) @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_eqrel_1) ).
thf(10332,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k6_eqrel_1 @ A @ ( k6_partfun1 @ A ) @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(1488,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(8830,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)],[1488]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v5_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_3_8_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_8_lattice3) ).
thf(6706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v5_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_8_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ A @ ( a_3_8_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(10712,plain,
v2_group_1 @ sk608,
inference(cnf,[status(esa)],[10707]) ).
thf(1686,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(9834,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)],[1686]) ).
thf(1773,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(10261,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)],[1773]) ).
thf(1128,axiom,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(7099,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(6850,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(753,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(5490,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)],[753]) ).
thf(2348,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r1_lattices @ A @ ( sk13 @ C @ B @ A ) @ B )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2345]) ).
thf(2352,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r1_lattices @ A @ ( sk13 @ C @ B @ A ) @ B )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[2348]) ).
thf(1452,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(8698,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)],[1452]) ).
thf(2012,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(11123,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)],[2012]) ).
thf(1095,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(6965,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)],[1095]) ).
thf(1739,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(10082,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)],[1739]) ).
thf(622,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(4851,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)],[622]) ).
thf(1110,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(7024,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)],[1110]) ).
thf(1102,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(6985,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)],[1102]) ).
thf(258,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_zfmisc_1 @ A ) @ A )
& ( m2_relset_1 @ B @ ( k1_zfmisc_1 @ A ) @ A ) )
=> ~ ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k6_domain_1 @ A @ C ) )
= C ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k10_relset_1 @ ( k1_zfmisc_1 @ A ) @ A @ B @ C ) )
= ( k1_funct_1 @ B @ ( k3_tarski @ C ) ) ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_lattices @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( l3_lattices @ C ) )
=> ~ ( ( ( u1_struct_0 @ C )
= A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( k15_lattice3 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_lattice3) ).
thf(3092,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_zfmisc_1 @ A ) @ A )
& ( m2_relset_1 @ B @ ( k1_zfmisc_1 @ A ) @ A ) )
=> ~ ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k6_domain_1 @ A @ C ) )
= C ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k10_relset_1 @ ( k1_zfmisc_1 @ A ) @ A @ B @ C ) )
= ( k1_funct_1 @ B @ ( k3_tarski @ C ) ) ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_lattices @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( l3_lattices @ C ) )
=> ~ ( ( ( u1_struct_0 @ C )
= A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( k15_lattice3 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1327,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(8028,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)],[1327]) ).
thf(814,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_filter_0) ).
thf(5749,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(690,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(5179,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)],[690]) ).
thf(1916,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(10767,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)],[1916]) ).
thf(1716,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(9966,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)],[1716]) ).
thf(1865,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(10595,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)],[1865]) ).
thf(609,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(4770,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)],[609]) ).
thf(1826,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(10464,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)],[1826]) ).
thf(959,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(6408,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)],[959]) ).
thf(1531,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(9092,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)],[1531]) ).
thf(1844,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(10526,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)],[1844]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_4_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_4_lattice3) ).
thf(7395,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_4_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_4_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(19623,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l2_struct_0 @ k1_xboole_0 )
| ( A != sk537 ) ),
inference(paramod_ordered,[status(thm)],[4339,9682]) ).
thf(19624,plain,
( ( v1_relat_1 @ ( sk150 @ sk537 ) )
| ( l2_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19623:[bind(A,$thf( sk537 ))]]) ).
thf(19317,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk259 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,15887]) ).
thf(19324,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk259 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19317]) ).
thf(26802,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ A ) ) )
| ( ( k1_card_1 @ ( k1_tarski @ B ) )
!= ( k1_card_1 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9891,26196]) ).
thf(26803,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k1_card_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[26802:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(1839,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(10508,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)],[1839]) ).
thf(790,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(5660,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)],[790]) ).
thf(5386,plain,
! [B: $i,A: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[5385]) ).
thf(2027,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(11176,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)],[2027]) ).
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 @ ( 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(6861,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)],[1074]) ).
thf(1197,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(7412,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)],[1197]) ).
thf(2105,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(11450,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)],[2105]) ).
thf(333,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(3447,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)],[333]) ).
thf(1228,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(7547,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)],[1228]) ).
thf(1762,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(10199,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)],[1762]) ).
thf(10796,plain,
v7_group_1 @ sk610,
inference(cnf,[status(esa)],[10794]) ).
thf(2215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
| ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
inference(cnf,[status(esa)],[2214]) ).
thf(562,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 ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(4559,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 ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1276,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(7765,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)],[1276]) ).
thf(133,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(2611,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)],[133]) ).
thf(2325,plain,
! [A: $i] : ( m1_relset_1 @ ( sk11 @ A ) @ k5_numbers @ A ),
inference(cnf,[status(esa)],[2320]) ).
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] :
( ( 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(10193,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)],[1761]) ).
thf(6980,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(cnf,[status(esa)],[6979]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(6674,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(229,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(2997,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)],[229]) ).
thf(2490,plain,
v4_group_1 @ ( g1_group_1 @ k1_numbers @ k33_binop_2 ),
inference(cnf,[status(esa)],[2488]) ).
thf(1952,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(10905,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)],[1952]) ).
thf(2305,plain,
! [C: $i,B: $i,A: $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 )
| ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[2304]) ).
thf(1354,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(8153,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)],[1354]) ).
thf(210,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ ( k2_relat_1 @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_finseq_3) ).
thf(2919,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ ( k2_relat_1 @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(482,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(4170,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)],[482]) ).
thf(1045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattices) ).
thf(6743,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(249,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(3056,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)],[249]) ).
thf(1465,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(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 )
=> ! [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)],[1465]) ).
thf(2658,plain,
v1_finseq_1 @ sk27,
inference(cnf,[status(esa)],[2657]) ).
thf(1792,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(10347,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)],[1792]) ).
thf(178,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(2775,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)],[178]) ).
thf(32776,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v1_xboole_0 @ B )
| ( v3_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,20936]) ).
thf(32777,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[32776:[bind(A,$thf( sk1 ))]]) ).
thf(32784,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ~ ( v1_xboole_0 @ A )
| ( v3_group_1 @ A ) ),
inference(simp,[status(thm)],[32777]) ).
thf(181,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(2792,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)],[181]) ).
thf(692,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(5184,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)],[692]) ).
thf(27711,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk612 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16644]) ).
thf(27724,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk612 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[27711]) ).
thf(1862,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(10578,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)],[1862]) ).
thf(15143,plain,
! [A: $i] :
( ( l2_lattices @ A )
| ( ( l3_lattices @ sk545 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9761,5694]) ).
thf(15144,plain,
l2_lattices @ sk545,
inference(pattern_uni,[status(thm)],[15143:[bind(A,$thf( sk545 ))]]) ).
thf(1832,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(10479,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)],[1832]) ).
thf(1041,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(6726,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)],[1041]) ).
thf(1642,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(9647,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)],[1642]) ).
thf(9755,plain,
v1_int_1 @ sk544,
inference(cnf,[status(esa)],[9754]) ).
thf(1923,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(10789,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)],[1923]) ).
thf(10659,plain,
v4_group_1 @ sk605,
inference(cnf,[status(esa)],[10654]) ).
thf(1311,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(7950,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)],[1311]) ).
thf(1386,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(8356,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)],[1386]) ).
thf(1735,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(10072,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)],[1735]) ).
thf(364,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(3613,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)],[364]) ).
thf(162,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(2707,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)],[162]) ).
thf(1977,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(10996,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)],[1977]) ).
thf(424,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(3864,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)],[424]) ).
thf(2074,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(11337,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)],[2074]) ).
thf(1357,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(8166,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)],[1357]) ).
thf(934,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k15_lattice3 @ A @ ( a_2_3_lattice3 @ A @ B ) ) )
& ( B
= ( k16_lattice3 @ A @ ( a_2_4_lattice3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattice3) ).
thf(6322,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k15_lattice3 @ A @ ( a_2_3_lattice3 @ A @ B ) ) )
& ( B
= ( k16_lattice3 @ A @ ( a_2_4_lattice3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(74,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(2389,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)],[74]) ).
thf(1063,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(6818,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1565,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(9234,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)],[1565]) ).
thf(341,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(3484,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)],[341]) ).
thf(1758,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(10169,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)],[1758]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_partfun1) ).
thf(2855,plain,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1473,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(8780,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)],[1473]) ).
thf(1677,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(9802,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)],[1677]) ).
thf(2290,plain,
! [B: $i,A: $i] :
( ~ ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
| ~ ( v1_int_1 @ B )
| ( r1_xreal_0 @ B @ A )
| ( m2_subset_1 @ ( sk6 @ B @ A ) @ k1_numbers @ k5_numbers ) ),
inference(cnf,[status(esa)],[2289]) ).
thf(2250,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ? [B: $i] : ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ) ),
inference(miniscope,[status(thm)],[2249]) ).
thf(2251,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finseq_1 @ A )
| ~ ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
| ( r2_hidden @ np__1 @ ( k4_finseq_1 @ A ) ) ),
inference(cnf,[status(esa)],[2250]) ).
thf(1496,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(8882,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1534,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(9102,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)],[1534]) ).
thf(77,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice4) ).
thf(2406,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(21381,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v3_struct_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,18439]) ).
thf(21382,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ~ ( v3_struct_0 @ A )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[21381:[]]) ).
thf(118,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(2554,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)],[118]) ).
thf(2532,plain,
v1_funct_1 @ sk19,
inference(cnf,[status(esa)],[2530]) ).
thf(314,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_0) ).
thf(3369,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(474,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(4125,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(4126,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ A ) ),
inference(cnf,[status(esa)],[4125]) ).
thf(11381,plain,
l1_group_1 @ sk636,
inference(cnf,[status(esa)],[11380]) ).
thf(14848,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk636 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11381,4719]) ).
thf(14849,plain,
l1_struct_0 @ sk636,
inference(pattern_uni,[status(thm)],[14848:[bind(A,$thf( sk636 ))]]) ).
thf(462,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(4042,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)],[462]) ).
thf(1784,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(10325,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(4791,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[4790]) ).
thf(1556,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(9205,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)],[1556]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ D @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_enumset1) ).
thf(6003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ D @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(830,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(5813,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)],[830]) ).
thf(1055,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(6770,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)],[1055]) ).
thf(399,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(3748,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)],[399]) ).
thf(1870,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(10610,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)],[1870]) ).
thf(370,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(3630,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)],[370]) ).
thf(1882,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(10648,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)],[1882]) ).
thf(223,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k1_finseq_3 @ A @ B )
= A )
<=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_finseq_3) ).
thf(2971,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( ( k1_finseq_3 @ A @ B )
= A )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) )
& ( ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) )
=> ( ( k1_finseq_3 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1979,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(11001,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)],[1979]) ).
thf(986,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(6494,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)],[986]) ).
thf(12462,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k6_finseq_1 @ A ) )
!= ( v1_xboole_0 @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7483,8888]) ).
thf(12474,plain,
! [B: $i,A: $i] :
( ( k6_finseq_1 @ A )
!= ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[12462]) ).
thf(13929,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[12474,9564]) ).
thf(132,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k4_finseq_1 @ A )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_finseq_1) ).
thf(2608,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( ( k4_finseq_1 @ A )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_relat_1 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_orders_1) ).
thf(2431,plain,
! [A: $i,B: $i] :
( ( ( v1_partfun1 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_relat_1 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1500,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(8897,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)],[1500]) ).
thf(232,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(3003,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)],[232]) ).
thf(38755,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( v3_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4339,20930]) ).
thf(38756,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[38755:[bind(A,$thf( sk1 ))]]) ).
thf(38796,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v3_group_1 @ A ) ),
inference(simp,[status(thm)],[38756]) ).
thf(595,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(4705,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)],[595]) ).
thf(1134,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(7120,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)],[1134]) ).
thf(422,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_0) ).
thf(3859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1136,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(7125,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)],[1136]) ).
thf(667,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
thf(5104,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
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_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(8083,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)],[1337]) ).
thf(1034,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(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 @ ( 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)],[1034]) ).
thf(30440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ B @ ( k2_xboole_0 @ C @ D ) )
| ( ( r1_tarski @ ( k4_xboole_0 @ ( k1_orders_1 @ k1_xboole_0 ) @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
!= ( r1_tarski @ ( k4_xboole_0 @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29990,2180]) ).
thf(30441,plain,
! [A: $i] : ( r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ ( k2_xboole_0 @ A @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[30440:[bind(A,$thf( A )),bind(B,$thf( k1_orders_1 @ k1_xboole_0 )),bind(C,$thf( A )),bind(D,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(5503,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(cnf,[status(esa)],[5502]) ).
thf(5505,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(simp,[status(thm)],[5503]) ).
thf(1984,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(11013,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)],[1984]) ).
thf(1850,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(10546,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)],[1850]) ).
thf(5581,plain,
l1_lattices @ sk235,
inference(cnf,[status(esa)],[5580]) ).
thf(14176,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_lattices @ sk235 )
!= ( l1_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5581,4103]) ).
thf(14177,plain,
l1_struct_0 @ sk235,
inference(pattern_uni,[status(thm)],[14176:[bind(A,$thf( sk235 ))]]) ).
thf(1874,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(10627,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)],[1874]) ).
thf(1057,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(6799,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)],[1057]) ).
thf(2004,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E )
<=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_latsubgr) ).
thf(11091,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) )
& ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) )
=> ( r3_lattices @ ( k11_group_4 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(2017,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(11145,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)],[2017]) ).
thf(629,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(4900,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)],[629]) ).
thf(1661,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(9736,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)],[1661]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ C @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_enumset1) ).
thf(4451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1010,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_0) ).
thf(6584,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(501,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(4261,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)],[501]) ).
thf(859,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(5922,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)],[859]) ).
thf(1547,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(9160,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)],[1547]) ).
thf(1806,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(10400,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)],[1806]) ).
thf(1418,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(8506,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)],[1418]) ).
thf(1718,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(9972,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)],[1718]) ).
thf(346,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ 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
= ( k5_lattice4 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice4) ).
thf(3529,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ 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
= ( k5_lattice4 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ 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 )
= ( k7_lattices @ A @ C ) ) )
=> ( B
= ( k5_lattice4 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1625,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(9559,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)],[1625]) ).
thf(179,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(2779,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) ) )
& ( ? [B: $i] :
( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B )
& ( A
= ( k2_relat_1 @ B ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(21757,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_struct_0 @ A )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4339,19540]) ).
thf(21758,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( v1_relat_1 @ ( sk150 @ sk1 ) )
| ( l1_struct_0 @ A ) ),
inference(pattern_uni,[status(thm)],[21757:[]]) ).
thf(2058,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(11287,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)],[2058]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_enumset1) ).
thf(5828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1201,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(7437,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)],[1201]) ).
thf(1765,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_6_lattice3) ).
thf(10210,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(14844,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk607 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10689,4719]) ).
thf(14845,plain,
l1_struct_0 @ sk607,
inference(pattern_uni,[status(thm)],[14844:[bind(A,$thf( sk607 ))]]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_partfun1) ).
thf(4197,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_partfun1) ).
thf(3324,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(928,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).
thf(6305,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1377,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(8272,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)],[1377]) ).
thf(687,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(5164,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)],[687]) ).
thf(686,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(5162,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)],[686]) ).
thf(511,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(4293,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)],[511]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_5_lattice3) ).
thf(7187,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1654,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(9701,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)],[1654]) ).
thf(41695,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ B ) @ k1_xboole_0 )
| ( ( k2_xboole_0 @ k1_xboole_0 @ A )
!= ( k2_xboole_0 @ C @ k1_numbers ) ) ),
inference(paramod_ordered,[status(thm)],[41649,15522]) ).
thf(41696,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[41695:[bind(A,$thf( k1_numbers )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(41794,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ k5_numbers @ A ) @ k1_xboole_0 ),
inference(simp,[status(thm)],[41696]) ).
thf(45346,plain,
r1_tarski @ k5_numbers @ k1_xboole_0,
inference(rewrite,[status(thm)],[41794,43667]) ).
thf(645,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_relat_1) ).
thf(4964,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1628,axiom,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(9568,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(9569,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[9568]) ).
thf(902,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(6181,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)],[902]) ).
thf(484,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(4175,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)],[484]) ).
thf(478,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(4153,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)],[478]) ).
thf(1704,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(9906,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)],[1704]) ).
thf(573,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(4591,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)],[573]) ).
thf(821,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(5781,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)],[821]) ).
thf(605,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(4759,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)],[605]) ).
thf(873,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(6018,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)],[873]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r4_lattice3 @ B @ C @ A )
<=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattice3) ).
thf(3267,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r4_lattice3 @ B @ C @ A )
=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r4_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(880,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice4) ).
thf(6045,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(669,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_1) ).
thf(5109,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(97,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2462,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1907,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(10738,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)],[1907]) ).
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 @ ( 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(8304,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)],[1378]) ).
thf(2064,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(11305,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)],[2064]) ).
thf(57,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(2330,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)],[57]) ).
thf(1896,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(10695,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)],[1896]) ).
thf(1562,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(9223,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)],[1562]) ).
thf(15138,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_lattices @ sk510 )
!= ( l1_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15102,4103]) ).
thf(15139,plain,
l1_struct_0 @ sk510,
inference(pattern_uni,[status(thm)],[15138:[bind(A,$thf( sk510 ))]]) ).
thf(2092,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(11405,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)],[2092]) ).
thf(1619,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(9537,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)],[1619]) ).
thf(122,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(2576,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)],[122]) ).
thf(1714,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(9955,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(885,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(6062,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)],[885]) ).
thf(1596,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(9421,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)],[1596]) ).
thf(2183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2181]) ).
thf(309,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(3351,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)],[309]) ).
thf(538,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(4446,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)],[538]) ).
thf(1005,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 ) )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_latsubgr) ).
thf(6569,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 ) )
=> ( r2_hidden @ ( k3_group_1 @ A @ C ) @ ( k1_funct_1 @ ( k1_latsubgr @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1457,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(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 ) )
=> ! [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)],[1457]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_2) ).
thf(5517,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( ( k4_funct_2 @ A @ C @ B )
= B )
& ( v2_funct_1 @ B ) )
=> ( C
= ( k6_partfun1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1743,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(10109,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)],[1743]) ).
thf(676,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice4) ).
thf(5128,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1757,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(10167,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)],[1757]) ).
thf(170,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(2739,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)],[170]) ).
thf(1196,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(7406,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)],[1196]) ).
thf(566,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(4570,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)],[566]) ).
thf(696,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(5196,plain,
! [A: $i] :
( ( l1_vectsp_1 @ A )
=> ( ( k2_vectsp_1 @ A )
= ( u1_vectsp_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
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 @ ( 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(8520,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)],[1420]) ).
thf(4306,plain,
v1_relat_1 @ sk145,
inference(cnf,[status(esa)],[4303]) ).
thf(351,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(3552,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)],[351]) ).
thf(1687,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(9839,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)],[1687]) ).
thf(1598,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(9427,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)],[1598]) ).
thf(716,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(5287,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)],[716]) ).
thf(1568,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_lattice4 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).
thf(9262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m2_lattice4 @ B @ 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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [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 @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(1621,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(9542,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)],[1621]) ).
thf(82,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(2421,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)],[82]) ).
thf(1003,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(6563,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)],[1003]) ).
thf(19627,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k2_xboole_0 @ ( k1_tarski @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4339,3995]) ).
thf(19628,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk150 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[19627:[bind(A,$thf( k2_xboole_0 @ ( k1_tarski @ F ) @ E )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(20580,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk150 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ) ),
inference(simp,[status(thm)],[19628]) ).
thf(849,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(5884,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)],[849]) ).
thf(2760,plain,
! [A: $i] : ( v1_finset_1 @ ( sk37 @ A ) ),
inference(cnf,[status(esa)],[2753]) ).
thf(12952,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( sk37 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2760,2173]) ).
thf(12953,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( sk37 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[12952:[bind(A,$thf( D )),bind(B,$thf( sk37 @ D ))]]) ).
thf(12967,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( sk37 @ B ) @ A ) ),
inference(simp,[status(thm)],[12953]) ).
thf(25338,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ k1_xboole_0 @ A ) ),
inference(rewrite,[status(thm)],[12967,17354]) ).
thf(1036,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(6703,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)],[1036]) ).
thf(318,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(3379,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)],[318]) ).
thf(693,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(5187,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)],[693]) ).
thf(841,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
thf(5852,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A )
& ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(4880,plain,
v1_relat_1 @ sk196,
inference(cnf,[status(esa)],[4877]) ).
thf(1158,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( C
= ( k3_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_0) ).
thf(7216,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( C
= ( k3_filter_0 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1859,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(10569,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)],[1859]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(5677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(634,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4917,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(2298,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ( r4_lattice3 @ A @ ( sk9 @ B @ A ) @ ( sk8 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[2294]) ).
thf(2302,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk8 @ A ) )
| ( r4_lattice3 @ A @ ( sk9 @ B @ A ) @ ( sk8 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[2298]) ).
thf(1548,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(9166,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)],[1548]) ).
thf(1898,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(10701,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)],[1898]) ).
thf(1519,axiom,
! [A: $i] :
( ( v1_int_1 @ A )
<=> ( r2_hidden @ A @ k4_numbers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_int_1) ).
thf(9034,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)],[1519]) ).
thf(19531,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk611 ) ),
inference(paramod_ordered,[status(thm)],[4339,14837]) ).
thf(19532,plain,
( ( v1_relat_1 @ ( sk150 @ sk611 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19531:[bind(A,$thf( sk611 ))]]) ).
thf(907,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(6201,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)],[907]) ).
thf(534,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(4399,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)],[534]) ).
thf(1094,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(6957,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)],[1094]) ).
thf(405,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(3785,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)],[405]) ).
thf(1990,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(11035,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)],[1990]) ).
thf(2151,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ~ ( l3_lattices @ B )
| ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(cnf,[status(esa)],[2138]) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( l3_lattices @ A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( l3_lattices @ B )
| ~ ( v15_lattices @ A )
| ~ ( v16_lattices @ A )
| ~ ( v15_lattices @ B )
| ~ ( v16_lattices @ B )
| ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ),
inference(simp,[status(thm)],[2151]) ).
thf(528,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(4378,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)],[528]) ).
thf(4658,plain,
( ! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(miniscope,[status(thm)],[4657]) ).
thf(4659,plain,
! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ),
inference(cnf,[status(esa)],[4658]) ).
thf(4661,plain,
! [A: $i] : ( v1_funct_1 @ ( k6_relat_1 @ A ) ),
inference(simp,[status(thm)],[4659]) ).
thf(14499,plain,
! [A: $i] : ( v1_funct_1 @ ( k6_partfun1 @ A ) ),
inference(rewrite,[status(thm)],[4661,10471]) ).
thf(1064,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(6822,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)],[1064]) ).
thf(2054,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(11271,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)],[2054]) ).
thf(1683,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(9823,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)],[1683]) ).
thf(126,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_filter_0) ).
thf(2587,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(427,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(3882,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)],[427]) ).
thf(1163,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(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_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)],[1163]) ).
thf(1781,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(10312,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)],[1781]) ).
thf(1824,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(10453,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)],[1824]) ).
thf(109,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(2522,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)],[109]) ).
thf(316,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(3373,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)],[316]) ).
thf(415,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(3837,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)],[415]) ).
thf(336,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(3464,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)],[336]) ).
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_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(7029,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)],[1112]) ).
thf(554,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(4523,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)],[554]) ).
thf(19557,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk611 ) ),
inference(paramod_ordered,[status(thm)],[4339,10816]) ).
thf(19558,plain,
( ( v1_relat_1 @ ( sk150 @ sk611 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19557:[bind(A,$thf( sk611 ))]]) ).
thf(816,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(5764,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)],[816]) ).
thf(169,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(2736,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)],[169]) ).
thf(2755,plain,
! [A: $i] : ( m1_finseq_1 @ ( sk37 @ A ) @ A ),
inference(cnf,[status(esa)],[2753]) ).
thf(19073,plain,
! [A: $i] : ( m1_finseq_1 @ k1_xboole_0 @ A ),
inference(rewrite,[status(thm)],[2755,17354]) ).
thf(38725,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v1_relat_1 @ ( sk150 @ B ) )
| ( v4_group_1 @ B )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6758,20184]) ).
thf(38726,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A ) ),
inference(pattern_uni,[status(thm)],[38725:[bind(A,$thf( sk1 ))]]) ).
thf(38737,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ sk1 )
| ( v1_relat_1 @ ( sk150 @ A ) )
| ( v4_group_1 @ A ) ),
inference(simp,[status(thm)],[38726]) ).
thf(1029,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(6671,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)],[1029]) ).
thf(734,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(5371,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)],[734]) ).
thf(984,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(6490,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)],[984]) ).
thf(1524,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(9051,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)],[1524]) ).
thf(1978,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(10998,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)],[1978]) ).
thf(569,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(4579,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)],[569]) ).
thf(656,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(5014,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)],[656]) ).
thf(1009,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(6580,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)],[1009]) ).
thf(1733,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(10054,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)],[1733]) ).
thf(1415,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(8489,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)],[1415]) ).
thf(1688,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(9844,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)],[1688]) ).
thf(14503,plain,
( ( ( k3_latsubgr @ sk1 @ sk1 @ k1_xboole_0 )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) )
| ( ( k6_partfun1 @ ( u1_struct_0 @ sk1 ) )
!= ( k6_partfun1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[14502,2119]) ).
thf(14504,plain,
( ( ( k3_latsubgr @ sk1 @ sk1 @ k1_xboole_0 )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) )
| ( ( u1_struct_0 @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[14503]) ).
thf(1437,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(8621,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)],[1437]) ).
thf(1480,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(8801,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)],[1480]) ).
thf(33595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_xboole_0 @ B @ D )
| ( ( r1_tarski @ ( k4_xboole_0 @ A @ k1_numbers ) @ ( k4_xboole_0 @ A @ k5_numbers ) )
!= ( r1_tarski @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19271,2260]) ).
thf(33596,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k1_numbers ) @ k5_numbers ),
inference(pattern_uni,[status(thm)],[33595:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ E @ k1_numbers )),bind(C,$thf( E )),bind(D,$thf( k5_numbers ))]]) ).
thf(33661,plain,
! [A: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ k1_numbers ) @ k5_numbers ),
inference(simp,[status(thm)],[33596]) ).
thf(1728,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(10036,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)],[1728]) ).
thf(494,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(4210,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)],[494]) ).
thf(1426,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(8557,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)],[1426]) ).
thf(1031,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(6682,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)],[1031]) ).
thf(144,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(2651,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)],[144]) ).
thf(1653,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(9697,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)],[1653]) ).
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 ) )
=> ! [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(8616,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)],[1436]) ).
thf(960,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(6411,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)],[960]) ).
thf(1424,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(8542,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)],[1424]) ).
thf(1489,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(8833,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)],[1489]) ).
thf(14842,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l1_group_1 @ sk610 )
!= ( l1_group_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10798,4719]) ).
thf(14843,plain,
l1_struct_0 @ sk610,
inference(pattern_uni,[status(thm)],[14842:[bind(A,$thf( sk610 ))]]) ).
thf(463,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(4051,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)],[463]) ).
thf(2042,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(11214,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)],[2042]) ).
thf(1231,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(7557,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)],[1231]) ).
thf(1367,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(8207,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)],[1367]) ).
thf(2334,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
| ( r4_binop_1 @ B @ E @ F ) ),
inference(cnf,[status(esa)],[2332]) ).
thf(803,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(5709,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)],[803]) ).
thf(628,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(4895,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)],[628]) ).
thf(2080,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(11362,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)],[2080]) ).
thf(2186,plain,
! [B: $i,A: $i] :
( ~ ( v1_int_1 @ A )
| ~ ( v1_int_1 @ B )
| ~ ( r1_xreal_0 @ A @ B )
| ( r2_hidden @ ( k6_xcmplx_0 @ B @ A ) @ k5_numbers ) ),
inference(cnf,[status(esa)],[2185]) ).
thf(506,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(4281,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)],[506]) ).
thf(2094,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(11415,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)],[2094]) ).
thf(1396,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(8424,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)],[1396]) ).
thf(19621,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A != sk15 ) ),
inference(paramod_ordered,[status(thm)],[4339,11545]) ).
thf(19622,plain,
v1_relat_1 @ ( sk150 @ sk15 ),
inference(pattern_uni,[status(thm)],[19621:[bind(A,$thf( sk15 ))]]) ).
thf(1038,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(6714,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)],[1038]) ).
thf(80,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(2417,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)],[80]) ).
thf(1331,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(8051,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)],[1331]) ).
thf(1829,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(10472,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)],[1829]) ).
thf(1042,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(6729,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)],[1042]) ).
thf(2363,plain,
! [B: $i,A: $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 )
| ( ( k1_binop_1 @ B @ ( sk14 @ B @ A ) @ ( sk14 @ B @ A ) )
!= ( sk14 @ B @ A ) )
| ( v3_binop_1 @ B @ A ) ),
inference(cnf,[status(esa)],[2361]) ).
thf(2366,plain,
! [B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ ( sk14 @ B @ A ) @ ( sk14 @ B @ A ) )
!= ( sk14 @ B @ A ) )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[2363]) ).
thf(923,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(6287,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)],[923]) ).
thf(728,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(5339,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)],[728]) ).
thf(26545,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk605 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16597]) ).
thf(26558,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk605 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[26545]) ).
thf(2040,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(11209,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)],[2040]) ).
thf(220,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k4_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_finseq_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_finseq_3) ).
thf(2961,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( k4_finseq_1 @ ( k1_finseq_3 @ A @ B ) )
= ( k4_finseq_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(921,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(6258,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)],[921]) ).
thf(1053,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(6765,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)],[1053]) ).
thf(952,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(6380,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)],[952]) ).
thf(845,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(5867,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)],[845]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(3426,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_lattice3) ).
thf(10237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(737,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(5378,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)],[737]) ).
thf(785,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(5642,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)],[785]) ).
thf(2096,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(11422,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)],[2096]) ).
thf(489,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(4193,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)],[489]) ).
thf(3422,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3421]) ).
thf(3424,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3422]) ).
thf(632,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(4912,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)],[632]) ).
thf(878,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(6040,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)],[878]) ).
thf(1088,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(6929,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)],[1088]) ).
thf(1709,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(9927,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)],[1709]) ).
thf(1575,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(9293,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)],[1575]) ).
thf(19777,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( k2_card_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,13527]) ).
thf(19778,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k2_card_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[19777:[bind(A,$thf( k2_card_1 @ C )),bind(B,$thf( C ))]]) ).
thf(20618,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( k2_card_1 @ A ) ) ),
inference(simp,[status(thm)],[19778]) ).
thf(1594,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(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 )
=> ( ( 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)],[1594]) ).
thf(2009,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(11114,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)],[2009]) ).
thf(1257,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(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 ) ) )
=> ( 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)],[1257]) ).
thf(1921,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(10781,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)],[1921]) ).
thf(724,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(5324,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)],[724]) ).
thf(1223,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(7525,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)],[1223]) ).
thf(1971,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(10981,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)],[1971]) ).
thf(2059,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(11290,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)],[2059]) ).
thf(1289,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(7819,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)],[1289]) ).
thf(116,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_xreal_0 @ ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k3_finseq_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_finseq_3) ).
thf(2549,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] : ( r1_xreal_0 @ ( k3_finseq_1 @ ( k1_finseq_3 @ A @ B ) ) @ ( k3_finseq_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1623,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(9547,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)],[1623]) ).
thf(448,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(3974,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)],[448]) ).
thf(1446,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_filter_0) ).
thf(8680,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(1601,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(9441,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)],[1601]) ).
thf(712,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(5275,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)],[712]) ).
thf(14652,plain,
( ( v1_xboole_0 @ ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[4353,14622]) ).
thf(14670,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk152 ),
inference(simp,[status(thm)],[14652]) ).
thf(15058,plain,
! [A: $i] :
( ( A != sk152 )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2254,14670]) ).
thf(15061,plain,
( ( k4_xboole_0 @ sk152 @ k1_xboole_0 )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[15058]) ).
thf(21680,plain,
( ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) )
!= sk152 ),
inference(rewrite,[status(thm)],[15061,2254]) ).
thf(16938,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( ( k3_latsubgr @ sk1 @ sk1 @ k1_xboole_0 )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) )
| ( A
!= ( u1_struct_0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[6758,14504]) ).
thf(16939,plain,
( ~ ( v1_xboole_0 @ ( u1_struct_0 @ sk1 ) )
| ( ( k3_latsubgr @ sk1 @ sk1 @ k1_xboole_0 )
!= ( k6_partfun1 @ ( u1_struct_0 @ ( k11_group_4 @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[16938:[bind(A,$thf( u1_struct_0 @ sk1 ))]]) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( B = k1_xboole_0 )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(cnf,[status(esa)],[2236]) ).
thf(2241,plain,
! [C: $i,B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ A @ B )
| ~ ( m2_relset_1 @ C @ A @ B )
| ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ),
inference(lifteq,[status(thm)],[2238]) ).
thf(2127,plain,
! [A: $i] :
( ~ ( l3_lattices @ A )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v16_lattices @ A ) ),
inference(cnf,[status(esa)],[2123]) ).
thf(621,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(4848,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)],[621]) ).
thf(8,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(2159,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(167,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m1_subset_1 @ ( k4_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finseq_1) ).
thf(2731,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m1_subset_1 @ ( k4_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(2089,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(11390,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)],[2089]) ).
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] :
( ( 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(8066,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)],[1333]) ).
thf(1679,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(9810,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)],[1679]) ).
thf(222,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
<=> ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finseq_3) ).
thf(2966,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
=> ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) ) )
& ( ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(932,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(6316,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(892,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(6099,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)],[892]) ).
thf(1937,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(10836,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)],[1937]) ).
thf(387,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(3701,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)],[387]) ).
thf(684,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(5151,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)],[684]) ).
thf(183,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(2803,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)],[183]) ).
thf(1648,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(9679,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( m1_finseq_1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_finseq_1) ).
thf(2847,plain,
! [A: $i,B: $i] :
( ( m1_finseq_1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(362,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(3605,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)],[362]) ).
thf(326,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(3411,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)],[326]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_2) ).
thf(2485,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(968,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(6435,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)],[968]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(3869,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ B @ C )
= C ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1974,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(10988,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)],[1974]) ).
thf(1329,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(8034,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)],[1329]) ).
thf(1604,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(9474,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)],[1604]) ).
thf(404,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(3772,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)],[404]) ).
thf(953,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(6383,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)],[953]) ).
thf(24899,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk611 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[5730,16342]) ).
thf(24912,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk611 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[24899]) ).
thf(908,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(6205,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)],[908]) ).
thf(1700,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(9895,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)],[1700]) ).
thf(1122,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(7071,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)],[1122]) ).
thf(1290,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(7829,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)],[1290]) ).
thf(10713,plain,
v3_group_1 @ sk608,
inference(cnf,[status(esa)],[10707]) ).
thf(1541,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(9124,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)],[1541]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattice3 @ B @ C @ A )
<=> ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
thf(3245,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattice3 @ B @ C @ A )
=> ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) )
& ( ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) )
=> ( r3_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(796,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(5681,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)],[796]) ).
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 ) )
=> ! [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(5060,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)],[658]) ).
thf(499,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(4239,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)],[499]) ).
thf(1214,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(7493,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)],[1214]) ).
thf(1263,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(7708,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)],[1263]) ).
thf(780,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(5623,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)],[780]) ).
thf(941,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(6348,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)],[941]) ).
thf(1940,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(10845,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)],[1940]) ).
thf(493,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(4206,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)],[493]) ).
thf(1731,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(10045,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)],[1731]) ).
thf(2097,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(11425,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)],[2097]) ).
thf(2029,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(11182,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)],[2029]) ).
thf(1279,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(7780,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_7_lattice3) ).
thf(9633,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(1717,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattices) ).
thf(9969,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ 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 ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_enumset1) ).
thf(5821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_enumset1 @ A @ B @ C @ D )
= ( k2_enumset1 @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_group_4 @ A ) )
& ( v3_lattices @ ( k11_group_4 @ A ) )
& ( v10_lattices @ ( k11_group_4 @ A ) )
& ( l3_lattices @ ( k11_group_4 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_group_4) ).
thf(10877,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_group_4 @ A ) )
& ( v3_lattices @ ( k11_group_4 @ A ) )
& ( v10_lattices @ ( k11_group_4 @ A ) )
& ( l3_lattices @ ( k11_group_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).
thf(1753,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(10146,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)],[1753]) ).
thf(19475,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk605 ) ),
inference(paramod_ordered,[status(thm)],[4339,10655]) ).
thf(19476,plain,
( ( v1_relat_1 @ ( sk150 @ sk605 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19475:[bind(A,$thf( sk605 ))]]) ).
thf(2072,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(11330,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)],[2072]) ).
thf(1748,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(10124,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)],[1748]) ).
thf(1470,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(8773,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)],[1470]) ).
thf(1780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v5_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_3_7_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_lattice3) ).
thf(10304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v5_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_7_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k4_lattices @ C @ D @ E ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ A @ ( a_3_7_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_partfun1) ).
thf(2687,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1918,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(10773,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)],[1918]) ).
thf(1261,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(7694,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)],[1261]) ).
thf(9489,plain,
v1_card_1 @ sk522,
inference(cnf,[status(esa)],[9488]) ).
thf(736,axiom,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).
thf(5376,plain,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(591,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(4691,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)],[591]) ).
thf(436,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(3918,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)],[436]) ).
thf(466,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(4088,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)],[466]) ).
thf(1233,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(7563,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)],[1233]) ).
thf(2372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( v1_funct_1 @ C ) ),
inference(cnf,[status(esa)],[2369]) ).
thf(1193,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(7392,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)],[1193]) ).
thf(840,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(5845,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)],[840]) ).
thf(2098,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(11430,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)],[2098]) ).
thf(2062,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( k4_lattices @ ( k11_group_4 @ A ) @ D @ E )
= ( k9_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_latsubgr) ).
thf(11298,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 @ ( k11_group_4 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k11_group_4 @ A ) ) )
=> ( ( ( D = B )
& ( E = C ) )
=> ( ( k4_lattices @ ( k11_group_4 @ A ) @ D @ E )
= ( k9_group_2 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(443,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(3950,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)],[443]) ).
thf(1325,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(8023,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)],[1325]) ).
thf(1174,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(7320,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)],[1174]) ).
thf(1580,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(9310,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)],[1580]) ).
thf(1347,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(8130,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)],[1347]) ).
thf(719,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_1) ).
thf(5293,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(176,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(2771,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)],[176]) ).
thf(19170,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k1_setfam_1 @ B ) @ A )
| ( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
!= ( k3_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3845,4292]) ).
thf(19171,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ ( k1_zfmisc_1 @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[19170:[bind(A,$thf( C )),bind(B,$thf( k1_zfmisc_1 @ C ))]]) ).
thf(19188,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ ( k1_zfmisc_1 @ A ) ) @ A ),
inference(simp,[status(thm)],[19171]) ).
thf(19617,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( l1_group_1 @ k1_xboole_0 )
| ( A != sk335 ) ),
inference(paramod_ordered,[status(thm)],[4339,7005]) ).
thf(19618,plain,
( ( v1_relat_1 @ ( sk150 @ sk335 ) )
| ( l1_group_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[19617:[bind(A,$thf( sk335 ))]]) ).
thf(235,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(3013,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)],[235]) ).
thf(345,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(3526,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)],[345]) ).
thf(20213,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk150 @ A ) )
| ( A
!= ( sk524 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4339,14319]) ).
thf(20214,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( sk524 @ A ) ) ),
inference(pattern_uni,[status(thm)],[20213:[bind(A,$thf( sk524 @ C )),bind(B,$thf( C ))]]) ).
thf(20737,plain,
! [A: $i] : ( v1_relat_1 @ ( sk150 @ ( sk524 @ A ) ) ),
inference(simp,[status(thm)],[20214]) ).
thf(1305,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(7900,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(1075,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(6864,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)],[1075]) ).
thf(43829,plain,
! [A: $i] :
( ( sk152 != k5_numbers )
| ( ( k4_xboole_0 @ k5_numbers @ A )
!= ( k4_xboole_0 @ sk15 @ ( k1_tarski @ ( sk305 @ sk15 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[43667,21680]) ).
thf(43835,plain,
! [A: $i] :
( ( sk152 != k5_numbers )
| ( sk15 != k5_numbers )
| ( A
!= ( k1_tarski @ ( sk305 @ sk15 ) ) ) ),
inference(simp,[status(thm)],[43829]) ).
thf(43891,plain,
( ( sk152 != k5_numbers )
| ( sk15 != k5_numbers ) ),
inference(simp,[status(thm)],[43835]) ).
thf(43938,plain,
( ( k1_xboole_0 != k5_numbers )
| ( sk15 != k5_numbers ) ),
inference(rewrite,[status(thm)],[43891,15924]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v6_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_3_10_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_10_lattice3) ).
thf(8184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( v6_lattice3 @ C )
& ( l3_lattices @ C )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_10_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
& ( A
= ( k3_lattices @ C @ E @ D ) )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ A @ ( a_3_10_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(925,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(6297,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)],[925]) ).
thf(151,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(2672,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)],[151]) ).
thf(41735,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ k1_xboole_0 )
| ( ( k2_xboole_0 @ k1_xboole_0 @ A )
!= ( k2_xboole_0 @ B @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[41649,30441]) ).
thf(41736,plain,
r1_tarski @ ( k1_orders_1 @ k1_xboole_0 ) @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[41735:[bind(A,$thf( k1_tarski @ k1_xboole_0 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(5877,plain,
v2_group_1 @ sk259,
inference(cnf,[status(esa)],[5873]) ).
thf(1187,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(7367,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)],[1187]) ).
thf(356,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(3580,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)],[356]) ).
thf(1835,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(10492,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)],[1835]) ).
thf(1278,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(7776,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)],[1278]) ).
thf(1903,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(10723,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)],[1903]) ).
thf(1422,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(8525,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)],[1422]) ).
thf(505,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(4274,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)],[505]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_0) ).
thf(4702,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(768,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(5542,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)],[768]) ).
thf(582,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_filter_0) ).
thf(4642,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1746,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(10118,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(577,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(4627,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)],[577]) ).
thf(1507,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(8940,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)],[1507]) ).
thf(864,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(5986,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)],[864]) ).
thf(755,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
<=> ( v1_filter_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_0) ).
thf(5494,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
=> ( v1_filter_0 @ B @ A ) )
& ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1267,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(7723,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)],[1267]) ).
thf(779,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(5618,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)],[779]) ).
thf(2206,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk3 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(608,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(4767,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)],[608]) ).
thf(324,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(3405,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)],[324]) ).
thf(1950,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(10900,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)],[1950]) ).
thf(708,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(5255,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)],[708]) ).
thf(1054,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(6767,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)],[1054]) ).
thf(748,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_lattice3) ).
thf(5445,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(1130,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(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 ) )
=> ! [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)],[1130]) ).
thf(1060,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(6810,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)],[1060]) ).
thf(1577,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(9297,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)],[1577]) ).
thf(1165,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(7267,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)],[1165]) ).
thf(1930,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(10817,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)],[1930]) ).
thf(94,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(2453,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)],[94]) ).
thf(10686,plain,
v7_group_1 @ sk607,
inference(cnf,[status(esa)],[10685]) ).
thf(6119,plain,
v1_relat_1 @ sk280,
inference(cnf,[status(esa)],[6118]) ).
thf(2170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ 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 )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( v1_funct_1 @ F )
| ~ ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r5_binop_1 @ A @ C @ D )
| ~ ( r5_binop_1 @ B @ E @ F )
| ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ),
inference(cnf,[status(esa)],[2167]) ).
thf(2347,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( r2_hidden @ ( sk13 @ C @ B @ A ) @ C )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[2345]) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( r2_hidden @ ( sk13 @ C @ B @ A ) @ C )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[2347]) ).
thf(877,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(6035,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)],[877]) ).
thf(2191,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( 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_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 ) ),
inference(cnf,[status(esa)],[2189]) ).
thf(1028,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(6668,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)],[1028]) ).
thf(14690,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
| ( ( l2_lattices @ sk261 )
!= ( l2_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5914,4466]) ).
thf(14691,plain,
l1_struct_0 @ sk261,
inference(pattern_uni,[status(thm)],[14690:[bind(A,$thf( sk261 ))]]) ).
thf(1485,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(8818,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)],[1485]) ).
thf(12455,plain,
! [A: $i] :
( ( v1_card_1 @ k1_xboole_0 )
| ( ( k1_card_1 @ k1_xboole_0 )
!= ( k1_card_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8072,7010]) ).
thf(12456,plain,
v1_card_1 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[12455:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(391,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
<=> ( r3_lattices @ 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',t8_lattice4) ).
thf(3721,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ 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 ) ) )
& ( ( r3_lattices @ 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 ) )
=> ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1393,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(8405,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)],[1393]) ).
thf(1444,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(8670,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)],[1444]) ).
thf(769,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(5574,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)],[769]) ).
thf(855,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_0) ).
thf(5911,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ 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_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(1078,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(6886,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)],[1078]) ).
thf(242,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(3035,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)],[242]) ).
thf(513,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(4298,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)],[513]) ).
thf(56827,plain,
$false,
inference(e,[status(thm)],[7373,5116,9180,5320,8200,9032,5385,42983,3021,2199,8062,9982,2822,7304,10917,4188,6836,3944,6979,19540,20007,9273,4835,6355,10373,11445,2295,3053,5857,9886,2306,7890,10638,2336,9077,3008,5593,2131,5136,11211,7569,5896,6976,11186,19347,2263,6544,3930,8114,9754,4183,3979,5390,10495,6855,26775,9685,10743,3969,20162,5205,6121,2544,5999,5778,6555,19572,14833,8475,6566,6954,4877,8828,6527,5582,10387,10832,2381,7322,5878,5793,10039,8988,11008,10658,6142,3681,6587,7040,4037,7886,2512,10795,4376,7477,10299,10149,2117,7940,7083,3317,10446,8044,7358,6918,7517,10431,4339,2231,43656,11043,9924,2644,4515,2908,5842,6463,2659,5242,11277,10567,3040,10912,2248,10711,8447,3108,7198,4711,8169,2282,5669,9191,11266,6426,2114,4326,2380,7182,10886,9572,5237,9759,9818,25459,6480,6732,24569,6214,3382,7813,5501,6971,6939,6665,10138,9218,10726,9278,2195,3017,9644,8101,10484,8765,36600,11112,8335,10433,3049,3745,16413,10181,8430,7573,11029,3332,6246,3367,3648,4097,10395,10093,8915,6127,7115,16688,2184,7096,8353,2316,8667,9565,2448,18438,6089,3338,11075,5257,2434,6416,40563,8342,3616,9494,10511,7147,2168,5674,8210,7422,2459,6996,19653,6759,7452,3313,8838,6370,5636,2844,6804,10991,2146,11549,4980,7748,3717,2360,10341,15791,9540,9481,5412,18425,4792,11335,7064,7729,29366,2173,7311,4941,7605,9443,11228,3335,8911,9424,11171,2216,3236,29532,5227,6466,5740,3545,2491,5393,8086,2763,3915,2985,10908,11382,5123,10474,6872,4266,3513,11273,9027,9379,9096,6009,9994,31774,3730,8472,8705,3898,13287,10698,7856,7343,5874,6102,11340,28843,10807,9657,32456,4322,2819,4948,2531,7592,4467,25427,11250,10501,19434,5797,5533,9116,3195,2269,20113,3574,3821,8654,9123,3891,4637,2654,3248,10042,9300,10903,15135,3221,10955,10121,2603,2916,13280,10437,6892,5585,3425,6552,9099,7262,4563,8494,10587,19626,19763,17366,21101,35671,8089,4151,8225,6547,2339,9432,3046,9216,3689,43667,6723,4761,11010,3061,6423,6749,5064,4654,2444,10221,7945,8951,3653,24526,8785,2274,11448,11458,9360,8214,6968,3125,11200,15146,2185,9909,10010,3845,2562,10606,3089,2488,6662,6006,5712,5289,3803,2126,8242,4428,6208,3043,3855,10469,6643,3713,8753,2356,7665,5279,10655,7011,2703,2691,4119,4358,3470,9039,4967,8257,5231,8770,11453,3840,5355,3385,8590,9800,7711,11463,4788,10687,2169,10850,38795,5199,7209,5802,15742,10891,5193,39948,6310,2767,16953,10074,6599,2373,11378,5925,6365,6936,8367,19927,9199,7215,7560,2520,5746,2158,4632,8703,6828,2301,3180,4390,16640,3602,7633,8738,6025,3231,10682,5077,4514,29641,3866,6487,2533,8161,7509,17855,4669,9768,7733,2829,5792,10871,3163,15150,5156,5834,2456,9401,2178,8109,11163,25965,10519,4696,4988,10729,3322,11314,8956,10950,15763,7792,3431,41091,14837,10641,17354,10746,9283,4329,2324,3199,9520,42944,5526,4443,9490,10623,17171,3724,4454,11293,29990,14847,30346,6895,6657,4733,8158,2259,7369,6419,6523,2451,2236,8791,3983,6189,8929,7376,6745,2880,7537,7845,2122,9860,10085,10816,5914,7532,10786,7739,6841,3357,2254,3569,5311,6559,10378,8759,2335,14500,6438,10201,4556,5259,8196,10602,3851,3986,21774,7645,3226,11367,2718,9875,2964,4718,8438,10799,19675,2367,11312,2437,3537,9897,6451,11325,8001,8595,5448,9616,4935,4033,2618,2833,3189,2281,6685,5220,8454,8575,5096,2190,6740,7381,3421,5101,7004,9865,8823,5648,7336,5772,3808,9140,2530,11413,2371,5343,4307,8347,3676,2137,8686,4924,10965,9187,3756,14622,10390,6021,2809,2242,8173,2799,10801,2286,9368,9236,3327,10839,6327,8443,4892,5819,4285,2154,10933,5824,4588,21107,7758,7354,10256,33768,2982,26243,9584,20736,19729,3510,5695,10690,8421,8523,3229,2204,6571,9384,2954,10779,30411,9703,9917,2922,7254,7535,9682,3459,5875,6560,5783,6406,4629,10362,6482,20528,9308,6015,5839,10561,20025,9221,3169,4480,7550,2646,11550,10139,21784,3635,2364,2164,5697,3186,11032,5167,7859,2118,5142,7937,5291,8959,15920,3995,6388,9009,7642,5416,4370,7005,5862,13519,2307,2296,4576,2641,19727,17363,9785,2496,2621,2660,10477,5334,2382,3550,4172,2773,11202,9881,10345,11545,2264,20416,6343,2541,9412,3889,10133,8113,8513,2589,3735,9488,4466,5611,5734,7042,2601,8778,6897,2428,2733,2805,3711,7989,14501,2249,6032,2277,4375,8756,8888,4878,7229,2133,11223,7161,7834,12970,8856,10426,10657,9207,21646,10409,3989,3069,9849,3239,45543,3371,9126,2606,11003,4449,16597,8081,5085,7692,3816,10548,3814,5396,2132,2414,5594,4160,11191,3207,9734,7301,9177,8623,4608,8651,21095,2200,10794,2958,8683,3307,5769,7308,10263,9113,8810,3191,10710,6926,2464,5879,7325,2873,3980,10634,10939,10330,5492,6432,8540,8788,2628,2670,7842,13282,8026,4585,7185,10826,7762,2332,9671,6043,4155,7449,2820,3750,3349,5690,9277,3578,10583,9758,7902,10765,5988,3894,15137,11174,5341,8181,2179,2181,19369,6392,7934,2213,4740,5658,3050,10958,2211,10235,2313,3763,4104,2547,2344,7853,8031,9613,3667,2228,11101,8104,3033,9829,4680,5515,3595,7686,5285,8073,6090,6888,9730,10529,16519,3001,3176,12372,15559,3968,5313,4123,7750,7346,3699,2300,3467,5626,2498,6413,5904,11356,7142,2157,2840,11133,3482,5145,20184,3254,2377,9804,4668,6801,19864,10295,4512,9355,10986,9073,3862,8009,10791,6375,6195,6477,8339,8414,9945,2359,9328,6459,9773,32657,7389,5577,12016,4544,11221,10644,8435,2694,10646,14666,10335,11057,2509,11435,9525,9977,2631,10152,29541,2724,10661,11128,3632,7698,7513,5373,5811,10398,6360,4840,10021,11189,3650,8567,7204,19478,9333,10882,2638,5233,5687,11467,2268,8815,3205,10678,4653,41734,3922,4291,6299,7101,8176,16068,9872,7091,4518,8704,14841,6518,10708,5694,4582,8864,2323,8017,7631,4983,9508,5915,3846,5181,3622,25133,5080,9662,6844,5651,7629,6593,24505,8251,11403,10498,4425,5791,6363,10381,2868,7318,5743,2419,13527,19373,2312,10776,5337,4938,20033,10798,2196,2240,19735,10936,4191,5588,8132,11046,10823,4648,3428,9288,11442,6978,7480,10688,2349,11026,2551,10539,7417,7577,6539,15126,6946,2666,6625,7976,10752,7895,2978,2649,8467,7682,2317,5387,4736,11248,6065,7749,43903,3115,9900,10720,3242,7668,10575,16889,11432,2285,8673,19790,11023,4846,9365,8013,17170,7340,10423,7651,7878,4384,17054,8072,2536,43773,39949,10666,2681,10834,5149,2304,2836,4508,7014,3059,6331,6999,5380,7508,5639,6788,3743,10735,3770,9893,2851,9761,2355,7485,7738,8690,6211,9448,19562,9630,2566,9112,10207,13718,7789,11184,6346,6908,10302,3409,10629,4902,4953,11261,10550,3064,4259,10866,3920,2272,2140,4086,8980,6224,9942,3083,3201,4223,10252,2370,20574,12962,4361,10406,10651,5310,8393,5887,7802,20614,2338,5170,19498,19459,8796,5112,21519,7150,3834,10802,11216,4352,10597,2203,10815,10929,11084,4644,11153,4288,10338,2761,8482,4625,7052,4567,2208,11125,3183,4889,10614,10740,9782,8361,3173,9044,10689,11546,3856,10656,6716,8559,11544,6812,17767,16644,3999,2368,9213,6378,2402,11196,8004,3639,2440,6688,2408,6756,11559,11065,6610,19878,4036,2189,10359,9744,6400,2423,9562,9226,4572,6497,11120,4550,9545,10556,9677,10030,2941,7160,2121,2235,10978,5679,6368,9484,9726,4919,6053,5722,11110,6507,11179,8903,2176,4708,4685,21800,2292,9765,14497,7582,2275,41077,7128,6615,2585,7512,9502,2717,5451,3607,35664,7010,5508,10079,8906,4657,11148,25201,9021,11016,9721,10993,19365,6001,8112,4393,6469,4797,10420,3523,7165,5016,35670,11063,3111,8718,7785,7118,3686,9650,3696,12778,10625,9049,6492,20720,5758,9974,9072,7212,4365,8807,2260,8909,11323,9157,10709,4465,5984,5535,10668,6140,11006,4041,7162,8015,4998,10155,3741,4662,11396,7714,4268,3234,11455,6916,3925,2859,2938,7639,2225,6617,4283,5488,4077,7497,33769,6510,3811,2791,2789,6312,7736,2657,7233,10963,4309,8470,2188,5121,2489,7073,7134,9025,7751,7440,5940,31778,10329,8894,8124,9531,5831,6229,9295,4032,4605,5099,9189,5876,2991,3590,2398,10435,2716,4381,5350,2817,10874,5799,9820,9952,19814,2827,12964,4505,9627,7038,7795,4526,22113,11370,3641,9681,7579,8244,32785,8767,2193,26512,3118,4127,4186,2326,8549,2293,2308,5011,3726,4837,20005,8841,10770,7689,5859,8862,4149,5331,5282,8359,6091,10051,6302,4764,9776,7094,2442,5190,2753,8344,7800,6638,9555,41071,9496,7671,7465,7145,3832,2166,6636,7455,15887,3619,5735,7006,2425,9290,6334,5997,6372,14835,3355,10953,2573,2319,11038,2358,5634,5580,19741,14502,6048,2361,7837,8445,19560,2945,4667,7632,11169,7995,21388,7158,6144,3678,7529,10842,5870,4790,2721,2119,8452,6059,21714,9575,10921,5212,4929,6942,15978,10429,10448,4228,10317,7594,3996,2538,7783,6308,5671,10910,6613,2478,3251,45557,11117,2229,5506,2214,8715,2383,6179,8799,13343,5520,8135,9903,4305,6147,3957,10675,3287,6815,19945,3419,19870,4914,4699,8120,26188,7328,3270,2284,2257,9047,2246,8693,10564,5880,8254,9920,2116,9570,4213,13334,11365,8561,3066,3586,7362,10115,11438,6216,4388,2180,4541,3006,2928,10970,10265,2824,4203,2182,7504,5511,4635,5114,8735,5816,9129,5202,9857,7768,8192,5920,14839,3027,10375,4882,4103,2314,2129,2343,7113,5730,10810,5894,9655,5082,9079,4462,19271,3073,8661,20001,11419,11205,7566,9642,2267,11073,2261,3800,4264,41235,3572,3932,8750,7033,11156,11158,7978,9756,10847,10136,6747,5656,6319,16802,6429,4296,8782,7869,10489,3971,10825,3583,9862,10412,10172,2289,6847,2252,9528,9511,11814,2664,30938,2278,9228,2329,15094,11375,10467,2911,5931,5641,11245,6504,3953,9106,11342,2303,9762,10402,8007,3480,11310,21513,3539,6255,4832,10660,4720,6574,2365,32457,9751,2350,9619,10444,2212,8456,3627,2171,8588,16238,8776,11041,20924,10514,9741,5482,10544,9899,4502,4373,10076,7469,11380,2369,7805,38738,10984,2931,2288,9366,10063,3310,11130,7200,5725,2535,8441,4304,19880,10707,6293,3178,2999,5693,2156,11193,2207,5139,26508,7507,7356,8763,3908,6485,29578,11359,10762,10692,9958,3444,4879,9111,10456,9054,4331,10417,11316,4690,5538,5587,2914,3031,10824,2614,19542,4013,10749,41649,10632,6542,7296,5881,6225,7403,2994,3395,10759,2271,9514,10354,9259,9430,7298,16342,10249,10091,4529,9826,3981,11077,6751,2124,2234,6191,4292,10384,7992,10814,19367,6056,12107,3048,2684,19344,10829,6853,7420,7122,3455,4688,2333,2597,20936,7137,8885,5807,6440,8477,8020,8194,5133,6973,10471,4986,19757,9202,4168,5991,2582,11547,6875,5414,6012,4749,6577,3376,6120,9847,2375,5399,8598,4922,7554,10797,6069,7026,8003,18449,8725,2715,6249,11327,10685,11461,6472,6453,10001,3913,19862,8143,4490,2661,5125,11098,10112,6621,2192,12963,3214,19118,8890,2143,6902,1057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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP650+2 : TPTP v8.1.2. Released v3.4.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 01:56:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.07/1.45 % [INFO] Parsing done (531ms).
% 3.18/1.46 % [INFO] Running in sequential loop mode.
% 3.56/1.67 % [INFO] eprover registered as external prover.
% 3.56/1.67 % [INFO] cvc4 registered as external prover.
% 3.56/1.68 % [INFO] Scanning for conjecture ...
% 4.68/1.97 % [INFO] Found a conjecture and 5673 axioms. Running axiom selection ...
% 7.03/2.83 % [INFO] Axiom selection finished. Selected 2110 axioms (removed 3563 axioms).
% 9.57/3.85 % [INFO] Problem is first-order (TPTP FOF).
% 10.02/3.90 % [INFO] Type checking passed.
% 10.02/3.90 % [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 ...
% 245.00/53.36 % External prover 'e' found a proof!
% 245.00/53.36 % [INFO] Killing All external provers ...
% 245.00/53.36 % Time passed: 52807ms (effective reasoning time: 51894ms)
% 245.00/53.36 % 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)>
% 245.00/53.37 % Axioms used in derivation (2110): t23_group_3, t7_filter_0, t107_group_3, t2_filter_0, t44_xboole_1, t60_group_2, t13_relset_1, t3_group_4, s2_group_4, t106_xboole_1, d13_group_3, t72_xboole_1, t86_partfun1, t15_finset_1, t8_group_3, t158_relat_1, t5_group_2, rc3_group_1, t38_funct_4, t133_group_3, t87_group_2, t51_filter_1, t42_xboole_1, t101_group_2, t26_group_4, t55_group_2, t185_group_2, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t32_finseq_3, t21_zfmisc_1, t76_group_4, d16_lattice3, t13_zfmisc_1, t30_funct_2, t24_filter_0, dt_k7_filter_0, d11_group_2, t24_latsubgr, t131_partfun1, t11_group_6, d13_filter_0, fc4_finset_1, t39_group_3, t48_group_2, d6_group_3, t19_group_3, t110_group_2, dt_m1_lattice4, dt_k3_group_3, d1_tarski, t114_group_3, t154_relat_1, t7_group_3, t56_filter_1, fraenkel_a_3_2_domain_1, t80_group_2, free_g1_group_1, fraenkel_a_3_6_lattice3, t39_lattices, t12_group_3, dt_k9_group_6, d1_group_1, t19_xboole_1, d4_group_1, t82_enumset1, t177_orders_1, t72_group_1, t69_group_6, t31_filter_0, t169_group_2, t17_xboole_1, t4_funct_4, t130_partfun1, t78_filter_0, t42_subset_1, 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, t23_card_1, t25_relset_1, d20_binop_1, t53_group_3, t66_funct_2, t67_relat_1, t62_filter_0, 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, d6_filter_0, rc4_finset_1, t79_funct_4, t20_funct_2, t48_filter_1, t73_xboole_1, dt_k11_group_6, t79_group_1, d14_binop_1, dt_k9_domain_1, t24_group_6, t59_group_1, t105_zfmisc_1, t54_filter_1, t140_zfmisc_1, fraenkel_a_1_0_filter_1, t83_group_3, t62_group_1, t109_xboole_1, idempotence_k3_xboole_0, redefinition_k9_domain_1, t22_latsubgr, t29_group_6, t82_group_2, t32_group_1, symmetry_r1_group_2, d10_binop_1, t35_filter_1, t10_group_2, t161_funct_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, t95_partfun1, t36_lattice4, 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, t29_filter_0, d1_group_3, d3_group_1, redefinition_k5_subset_1, t9_setfam_1, t23_group_2, t3_xboole_1, t180_orders_1, d4_lattice4, t3_realset1, d3_subset_1, t128_group_3, t34_xboole_1, rc7_finseq_1, t34_card_1, t8_subset_1, t38_funct_1, t53_funct_2, t156_funct_1, redefinition_k7_funct_2, d9_vectsp_8, fc1_xboole_0, t53_filter_1, t42_filter_0, t25_funct_1, cc6_lattices, t104_group_3, t51_lattice3, t40_group_2, t16_funct_2, t73_funct_4, t175_group_2, t113_zfmisc_1, t140_partfun1, t70_finseq_3, dt_k7_domain_1, t109_group_2, t25_numbers, t27_group_3, t116_partfun1, t48_domain_1, t44_group_4, t113_xboole_1, dt_k2_subset_1, fraenkel_a_1_0_group_4, t68_card_1, t55_lattice3, t81_partfun1, d15_group_6, t56_partfun1, existence_l1_lattices, t84_group_4, t72_finseq_3, t141_group_3, reflexivity_r1_group_2, t6_funct_4, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t31_group_6, d6_group_6, t37_funct_4, t50_group_6, t19_lattices, rc4_group_1, t4_ordinal1, t1_group_6, t59_partfun1, redefinition_k3_finseq_1, t43_lattices, t44_relat_1, t120_finseq_3, t1_subset, t147_relat_1, t10_partfun1, t28_lattice3, t71_card_1, t158_partfun1, redefinition_k2_group_6, t81_zfmisc_1, t124_group_3, t18_xboole_1, t90_group_1, d5_xboole_0, t167_group_2, t29_subset_1, t24_group_2, t63_group_3, t15_numbers, t92_group_6, t4_lattice4, d7_group_4, t52_zfmisc_1, t144_relat_1, t57_domain_1, t134_group_3, t9_group_3, fc4_subset_1, t61_group_2, t22_funct_1, t79_group_6, t28_group_1, existence_l3_lattices, t53_lattices, fc1_numbers, dt_k3_funct_2, t65_group_4, t80_card_1, t31_funct_4, t168_funct_2, t43_xboole_1, dt_k5_lattices, t7_funct_2, t25_filter_1, t8_group_2, rc1_group_2, t10_relset_1, t135_partfun1, t143_group_3, t3_mcart_1, d2_group_6, fc3_relat_1, t96_zfmisc_1, t44_group_3, t6_lattice3, t28_group_4, t43_lattice3, t14_binop_1, t119_group_3, dt_k1_subset_1, t73_group_1, t85_group_2, d5_group_6, t131_group_3, t117_partfun1, t90_group_6, t6_xboole_1, t30_filter_1, t132_group_3, d8_funct_1, t19_relat_1, t70_xboole_1, t28_binop_1, dt_k13_domain_1, t100_group_3, t38_group_2, t69_filter_0, t40_group_6, t21_latsubgr, d5_setfam_1, t72_card_1, t35_lattice4, t27_group_4, t28_group_6, t156_group_2, dt_m1_realset1, t23_filter_0, t47_relat_1, t18_group_2, fc9_relat_1, t6_group_3, t148_partfun1, t36_partfun1, redefinition_k4_card_1, t77_group_6, t68_xboole_1, d7_binop_1, t30_latsubgr, commutativity_k9_group_2, t19_finset_1, t71_group_1, t25_xboole_1, t61_card_1, existence_m3_lattice4, t15_group_6, t2_boole, dt_m1_filter_1, t18_filter_0, dt_k3_lattice4, t11_vectsp_8, t82_relat_1, t117_zfmisc_1, t29_funct_4, t65_partfun1, t186_partfun1, t44_funct_2, t56_lattice3, fraenkel_a_2_0_lattice4, t103_group_2, t49_group_1, t19_latsubgr, t14_card_1, t148_group_3, t117_funct_1, d10_filter_0, t92_group_3, t36_group_1, t53_lattice3, t94_finseq_3, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, t122_zfmisc_1, reflexivity_r1_group_6, t4_mcart_1, dt_k1_struct_0, t69_group_4, existence_m1_filter_1, t33_group_6, dt_k8_relset_1, d6_vectsp_8, t178_group_2, t43_zfmisc_1, t60_group_3, t52_group_3, d7_group_2, dt_u2_struct_0, t14_filter_0, t104_enumset1, t18_relat_1, rc3_funct_1, t78_group_6, rc2_finseq_1, t89_group_6, dt_m2_filter_1, t69_zfmisc_1, rc1_group_6, t22_lattice3, t42_group_6, t63_partfun1, t95_zfmisc_1, t96_partfun1, t15_relset_1, t61_group_6, t29_numbers, t84_finseq_1, fraenkel_a_2_0_filter_0, dt_k15_group_2, t79_group_2, t99_zfmisc_1, rc2_partfun1, t42_group_3, t46_group_3, t97_orders_1, cc4_lattices, t86_group_4, fc1_filter_0, fraenkel_a_3_9_lattice3, t81_xboole_1, t48_filter_0, t47_setfam_1, existence_m1_finseq_1, d9_lattice4, 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, rc3_finseq_1, t7_orders_1, t176_group_2, t162_partfun1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t56_group_4, t10_latsubgr, t34_lattice3, rc1_finseq_1, dt_k6_partfun1, symmetry_r2_group_3, d15_group_1, t79_finseq_3, t63_group_6, t41_group_6, t50_funct_2, dt_k5_filter_0, dt_k3_filter_0, t18_group_6, d1_struct_0, t97_group_2, dt_k7_funct_2, t8_group_4, t66_group_3, t76_card_1, commutativity_k3_xboole_0, t20_group_2, t29_latsubgr, 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, t116_enumset1, 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, fraenkel_a_3_4_lattice3, t30_card_1, t36_subset_1, redefinition_k6_setfam_1, t49_zfmisc_1, t43_group_4, t105_enumset1, t29_partfun1, t33_lattice4, t140_group_3, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, dt_k10_filter_1, t70_partfun1, t79_card_1, t93_group_2, t114_group_2, t3_setfam_1, t26_filter_0, t81_card_1, t146_group_2, t47_filter_1, t152_funct_2, t155_group_2, fc11_finset_1, t31_lattices, t17_binop_1, t33_group_4, d6_binop_1, t64_funct_2, t64_group_4, t115_zfmisc_1, t55_group_1, t62_funct_1, t76_funct_2, t65_funct_2, d10_group_2, t19_funct_1, redefinition_k9_group_2, dt_m2_lattice4, d11_filter_0, d8_group_4, t58_group_6, d12_group_2, dt_k10_group_3, t39_group_4, t13_funct_4, existence_m1_group_2, dt_k4_lattice3, t24_funct_2, t29_finset_1, t85_group_3, fc6_group_6, t82_group_6, dt_k2_binop_1, t137_zfmisc_1, 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, d3_latsubgr, t37_group_2, t53_filter_0, s2_card_1, t23_group_6, t25_funct_2, fc2_xboole_0, t87_partfun1, dt_l1_group_1, t102_group_2, t47_group_6, t150_group_3, t31_relat_1, fraenkel_a_2_0_group_4, d13_group_2, cc3_vectsp_1, t84_group_2, t12_group_4, t15_binop_1, t26_finseq_1, t37_lattice3, dt_m2_realset1, d12_group_4, t32_subset_1, t33_finseq_3, t13_group_6, t155_group_3, t107_group_2, t76_partfun1, redefinition_k6_filter_0, dt_k1_filter_0, dt_k3_group_4, t108_enumset1, t126_group_2, redefinition_k1_group_4, t147_group_2, t34_group_6, t30_finset_1, fraenkel_a_3_0_filter_0, t175_partfun1, t21_funct_4, t15_relat_1, t50_group_1, t154_funct_2, t98_group_2, t48_funct_2, d18_lattice3, fraenkel_a_3_7_domain_1, t12_funct_4, t27_relat_1, t121_group_2, t32_group_6, d16_lattice4, t70_filter_0, t156_funct_2, t65_group_1, t78_funct_4, t43_group_3, d1_xboole_0, t53_group_2, dt_m1_eqrel_1, t49_funct_1, t108_xboole_1, dt_k4_finseq_1, t56_filter_0, t40_funct_1, d3_group_6, t44_card_1, t60_group_1, t72_filter_0, dt_k4_card_1, t69_card_1, d6_group_2, t32_group_3, t46_filter_0, d1_group_2, t64_relat_1, t40_group_3, rc6_finseq_1, t25_subset_1, t138_zfmisc_1, t59_group_2, t71_group_3, t37_filter_0, t75_group_4, t36_filter_1, t18_finseq_1, rc3_lattices, t52_filter_0, t68_group_6, 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, t48_group_4, t75_funct_2, t57_filter_0, t31_finset_1, dt_l1_lattices, t32_lattice3, t29_funct_2, t14_relset_1, dt_k7_lattices, t33_card_1, t27_relset_1, t52_domain_1, dt_k4_lattice4, t34_funct_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, t8_funct_2, dt_k6_finseq_1, fc10_finset_1, t76_group_3, t113_group_3, t60_partfun1, t163_group_3, t89_group_3, existence_m1_realset1, t26_finset_1, t33_lattice3, fraenkel_a_2_6_lattice3, t36_group_6, t137_group_2, t39_lattice4, t16_relset_1, t38_lattice4, dt_m4_vectsp_8, t39_funct_4, t107_enumset1, t6_mcart_1, t91_group_3, t56_domain_1, t46_zfmisc_1, t45_group_1, t181_group_2, t33_eqrel_1, t31_partfun1, fraenkel_a_3_0_group_3, t37_partfun1, t171_partfun1, d15_lattice4, fc2_funct_2, t164_funct_2, t76_finseq_3, 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, t85_group_6, t63_funct_1, t86_group_1, fraenkel_a_3_2_lattice3, 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, t2_filter_1, t78_int_1, t59_filter_0, t55_group_6, t185_partfun1, dt_k1_funct_4, t18_latsubgr, t2_group_6, commutativity_k2_xboole_0, t5_subset, t44_filter_1, t36_lattice3, t1_xboole_1, t138_group_2, t26_relset_1, t29_relat_1, d14_lattice4, t108_group_2, d19_vectsp_1, t64_partfun1, t52_relat_1, symmetry_r4_group_3, t77_funct_2, t59_domain_1, t105_finseq_3, t20_funct_1, t78_finseq_3, t154_group_3, existence_l2_struct_0, t25_group_3, t55_relat_1, t32_lattices, t60_card_1, t34_filter_0, t7_setfam_1, t5_lattice4, t3_partfun1, t4_setfam_1, t32_partfun1, redefinition_k4_funct_2, t83_partfun1, t46_card_1, t164_group_3, d2_group_1, rc8_vectsp_1, t26_binop_1, t28_subset_1, t19_filter_0, t52_xboole_1, t44_lattice4, 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, t32_finseq_1, t49_filter_0, t34_relat_1, t79_partfun1, t59_group_6, d17_lattice4, d3_group_3, t39_partfun1, t112_enumset1, t30_lattice3, t57_group_6, t129_group_2, t96_finseq_3, d2_int_1, t33_group_1, t63_group_2, t142_group_3, t45_funct_2, t79_zfmisc_1, fraenkel_a_3_3_lattice3, t89_group_2, t84_group_3, t37_group_1, t94_zfmisc_1, fc4_numbers, t8_lattice4, t4_xboole_0, t65_finseq_1, d2_realset1, t41_group_2, t123_enumset1, t65_xboole_1, t68_finseq_3, t22_filter_1, fc17_finseq_1, t23_binop_1, d6_partfun1, t150_relat_1, existence_m1_relset_1, t68_group_1, t20_finseq_1, t35_group_6, commutativity_k5_subset_1, t14_group_1, t55_setfam_1, fraenkel_a_2_3_lattice3, d4_finseq_1, d8_group_1, t1_zfmisc_1, t50_lattices, t53_group_6, dt_l3_lattices, d7_group_3, d2_enumset1, t95_finseq_3, t5_setfam_1, t52_funct_1, t45_lattice3, t92_group_1, t14_latsubgr, t19_relset_1, t123_zfmisc_1, fc2_subset_1, t42_group_2, t46_group_4, t25_group_4, t17_filter_1, t5_funct_2, t21_group_2, dt_k8_funct_2, t54_group_4, t167_funct_2, t40_funct_2, d14_group_3, dt_k10_group_2, t77_group_3, t122_funct_1, t143_group_2, d18_group_2, d2_latsubgr, t99_group_3, t50_lattice3, t24_filter_1, cc1_finseq_1, t24_finset_1, t96_group_1, fc1_orders_1, dt_l2_lattices, t97_zfmisc_1, t108_group_3, t158_group_3, t11_funct_2, d2_group_4, fc2_funct_1, t77_finseq_3, t40_filter_0, redefinition_k3_group_6, t24_binop_1, fraenkel_a_3_0_group_6, dt_k3_latsubgr, t72_partfun1, t28_relset_1, dt_k2_group_4, t81_group_3, t121_funct_1, t86_card_1, t9_relat_1, t2_tarski, t16_funct_1, t79_relat_1, t14_relat_1, t25_finseq_3, t142_funct_2, d4_group_6, t33_relat_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, t47_lattices, t52_setfam_1, d20_lattices, d1_filter_1, t4_filter_0, t2_zfmisc_1, t89_filter_0, t16_funct_4, rc1_group_3, t114_xboole_1, t1_filter_1, d6_realset1, t39_filter_1, t67_zfmisc_1, t38_filter_0, d1_funct_4, dt_k1_partfun1, t84_xboole_1, t17_group_2, cc5_lattices, 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, t52_subset_1, t60_filter_0, dt_k9_filter_1, t5_ordinal1, t4_boole, t36_funct_2, t53_xboole_1, redefinition_k9_group_6, t26_group_1, d2_funct_2, t75_group_1, d21_lattice3, t49_card_1, t35_lattice3, t133_funct_2, t125_funct_1, t21_xboole_1, t98_zfmisc_1, t114_partfun1, d12_group_3, t22_group_3, t58_subset_1, t135_group_2, t162_funct_1, t34_lattice4, dt_k11_relset_1, t44_group_6, t73_group_6, t38_subset_1, t31_latsubgr, d1_int_1, t80_group_4, t62_group_4, t169_funct_2, t166_group_2, t44_lattices, 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, t76_relat_1, d8_filter_0, t32_xboole_1, d13_group_6, t94_group_2, dt_k8_filter_0, t14_funct_1, t43_funct_1, t42_filter_1, t6_group_1, t141_zfmisc_1, t45_lattices, t79_int_1, t17_funct_2, t74_card_1, t10_group_1, t59_funct_1, t132_funct_2, redefinition_r4_group_3, d3_group_2, t184_group_2, d9_group_3, t80_xboole_1, t147_partfun1, 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, t67_xboole_1, d12_binop_1, t52_filter_1, d5_group_3, t39_setfam_1, existence_m2_realset1, t20_group_3, t44_lattice3, t67_group_6, t119_enumset1, d3_lattice3, redefinition_k10_relset_1, t52_group_6, t145_group_3, dt_k4_group_4, redefinition_k5_setfam_1, t35_card_1, t61_group_3, dt_k7_group_6, dt_k1_domain_1, t6_group_4, t58_zfmisc_1, t104_group_2, t93_partfun1, dt_k5_group_1, d2_lattice4, t161_group_3, t29_xboole_1, t75_filter_0, t5_orders_1, fc1_realset1, t29_group_4, t70_group_3, cc1_funct_1, d17_lattice3, t30_group_6, d10_setfam_1, t77_relat_1, t45_relset_1, t139_zfmisc_1, t32_group_4, t7_boole, t72_group_3, redefinition_r2_group_3, d14_group_6, t160_funct_2, t4_funct_2, t81_finseq_3, d2_filter_1, t115_group_3, t15_group_4, d9_group_1, t136_partfun1, t11_group_3, d10_lattice4, t36_setfam_1, dt_k5_lattice4, t11_binop_1, t54_group_2, dt_k7_group_2, t138_partfun1, dt_k6_group_3, rc3_struct_0, t28_card_1, t70_group_6, t65_group_2, t55_filter_0, d8_vectsp_8, 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, commutativity_k2_struct_0, dt_k10_group_4, fraenkel_a_2_2_group_3, t22_relat_1, redefinition_k6_partfun1, dt_k3_finseq_1, t75_group_6, t48_xboole_1, dt_k6_domain_1, t21_lattice3, t157_funct_1, t85_partfun1, t3_ordinal1, t25_group_2, dt_k6_group_6, t34_group_3, t164_group_2, cc1_group_1, t129_group_3, t68_filter_0, t162_funct_2, t21_funct_2, dt_k9_group_4, t24_xboole_1, t11_latsubgr, t33_filter_1, t61_group_4, 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, t10_group_4, dt_k8_filter_1, t69_partfun1, t122_group_2, t7_ordinal1, t153_relat_1, rc2_funct_1, t125_group_2, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, t37_filter_1, t64_funct_1, t149_funct_2, t158_funct_2, t116_group_3, fraenkel_a_3_7_lattice3, dt_k9_filter_0, t48_funct_1, t32_card_1, t90_filter_0, d10_group_6, 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, t26_filter_1, t30_funct_4, t122_group_3, t85_xboole_1, t10_group_6, t22_finset_1, t67_funct_1, t38_group_4, t5_group_4, t88_group_2, t85_group_4, t73_group_3, rc1_funct_2, t91_orders_1, fraenkel_a_2_0_group_3, t64_zfmisc_1, t58_filter_1, t178_orders_1, t151_group_2, t65_funct_1, t28_group_3, t27_group_2, t2_latsubgr, t118_group_2, t113_funct_2, t71_partfun1, t5_filter_0, dt_k13_group_6, t69_xboole_1, t41_lattices, t92_group_2, t76_int_1, 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, existence_m1_filter_0, t83_xboole_1, t51_setfam_1, t30_filter_0, t35_group_2, d11_group_3, t40_lattice4, t78_group_3, t45_relat_1, dt_m2_finseq_1, d3_group_4, t34_finseq_3, dt_k2_struct_0, t155_funct_2, t49_lattices, t14_funct_2, dt_k3_group_1, t27_binop_1, dt_k8_group_4, t48_lattices, t20_xboole_1, t4_group_6, dt_k7_rlvect_1, commutativity_k3_setfam_1, t9_filter_0, dt_k11_group_3, t16_zfmisc_1, t40_lattices, t101_zfmisc_1, t5_latsubgr, t30_group_2, t56_funct_1, t43_group_2, fc1_group_3, t124_zfmisc_1, t47_lattice3, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, t46_filter_1, t82_xboole_1, t35_funct_4, dt_k8_group_2, t21_card_1, t49_group_6, t20_group_4, t54_xboole_1, t40_lattice3, t23_funct_4, t78_relat_1, t26_group_6, existence_m1_subset_1, t91_group_2, cc2_funct_1, t120_zfmisc_1, dt_k16_lattice3, t46_setfam_1, dt_k15_lattice3, 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, dt_k5_int_1, dt_k4_funct_2, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, t25_binop_1, d2_binop_1, d6_lattice4, s1_domain_1, t12_filter_0, t75_group_2, t160_group_3, t124_funct_1, t138_group_3, t2_group_3, t58_group_2, t60_group_4, t51_group_2, t79_funct_2, t46_funct_1, t23_latsubgr, t55_subset_1, t41_lattice4, idempotence_k1_funct_4, dt_k6_setfam_1, t105_group_3, t41_group_3, dt_u1_lattices, fraenkel_a_2_1_domain_1, t53_group_4, t82_card_1, t17_group_4, t27_card_1, t19_group_1, t111_enumset1, fraenkel_a_3_10_lattice3, t35_group_1, t41_funct_4, t110_enumset1, t95_group_3, t31_finseq_3, t3_relat_1, t22_filter_0, dt_k1_group_2, dt_k8_rlvect_1, redefinition_k4_subset_1, t44_zfmisc_1, fc5_group_6, dt_k13_group_2, d2_filter_0, t155_relat_1, t17_relset_1, t9_group_2, t74_group_6, d9_binop_1, t93_group_4, t35_xboole_1, t118_enumset1, t49_group_2, t130_group_3, t123_group_3, s1_int_1, dt_k12_group_2, t125_zfmisc_1, t73_funct_2, t42_lattice3, t30_subset_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d1_group_6, t148_group_2, t38_lattice3, t73_filter_0, 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, fraenkel_a_3_5_lattice3, t134_funct_2, t109_enumset1, t78_group_2, t19_numbers, t61_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, t44_filter_0, t48_setfam_1, t27_group_6, cc3_lattices, d5_subset_1, t92_zfmisc_1, t146_relat_1, t28_latsubgr, t14_group_2, d8_group_2, t74_finseq_3, t99_partfun1, t9_realset1, existence_m2_subset_1, t26_latsubgr, t121_funct_2, t100_zfmisc_1, d4_binop_1, t139_group_2, d15_group_3, existence_m2_lattice4, t116_funct_2, t142_partfun1, t48_lattice3, t114_zfmisc_1, t31_zfmisc_1, t58_partfun1, dt_k11_group_4, d1_zfmisc_1, t16_xboole_1, d8_setfam_1, t9_lattice4, t79_group_4, d1_filter_0, t27_filter_0, t26_xboole_1, t63_xboole_1, t52_group_1, t15_xboole_1, t4_latsubgr, redefinition_k7_filter_0, t8_funct_4, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, dt_k5_group_2, t57_setfam_1, t39_filter_0, t73_card_1, t3_group_6, t11_lattice4, t125_enumset1, t11_filter_0, t26_group_2, t91_partfun1, rc2_relat_1, t49_lattice3, dt_k5_subset_1, existence_m2_relset_1, t7_group_6, d11_group_4, existence_l1_vectsp_1, t64_filter_0, t51_group_6, dt_k12_finseq_1, t78_group_4, t92_group_4, t90_group_3, t40_group_4, t168_partfun1, 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, t113_enumset1, d2_group_3, t94_partfun1, d3_lattice4, t142_group_2, fraenkel_a_2_3_group_3, fraenkel_a_3_6_domain_1, redefinition_m1_group_6, t157_relat_1, t18_group_4, rc2_int_1, t51_filter_0, t17_numbers, dt_k8_group_1, fraenkel_a_2_4_lattice3, t37_lattice4, t17_finseq_1, t92_partfun1, t26_subset_1, dt_k1_finseq_3, redefinition_k2_binop_1, t21_group_1, t87_group_6, t7_latsubgr, t1_group_3, d5_group_1, t82_partfun1, existence_m2_filter_1, t51_subset_1, t1_latsubgr, t21_subset_1, existence_m1_lattice4, t111_xboole_1, t8_group_6, cc5_vectsp_1, d5_filter_0, d16_group_2, involutiveness_k7_setfam_1, t22_xboole_1, fraenkel_a_2_2_lattice3, d4_filter_0, t8_setfam_1, d14_group_2, t14_group_6, t41_subset_1, symmetry_r6_group_3, t97_finseq_3, dt_m3_lattice4, dt_k5_group_6, t25_lattice4, t145_group_2, t73_finseq_1, t75_int_1, dt_k3_partfun1, 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, t69_group_2, t3_latsubgr, t37_group_4, t46_subset_1, fc1_struct_0, d8_filter_1, t18_binop_1, t29_group_3, dt_l1_vectsp_1, cc6_funct_2, t59_group_3, t71_group_6, t51_group_3, t12_group_2, redefinition_k1_struct_0, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, t5_xboole_0, t16_int_1, t64_group_2, t131_funct_2, t119_zfmisc_1, d15_lattices, reflexivity_r4_group_3, rc1_relat_1, d7_filter_1, d6_card_1, t13_xboole_1, t60_relat_1, t54_funct_1, t83_funct_2, t44_group_1, t45_group_3, t22_group_2, t11_group_4, t40_subset_1, t83_zfmisc_1, d6_group_1, rc1_lattice4, t27_latsubgr, t111_group_2, fraenkel_a_2_5_lattice3, t149_group_3, t54_zfmisc_1, t174_group_2, t147_group_3, fraenkel_a_3_4_domain_1, t19_lattice4, 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, d2_orders_1, t143_funct_2, t5_mcart_1, t18_funct_2, t67_finseq_3, t17_funct_4, dt_k9_group_1, dt_k2_card_1, t34_funct_2, t48_relat_1, dt_k10_relset_1, dt_k6_relat_1, t144_group_2, dt_k11_group_2, t51_group_1, t68_group_4, t121_zfmisc_1, t10_subset_1, t93_finseq_3, dt_k7_filter_1, dt_l2_struct_0, t56_setfam_1, t24_lattice3, reflexivity_r2_setfam_1, t7_lattice3, t96_group_3, t3_group_2, t25_group_1, redefinition_k1_partfun1, t41_filter_0, dt_k1_latsubgr, t52_lattices, t19_group_2, t1_realset1, t48_group_1, t38_group_3, t2_xboole_1, t118_group_3, t20_latsubgr, t52_group_4, t43_group_6, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_relset_1, t15_group_3, t34_setfam_1, t10_group_3, dt_g3_lattices, fc6_relat_1, t1_partfun1, t111_finseq_3, t41_xboole_1, t168_group_2, t58_group_3, rc6_lattices, t59_group_4, d15_binop_1, t116_group_2, t3_lattice4, t2_setfam_1, d4_xboole_0, t7_funct_4, t22_group_6, t13_group_4, t90_xboole_1, t51_relat_1, t19_int_1, t84_partfun1, t55_group_3, free_g3_lattices, t113_partfun1, fraenkel_a_3_0_group_2, t46_relat_1, t77_filter_0, fc1_setfam_1, existence_m4_vectsp_8, t141_group_2, t66_funct_1, t39_group_2, t35_funct_1, t93_group_3, t75_finseq_3, t18_zfmisc_1, dt_k17_group_2, t29_relset_1, t8_card_1, t3_group_3, t47_filter_0, t101_group_3, dt_m1_finseq_1, cc2_group_2, dt_k5_setfam_1, rc3_finset_1, t81_group_6, d6_eqrel_1, t83_group_2, d9_group_2, existence_m1_eqrel_1, t36_xboole_1, t51_zfmisc_1, t62_group_2, t12_group_6, rc8_finseq_1, t27_numbers, dt_k5_group_3, d7_lattice4, t128_group_2, fraenkel_a_2_0_group_2, t22_int_1, t47_subset_1, fc2_filter_1, t58_filter_0, t151_funct_2, dt_k12_domain_1, t46_relset_1, t54_group_1, dt_k7_group_1, t81_group_2, t152_group_2, t12_group_1, t18_lattice4, t64_xboole_1, t40_filter_1, t26_card_1, fc1_relat_1, t27_group_1, t80_zfmisc_1, t59_filter_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, t77_group_4, t12_funct_2, d16_binop_1, t53_funct_1, t27_finseq_1, rc1_finset_1, dt_k2_latsubgr, t54_subset_1, t73_finseq_3, t20_filter_0, dt_k7_setfam_1, 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, t29_lattices, t21_funct_1, t50_funct_1, t88_filter_0, fc12_finset_1, t99_group_4, dt_k1_group_1, t42_funct_1, abstractness_v3_lattices, t136_zfmisc_1, dt_k2_group_6, t65_group_6, t77_xboole_1, d6_relat_1, t10_setfam_1, t8_boole, rc1_xboole_0, t9_group_6, t54_filter_0, t1_mcart_1, t103_enumset1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, t48_group_6, d1_orders_1, t33_relset_1, t15_filter_0, t130_group_2, t153_group_2, t67_group_3, t24_zfmisc_1, rc5_struct_0, d5_card_1, t2_subset, d11_group_1, fc7_relat_1, t60_funct_1, t63_group_4, t162_group_3, d13_group_4, t60_domain_1, t126_zfmisc_1, dt_k3_group_2, dt_m1_orders_1, t165_group_2, t59_funct_2, t12_xboole_1, t41_group_4, reflexivity_r1_partfun1, d9_filter_0, 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, reflexivity_r6_group_3, dt_k8_group_3, fc2_relat_1, t23_group_1, redefinition_m2_finseq_1, t14_finseq_1, t37_zfmisc_1, t46_group_1, t65_relat_1, t140_group_2, t21_relat_1, dt_k6_filter_0, t156_relat_1, t28_filter_1, t30_group_4, t117_enumset1, 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, dt_m1_filter_0, t49_relat_1, redefinition_r1_group_2, t180_group_2, fc8_relat_1, t27_funct_1, t10_realset1, fraenkel_a_2_7_lattice3, 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, d1_lattice4, t156_group_3, t34_lattices, t51_lattices, dt_k2_group_2, fc2_realset1, t74_xboole_1, d18_binop_1, t36_group_2, t23_lattice3, t50_group_3, redefinition_k10_group_1, t58_domain_1, t115_funct_2, idempotence_k2_xboole_0, dt_k2_group_1, t25_latsubgr, 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, t115_partfun1, t146_group_3, d6_group_4, t57_filter_1, reflexivity_r2_group_6, t32_filter_1, t31_group_4, t61_group_1, t9_tarski, t24_group_1, t145_relat_1, t6_group_2, t42_lattice4, t50_subset_1, t65_filter_0, t77_group_1, t46_xboole_1, d10_xboole_0, t100_group_2, t20_int_1, cc1_int_1, t27_filter_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, t33_funct_1, t57_funct_1, t67_partfun1, redefinition_k6_subset_1, t134_group_2, t12_relset_1, t86_group_3, existence_l1_struct_0, t5_xboole_1, t90_group_2, t37_funct_1, t157_group_3, t45_filter_0, t49_subset_1, rc1_card_1, t7_tarski, rc2_group_1, t115_group_2, t41_lattice3, t78_card_1, rc1_partfun1, dt_k8_finseq_1, t71_filter_0, t85_group_1, t18_int_1, t66_group_6, t3_xboole_0, symmetry_r1_partfun1, d8_group_3, d13_vectsp_1, t47_card_1, t23_filter_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, t92_funct_2, t46_group_6, fraenkel_a_2_0_lattice3, t119_finseq_3, t44_funct_1, cc5_funct_2, fc1_lattice4, dt_k1_group_6, redefinition_m2_subset_1, dt_u2_lattices, t71_finseq_3, t43_filter_1, t25_relat_1, t22_funct_2, t94_group_4, t5_funct_4, t17_group_6, dt_k3_group_6, t13_binop_1, t149_group_2, t80_relat_1, t55_filter_1, fc2_group_6, t87_xboole_1, d3_filter_0, reflexivity_r2_group_3, t40_xboole_1, existence_m3_vectsp_8, t4_group_3, fc14_finset_1, t19_setfam_1, fraenkel_a_2_1_group_3, t50_filter_0, t26_funct_4, rc4_struct_0, dt_k10_domain_1, t150_group_2, t16_binop_1, fc13_finset_1, t66_filter_0, t15_funct_4, t139_partfun1, d16_group_1, t43_lattice4, t47_group_3, t6_filter_0, t136_group_2, t139_group_3, d13_binop_1, t132_group_2, idempotence_k4_subset_1, t72_group_6, redefinition_k8_group_6, d14_group_1, t143_partfun1, t81_relat_1, t95_group_1, t40_zfmisc_1, t54_lattice3, t22_funct_4, t177_group_2, rc2_xboole_0, t25_finseq_1, t70_group_1, t67_group_2, t63_filter_0, t174_partfun1, t186_group_2, t55_funct_2, t45_xboole_1, d4_group_4, fraenkel_a_3_5_domain_1, dt_k4_group_2, d5_group_2, existence_m1_orders_1, rc4_finseq_1, t41_filter_1, t97_group_3, t172_group_2, existence_m2_finseq_1, dt_m3_vectsp_8, d3_setfam_1, d13_group_1, cc1_group_2, d9_vectsp_1, 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, t45_group_6, redefinition_k4_finseq_1, t6_lattice4, t22_group_1, t172_partfun1, t33_subset_1, t159_relat_1, d17_group_2, t29_filter_1, t86_group_6, free_g4_vectsp_1, t32_latsubgr, t32_funct_4, t30_partfun1, t65_zfmisc_1, dt_k14_group_2, t63_subset_1, t112_partfun1, t73_group_4, t14_group_3, t13_filter_0, d3_xboole_0, t144_group_3, t38_xboole_1, t19_funct_4, dt_k10_group_6, t62_group_6, t39_xboole_1, t31_group_1, t3_filter_0, t17_group_1, t13_card_1, fraenkel_a_3_8_lattice3, t56_group_3, t46_lattice3, t83_group_6, t18_group_1, t26_finseq_3, t71_relat_1, t5_group_1, t10_lattice4, t20_funct_4, antisymmetry_r2_hidden, d19_binop_1, t53_setfam_1, t79_group_3, t52_lattice3, t55_group_4, d8_group_6, d8_lattice4, t53_relat_1, t82_group_1, t21_group_4, dt_g1_group_1, abstractness_v1_group_1, t22_subset_1, redefinition_k6_domain_1
% 245.00/53.37 % No. of inferences in proof: 5372
% 245.00/53.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 52807 ms resp. 51894 ms w/o parsing
% 248.03/54.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 248.03/54.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------